TRANSPORTATION MODEL FOR WASTE COLLECTION IN THE KUMASI
METROPOLIS
By
Agyen Kwaku James B. Sc. (Hons.)
A Thesis Submitted to Department of Theoretical and Applied Biology, Kwame
Nkrumah University of Science and Technology in Partial Fulfilment of the
Requirements for the Degree of
MASTER OF SCIENCE (ENVIRONMENTAL SCIENCE)
Faculty of Biosciences, College of Science
January 2011
i
DECLARATION
I hereby declare that this submission is my own work towards the MSc and that, to the best of my knowledge, it contains no material previously published by another person nor material, which has been accepted for the award of any other degree of the university, except where due acknowledgement has been made in the text.
AGYEN Kwaku James ...... PG 88686-05 Signature Date (Student Name& ID)
Dr. F. T. Oduro ...... (Supervisor) Signature Date
Dr. P.K. Baidoo ...... (Head of Department) Signature Date
ii
ABSTRACT
This thesis seeks to provide waste management companies, especially Kumasi Metropolitan
Assembly-Waste Management Department (KMA-WMD) an alternative way of allocating limited collection trucks over the numerous collection points and to ensure minimum total cost.
Data were collected from the KMA-WMD their contracted companies as regards to the waste generation levels of all the collection points in the metropolis, and how much of these refuse are collected to the two dump sites over a period of three months.
The data gathered were modelled as linear programming problem with clear objective functions for each month under consideration subject to its associated constraints. These objective functions and constraints were minimized using a computer software solver,
EXCEL, to generate an optimal solution. The objective function value represented the minimized cost for the period under consideration if the waste generation levels of all the collection points were constant within the data collection period.
iii
DEDICATION
This study is dedicated to the Almighty God, my mother, the late Afia Akyaa, my dear wife
Mrs. Ruth Agyen and my God sent daughter Ohenewaa-Kobi Akyaamaa Nyantakyiwaa
Agyen.
iv
ACKNOWLEDGMENTS
My deepest gratitude goes to the Almighty God for seeing me through this work successfully.
I wish to express my sincere appreciation to all people who contributed to this master piece in one way or the other. Especially, I want to thank Dr. F.T. Oduro for giving me the chance to work on this topic. I owe my gratitude to the supervision, helpful comments, discussions and support he readily offered me, I am indebted to Prof Kwadwo Obiri-Danso for helping me choose search public bordering topic, Dr. P.K. Baidoo and Dr. J.I Adam for the tuition and advice they gave me throughout the entire course. My deepest appreciation goes to the lecturers and all the workers at the department of Theoretical and Applied Biology.
I am also indebted to my family and friends for all the love, support, and humour that I have received from them, especially my wife for giving me the moral support and encouragement even in the most difficult times.
I would also like to thank the management of Kumasi Metropolitan Assembly-Waste
Management Department, Zoomlion Ghana Limited, Maersk Waste limited and ABC waste limited, for providing helpful data and assistance for my work.
v
TABLE OF CONTENT
CONTENT PAGE
DECLARATION...... ii
ABSTRACT...... iii
DEDICATION...... iv
ACKNOWLEDGMENTS...... v
TABLE OF CONTENT...... vi
LIST OF TAABLES...... x
LIST OF FIGURES...... xii
CHAPTER 1
Introduction...... 1
Background to the Study...... 1
Statement of the Problem...... 2
Justification...... 2
Objectives of the Study...... 2
Methodology...... 3
CHAPTER 2
Introduction...... 4
Definition of Waste...... 6
Classification of Waste...... 6
Solid Waste Transportation...... 6
Motor Vehicle Transport...... 7
Railway Transport...... 7
Water Transport...... 7
Solid Waste...... 8 vi
Solid Waste Disposal...... 8
Landfill...... 9
Composting...... 10
Incineration...... 11
Ocean or Sea Dumping...... 12
CHAPTER 3
Introduction...... 13
Linear Programming...... 13
Standard Form...... 13
Simplex Method...... 14
Definition of the Transportation Model...... 16
Methods of Solving Transportation Model...... 16
Solution Techniques of Transportation Model...... 17
Solving the Transportation Model Using Simplex Method...... 28
Overview of Domestic – Type Refuse Management In The Kumasi Metropolis...... 29
Refuse Collection Equipment...... 30
Structure of the Waste Management Problem to Solve...... 30
Storage...... 31
Collection...... 31
Transportation...... 32
vii
Treatment of Domestic-Type Refuse In the Metropolis...... 32
Material Recovery/Recycling...... 33
Refuse Disposal...... 33
Data Collection Methods...... 34
CHAPTER 4
Introduction...... 37
Explicit Model Formulation...... 37
Parameters of the model...... 40
DISCUSION...... 44
CHAPTER 5
SUMMARY CONCLUSION AND RECOMMENDATION...... 53
SUMMARY...... 53
Conclusion...... 53
Recommendation...... 53
Suggestion for Future Research...... 54
REFFERENCES...... 55
viii
APPENDIX
Appendix I...... 57
Constraints Table, Dompoase...... 62
Sensitivity Report Table, Dompoase...... 65
Sensitivity Constraints Table, Dompoase...... 71
Limits Report Table, Dompoase...... 74
Appendix II...... 79
Answer Report, Bohyen...... 79
Constraint Table, Bohyen...... 82
Sensitivity report table, Bohyen...... 83
Sensitivity: Constrint report table, Bohyen...... 85
Limits report table, Bohyen...... 85
ix
LIST OF TAABLES
TITLE PAGE
TABLE 1: Come refuse related diseases in Kumasi metropolis...... 5
TABLE 2: Transportation tableau...... 20
TABLE 3: Transportation tableau...... 20
TABLE 4: Transportation tableau displaying allocations under NWCR………………21
TABLE 5: Transportation tableau displaying allocations under LCM…………………21
TABLE 6: Transportation tableau displaying allocations under VAM…………………22
TABLE 7: Transportation tableau displaying allocations under NECR………………..23
TABLE 8: Transportation tableau displaying allocations under LCM...... 23
TABLE 9: Transportation tableau displaying allocations under VAM…………………24
TABLE 10: A balanced transportation model table...... 25
TABLE 11: Connected cells in a balanced transportation tableau...... 26
TABLE 12: Quantity (in tons) of refuse conveyed by the trucks per trip….....……...... 35
TABLE 13: Parameters of the model...... 40
TABLE 14: Parameters of the model...... 43
TABLE 15: Optimal number of trips, Dompoase………………………………………...46
TABLE 16: Optimal number of trips, Bohyen...... 51
TABLE A 1: Real cost of transporting waste from parts of the metropolis to the
Dompoase landfill site...... 57
TABLE A 2: Values from EXCEL transportation solution...... 57 x
TABLE A 3: Values from EXCEL transportation solution showing constraints and slack...... 62
TABLE A 4: Values from EXCEL transportation solution for sensitivity analysis...... 65
TABLE A 5: Values from EXCEL transportation solution showing sensitivity output constraint...... 71
TABLE A 6: Final cost as displayed by EXCEL transportation solution...... 74
TABLE A 7: Values from EXCEL transportation solution showing upper limits...... 74
TABLE B 1: Real cost of transporting waste in parts of the metropolis to the Bohyen Landfill site...... 79
TABLE B 2: Values from EXCEL transportation solution……………………………...79
TABLE B 3: Values from EXCEL transportation solution showing constraints and slack………………………………………………………………………………………….82
TABLE B 4: Values from EXCEL transportation solution for sensitivity analysis...... 83
TABLE B 5: Values from EXCEL transportation solution showing sensitivity output constraint...... 85
TABLE B 6: Values cost limits for using ERF trucks...... 86
TABLE B 7: Values from EXCEL transportation solution showing upper limits...... 86
xi
LIST OF FIGURES
TITLE PAGE
Figure 1: Map of Kumasi Metropolitan Area...... 29
Figure 2: A ERF truck on a weighing bridge...... 32
Figure 3: A Skip and a ERF truck offloading at Dompoase landfill site...... 34
xii
CHAPTER 1
INTRODUCTION
1.1 Background to the Study
The rapid rate of uncontrolled and unplanned urbanization in the developing nations of Africa has brought environmental degradation. Indeed, one of the most pressing concerns of urbanization in the developing world, especially in Africa, has been the problem of solid-, liquid-, and toxic-waste management. Recent events in major urban centres in Africa have shown that the problem of waste management has become a monster that has aborted most efforts made by city authorities, state and federal governments, and professionals alike. A visit to any African city today will reveal aspects of the waste-management problem such as heaps of uncontrolled garbage, roadsides littered with refuse, streams blocked with junk, disposal sites constituting a health hazard to residential areas, and inappropriately disposed toxic wastes. The high rate of urbanization in African countries implies a rapid accumulation of refuse and Ghana is of no exception.
The high rate of urbanization in the country‘s regions mainly in the densely population areas
(the cities) implies a rapid accumulation of refuse. These wastes, usually solid, consist of waste generated from human. Because these wastes are considered as useless they are disposed of. In the metropolis, Domestic, Industrial and commercial wastes are generated.
Solid Industrial, Commercial and Domestic wastes are referred to as refuse, solid wastes generated in the households are referred to as domestic-type refuse.
The operational cost of the collection and transportation of municipal solid waste to the
Kumasi metropolitan Assembly - Waste Management Department (KMA-WMD) is currently
(2007) Gh¢ 9.00 (Nine Ghana Cedis) per ton, an average of 850 tons of solid waste is
[1] generated per day in the municipality and this costs the KMA-WMD Gh¢ 7,650 per day. This means the waste management department spends Gh¢ 229500.00 per month or an annual cost of Gh¢ 2,754,000. The collection and transportation of the solid waste is funded partly by the
KMA and partly by the government of Ghana (KMA-WMD, 2006, Final Annual Cost
Report). The figure above only takes into consideration the solid waste collection and transportation cost. Due to the financial base of the Assembly, it is difficult to fund adequately the solid waste collection and transportation (Jumah, 2002). There is a need, in particular, to rationalize the transportation system so as to help bring down the cost of waste collection operations in the municipality.
1.2 Statement of the Problem
The aim of the research is to determine from the mathematical modeling point of view, how to minimize operational cost by determining the type, number and size of vehicles to access and collect refuse at various collection points taking into consideration various capacities and demand levels.
1.3 Justification
A transportation arrangement that is cost effective for waste or refuse collection and disposal and that will effectively be used to convey the refuse from the various collection points in the metropolis to the dump site, will also be able to help minimize the negative effects these waste cause to human health and the environment.
1.4 Objectives of the Study
The general objective of the study is to systematically and critically identify methods of collection and transportation of domestic – type refuse from the various collection points to the disposal sites and then formulate a mathematical model that will yield an optimal solution to the refuse collection problem.
[2]
The specific objectives are to
(1) construct a transportation model for the waste collection problem
(2) solve the model using data from the KMA-WMD.
(3) use results to recommend a cost effective way of managing transportation aspects of
the waste collection operations in the metropolis
1.5 Methodology
Data will be collected from the Kumasi Metropolitan Assembly which is the site for this research. The model will be based on the transportation algorithm of Linear programming which will be solved using EXCEL solver. The research will also involve relevant literature from the library and the internet as well as other documented data made available by the waste management department of the KMA and other relevant information to be gathered from the field trips and interviews in respect of workers and management personnel.
[3]
CHAPTER 2
LITERATURE REVIEW
2.1 Introduction
Every society wishes to grow in knowledge, population, and value. However, a peak is always reached in the management of this growth, at which point additional development becomes counterproductive. It must also be said that values and production can diminish even before this peak is reached. This might be a result of poor management, poor programs, inadequate facilities, and so on. This is perhaps best illustrated by the positive and negative impacts of the urbanization process in Ghana.
Urbanization introduces society to a new, modern way of life, an improved level of awareness, new skills, a learning process, and so on. However, when the rate of urbanization gets out of control, it poses a big challenge to governance — optimizing forces become weakened, institutional capabilities become inadequate and ineffective, and, with these, the problems of urbanization are compounded.
Handling of domestic-type refuse in the Kumasi metropolis has been a very challenging task from time immemorial, mainly due to the public's attitude and its multi-sectorial involvement
(K.M.A-2001, end of year report on solid waste). Management of domestic waste involves a range of technologies associated with the control of the generation, storage, collection, transportation and disposal of all forms of solid wastes. To satisfy the World Health
Organization (WHO) standards all of these processes need to be carried out within acceptable legal and social guidelines that will prevent solid waste hazards to the public, animals and the environment as a whole. These guidelines must be hygienically, aesthetically and economically acceptable.
[4]
In this respect, waste management authorities must be responsive to public attitudes, collection, transportation, and treatment and disposal process (AMA, 2003). With the rapid increment in the population of Kumasi Metropolitan Assembly, from 256,781 in 1984 to
1,170,270 in 2000 (Ghana Statistical Service, 2000), general sanitation of the metropolis has been so challenging and has led to environmental and health problems (Environmental
Protection Agency, 1999). The domestic and commercial wastes are left in the various points of collection (KMA, 1996). This has led to an environmental and health nuisance for instance with regard to the destruction of the aesthetic nature of the environment, air pollution and outbreaks of waste related diseases like malaria, cholera and typhoid fever (Ministry of
Health, Ghana, 2002).
In view of these the WHO in 1971 declared that ―solid waste management is an important aspect of environmental hygiene and needs to be integrated with total environmental planning‖. Aesthetic wise, indiscriminate waste or refuse dumping destroys the natural beauty of the environment and even the ―man created‖ environment. Refuse left unattended to at the various collection points in the communities lead to disease out breaks. According to the MOH, Kumasi, the morbidity cases of some waste related diseases is as shown below;
Table 1: Some Refuse related Diseases in Kumasi Metropolis
Grand total Year Diseases Morbidity % (Overall Diseases) Malaria 193,280 28.33
2004 Typhoid Fever 5,541 0.81 682,223 Intestinal worms 12,046 1.76 Malaria 257,552 39 2003 Typhoid fever 1,894 523,551 0.36 Intestinal worms 8,213 1.5 Malarial 220,025 35.4
2002 Typhoid Fever 1,226 0.19 620,588 Intestinal worm 13,507 2.1 Source: MOH, Kumasi
[5]
2.2 Definition of Waste
Waste may be defined as a discarded material, which has no consumer value to the generator
(Hagerty et al., 1973; Kreith et al, 1994). The term solid waste includes any garbage, refuse, sludge from a waste treatment plant, water supply treatment plant, or air pollution control facility, and other discarded material, including solid, liquid, semi-liquid, or contained gaseous materials resulting from industrial, commercial, mining, and agricultural operations and from community activities (Hagerty et al., 1973). This does not include solid or dissolved materials in domestic sewage or solid or dissolved materials in irrigation return flows or industrial discharges. Also excluded are agricultural wastes, including manures and crop residues, returned to the soil as fertilizers or solid conditioners (Hagerty et al., 1973).
2.3 Classification of Waste
There are varieties of solid waste which includes: food waste which may comprise of remnants of food stuff, Rubbish and these may be combustible (plastics, wood, textiles, leather, garden trimmings, papers etc) or non-combustible (tin cans, metal scraps, glass etc),
Demolition and construction waste (construction waste and waste from razed building) Ashes and residues mainly from burnt woods, there are also Agricultural waste, Hospital waste etc.
For the purpose of this study, only domestic – type refuse generated in the metropolis will be considered.
2.4 Solid Waste Transportation
Solid waste is been transported by three (3) main means, namely Motor vehicles, Railways and Water transport. Hydraulic and Pneumatic systems have also been used (Hagerty et al.,
1973). In the Kumasi metropolis, refuse is been transported by motor vehicles and this process is known as direct haul.
[6]
2.4.1 Motor Vehicle Transport
Using of motor vehicles for the transportation of solid waste is possible where the collection point and the final disposal site are accessible by motor vehicles. Even though all vehicles can be used, usually the vehicles used include; semi-trailers, trailers, container trucks and compactors (Feachem et al., 1983). In the Kumasi metropolis, vehicles used must satisfy the following requirements:
(1) Vehicles must be designed for highway traffic.
(2) Vehicle capacity must be such that the standard weight limits are not exceeded.
(3) Waste must be covered during the transportation.
(4) Methods of unloading must be simple and dependable.
(5) Transportation cost of the vehicle must be acceptably minimum.
2.4.2 Railway Transport
Transportation of solid waste via railways were common in the past, currently, in communities where road traffic is heavy, railways are used to transport wastes to remote areas where they are disposed. Areas where highway travel is difficult and railway lines exist, and where land for filling is available railway transport is used (Kreitht et al, 1994).
Currently there is nowhere in the metropolis that railway transport is used.
2.4.3 Water Transport
Barges, scows and special boats have been used in the past to transport solid waste to processing locations and to seaside and ocean disposal sites. This was common in the United
States and other advanced countries, but ocean disposal is no longer practiced by the United
States, although some self-propelled vessels (such as the United States Navy garbage scows and other special boats) have been used. The most common practice is to use vessels towed
[7] by tugs or other special boats (Hagerty et al., 1973).
Major problem encountered when ocean vessels are used for the transportation of solid waste is that it is often impossible to sail the barges and boats during storm or times of heavy seas.
In such cases, the waste must be stored and construction of expensive storage facilities may be necessary (Ivor and Seeley, 1992). Other means by which solid waste has been transported by water is the hydraulic and the pneumatic methods. The famous Walt Disney World amusement park in Orlando, Florida in the United States uses these methods. Other systems have been suggested for transportation of solid waste, these include conveyors, air-cushion and rubber-tyre trolleys, and underground conduits with magnetically transported gondolas.
Unfortunately these systems have not been put into practice (Hagerty et al., 1973).
2.5 Solid Waste.
Solid wastes are waste materials that contain less than 70% water. This class includes such materials as household garbage, some industrial wastes, some mining wastes, and oilfield wastes such as drill cuttings. There are different types of solid waste depending on their moisture content. In the metropolis, household garbage forms about 85% of the total solid waste generated with industrial-type and the commercial type-solid waste refuse forming
15%.
2.5.0 Solid Waste Disposal
There are so many ways of disposing solid waste but the most recommended ones are the
Landfill, Composting and the Combustion/incineration methods. The Landfill method is the most common and probably accounts for more than 96% of the metropolis' solid waste.
[8]
2.5.1 Landfill
Studies has shown that sanitary landfill is the cheapest satisfactory means of disposal (Kreith et al, 1994), but only if suitable land is within economic range of the source of the wastes; typically, collection and transportation account for 75% of the total cost of solid waste management. In a modern landfill, refuse is spread in thin layers, each of which is compacted by a bulldozer before the next is spread. When about 3 metre (about 10 ft) of refuse has been laid down, it is covered by a thin layer of clean earth, which also is compacted. Pollution of surface and groundwater is minimized by lining and contouring the fill, compacting and planting the cover, selecting proper soil, diverting upland drainage, and placing wastes in sites not subject to flooding or high groundwater levels. Gases are generated in landfills through anaerobic decomposition of organic solid waste. If a significant amount of methane is present, it may be explosive; proper venting eliminates this problem. Sites suitable for sanitary landfill are quarries, gravel pits, low- lying swamps, marshes etc. The best soil for a landfill is clay because clay is less permeable than other types of soil.
In choosing a place for a landfill site, the following must be considered.
(1) Proximity to residential areas.
(2) Wind direction, and access by road, rail or water.
(3) Areas close to airports must be avoided to prevent bird-strikes.
(4) Site hydrogeology must be conducted to prevent pollution of water supplies and the
underground water.
The essence of the thin layer of clean earth used and the compaction is to control the tip in the following ways:
(1) Limit the odour emission
[9]
(2) Check the emergence of fly larvae
(3) Check the breeding of flies and other insects
(4) Allow easy rat control
(5) Prevent light refuse being blown away
(6) Make tip less attractive to birds
(7) Reduce the risk of fire
(8) Provide good conditions for the biological degradation of organic matter in the tip
In the metropolis, the only landfill is the Dompoase sanitary landfill, it covers 65km2 of land in the outskirt of the Dompoase township.
2.5.2 Composting
Composting involves the biological stabilization of solid matter either under aerobic or anaerobic conditions (Purdom et al, 1971). This ultimately degrades susceptible organic matter to water, carbon dioxide and stabilized residue, principally humid substance called
Compost. Even though composting is gaining grounds in the advanced countries it still the mostly used in the developing countries this is as the result of the diminishing availability of landfill sites, the high cost and the relatively high degree of sophistication needed to operate inc incinerator safely and economically, also materials with carbon-nitrogen ratio greater than
50% are very slow to compost (Kreith et al, 1994). There are two main methods namely windrow composting which the Kumasi metropolis uses and the compost digesting. In composting, materials are spread out over a large land area so that microbes can decompose them, in the developed countries where there is enough resource for waste management the decomposable refuse is separated from the non-decomposable refuse and the decomposable
[10] one composted. In the developing countries the opposite is what is practiced, both the decomposable and the non-decomposable refuse are put together and composted. Maximum depth of 5-8 feet prevents compaction, but a depth of 4 feet is needed for insulation. The heap of compost is made by spreading the refuse for a marked duration, in open air windrows to allow biological activities to degrade the wastes (Purdom et al, 1971); the compost must be turned several times per week to supply sufficient oxygen time to keep the windrow aerobic and the biological activity constant.
The length of time required to produce compost varies with the number of times that the compost is been turned and also partially on the temperature of the compost. The time can vary from 3 or 4 weeks to several months, other factors are ambient temperatures and the chemical composition of the raw material. Where land limitations do not permit windrow composting to be practical, the compost digesting is used, in this process the refuse is placed in digesters and air is supplied from mechanical blowers, because air is forced through the piles of refuse there is no need to turn the compost to supply oxygen.
2.5.3 Incineration
In incinerators of conventional design, refuse is burned on moving grates in refractory-lined chambers; combustible gases and the solids they carry are burned in secondary chambers.
Combustion is 85 to 90 percent complete for the combustible materials. In addition to heat, the products of incineration include the normal primary products of combustion—carbon dioxide and water—as well as oxides of sulfur and nitrogen and other gaseous pollutants; nongaseous products are fly ash and unburned solid residue. Emissions of fly ash and other particles are often controlled by wet scrubbers, electrostatic precipitators, and bag filters. It is very expensive to operate an incinerator due to the high power consumption nature of the
[11] incinerators to ensure complete combustion. Also the end products of the incinerators are always harmful to lives and a lot of resources are used to mitigate their harmful nature.
2.5.4 Ocean or Sea Dumping
The modern-day sea disposal operation exists because of legislation, which spells out the operational details on the Dumping at Sea Act 1974 (Hagerty et al., 1973). It was taught in the past that Oceans and Seas were capable of receiving and making safe difficult toxic and hazardous waste, sewage sludge and radioactive waste deposited in them. One could suppose that this method is the ultimate ―dilute and disperse‘‘ option.
[12]
CHAPTER 3
METHODOLOGY
3.1 Introduction
In this chapter the theory of linear programming, and the transportation algorithm as well as their methods of solution will be considered. Subsequently we will describe the profile and operation of waste management organization to be studied.
3.2 Linear Programming
This work will be formulated into mathematical equations which will be solved using linear programming. Linear Programming is a mathematical programming model which deals with the allocation of resources to known activities with the objective of meeting a required goal such as maximizing profit or minimizing cost (mathworld.wolfram.com). The concept applied in linear programming is that all equations to be used in the analysis must be linear
(straight line equations).Thus, there will be a formulation of linear equations that will determine (profit or cost) of operation, these will be referred to as ―objective function‖ and those linear equations which will describe the limitations under which the system must operate, called the ―constraints‖.
3.2.1 Standard Form
The simplex method for solving linear programming problems requires that the problem be expressed in standard form. A linear programming problem with all the constraints in equation form is said to be in its standard form. Since constraints of linear programming problem are often expressed as inequalities rather than equations, the inequalities are
[13] converted to equations by introducing variables to represent the slack or surplus between the left-hand side and right- hand side of the each inequality.
The main features of the standard form are:
(1) The objective function is of the maximization or minimization type.
(2) All constraints are expressed as equations.
(3) All variables are restricted to be nonnegative.
(4) The right-hand side constant of each constraint is nonnegative.
Basically the standard form reduces the linear program to a set of m equations in (m + n) unknowns which eventually lead to an infinite number of solutions. It should be noted that, it is computationally very difficult to determine every feasible point, it is therefore important to employ a method that locates the optimum solution after checking a finite number of solution points.
3.2.2 Simplex Method
The simplex method as developed by G. B. Dantzig(1947) is an iterative procedure for solving linear programming problems expressed in standard form. In addition the simplex method requires that the constraint equations be expressed as a canonical system from which a basic feasible solution can be readily obtained.
(1) Start with an initial basic feasible solution in canonical form.
(2) Improve the initial solution if possible by finding another basic feasible solution with
a better objective function value.
(3) Step two is repeated until a particular basic feasible solution cannot be improved any
further and this feasible solution eventually becomes the optimal solution and the
simplex method terminates.
[14]
Definitions associated with the simplex method are;
Basis matrix: This is an m x m non-singular matrix formed from m columns of the
constraint matrix A. Since rank (A) = m, A contains at least one basis matrix.
Basic variable: A variable x1 is said to be a basic variable in a given equation if it
appears with a unit coefficient in that equation and zero in all other equations.
Non-basic variable: These are variables which are not basic, and there fore do not
correspond to the columns of the basis matrix.
Basic solution: The solution obtained from a canonical system by setting the non-
basic variables to zero and solving for the basic variable.
Basic Feasible Solution: A basic feasible solution is a basic solution in which the
values of the basic variables are nonnegative.
Non-degenerate basic feasible solution: This is a basic feasible solution with exactly
m positive components.
Optimal solution: This is vector X such that it is feasible and its value of the objective
function is larger than that of any other feasible solution. That is it is a feasible
solution, which minimizes or maximizes the objective function.
Pivot Operation: A pivot operation is a sequence of elementary operations that
reduces a given system to an equivalent system in which a specified variable has a
unit coefficient in one equation and zero elsewhere.
By so doing, columns are introduced into and rows are eliminated from the basis matrix. The column that corresponds to the non-basic variable, which is about to be introduced into the basis, is called pivot column. The row that corresponds to the basic variable, which will leave the basis matrix as the algorithm iterates from one feasible solution to another, is called pivot row. The elements of the simplex tableau that is in both the pivot row and pivot column is called pivot elements.
[15]
3.2.3 Definition of the Transportation Model
The transportation model aims at determining the transportation plan for a tonne of domestic type refuse from a number of sanitary sites (collection points) to a number of destinations
(disposal sites). The parameters of the transportation model should include.
(1) The quantity of refuse generated at each collection point and the capacity of the
trucks used to haul the refuse to the disposal sites.
(2) The unit transportation cost of hauling from a collection point to a disposal site.
(3) The distance (km) between a collection point and a disposal site and time taken in
hours.
3.2.4 Methods of Solving Transportation Model
After the formation of the transportation model an initial basic feasible solution would have to be obtained since without it the m initial complex tableau cannot be formed. There are two basic approaches to finding an initial basic feasible solution.
(1) By Trial and Error.
In this case a basic variable is chosen arbitrarily for each constraint and the system is reduced to canonical form with respect to those basic variables. If the resulting canonical system gives a basic feasible solution, then the initial tableau can be set up to start the complex method. If the resulting canonical system does not give a basic feasible solution, the process can be repeated by trying a different set of basic variable for the canonical reduction till a basic feasible solution is obtained. This method is inefficient and expensive and thus not advisable to be used.
(2) Use of Artificial Variables
[16]
This is a systematic way of getting a canonical system with a basic feasible solution when none is available by inspection. First the lined programming problem is converted to standard form.
Each constraint is then examined for the existence of a basic variable. If none is available, a new a variable is added to act as the basic variable and by a new variable is added to act as the basic variable in the constraint to make the system canonical so that an initial complex tableau can be formed readily.
The additional variables are called the artificial variables. This method is efficient and easy and also less expensive. It will therefore be very necessary to use artificial variables to obtain an initial basic feasible solution. That notwithstanding, when the transportation tableau is used, the initial basic feasible solution can be easily obtained directly by any of the following solution techniques of transportation models:
The Northwest Corner Rule
The least cost
The Vogel‘s approximation
Because of the smaller objective function values associated with these methods they provide better initial basic feasible solutions.
3.2.5 Solution Techniques of Transportation Model
Transportation techniques are variants of the Simplex method and so they require initial basic feasible solution (BFS) to start with. The initial BFS may be obtained by the North-West
Corner Rule, Least Cost Method or the Vogel‘s Approximation Method. The other methods which have been devised to improve the starting solution to optimality are the Stepping Stone
Method (SSM) and Modified Distribution method (MODI). These solution methods are classified into two and are discussed as follows.
[17]
(α) Initial Basic Feasible Solution Methods:
(i) North-West Corner Rule (NWCR)
The method starts by making the maximum allocation allowable by the supply and demand constraints to cell (1, 1), the north-west corner or the tableau. The satisfied row or column is then crossed out row or column is zero (0). If a row and a column are satisfied simultaneously, either one may be crossed out. This condition guarantees automatic location of zero basic variables, if any. After adjusting the amount of supply and demand for all uncrossed out rows and columns, the maximum feasible amount is allocated to the first uncrossed out cell in the new column or row. The process is completed which exactly one row or column remains uncrossed out. In certain cases, the solution obtained by the method is degenerate. This happens because whenever a supply is used up there is always an unfulfilled demand in the column.
(ii) Least Cost Method (LCM)
The Least Cost Method identified the least unit cost in the transportation tableau and allocated as much as possible to the associated cell without violating any of the supply or demand constraints. The satisfied row or column in then deleted. The next least unit cost is identified and as much as possible is allocated its cell without violating any of the supply or demand constraints. At this point also, the satisfied row or column is deleted. This procedure is continued until all rows and columns have been deleted. This method performs better than the North-West Corner Rule.
(iii) Vogel’s Approximation Method (VAM)
It provides a BFS which is optimal or close to it and moreover, performs better than the Least
Cost method and North-West Corner Rule. The basic idea of VAM is to avoid shipments that have high cost. This is achieved by computing column penalties by identifying the least unit
[18] cost and the next least unit cost in that column and taking their positive difference. In a similar way row penalties are computed by taking the positive difference between the least unit cost and the next least unit cost in a row. This method is a variant of the Least Cost method and is based on the idea that if for some reason, the allocation cannot be made to the least unit cost cell in a row or column then it is made to the next least unit cost cell in that row or column and the appropriate penalty is paid for not being able to make the best allocation. Column penalties are shown below columns and row penalties to the right of each row of the transportation tableau. The VAM is summarized in the following steps:
A. Evaluate the column and row penalties by subtracting the smallest unit cost in
each row or column from the next smaller unit cost in the same row or
column.
B. Select and circle the row or column with the highest penalty, breaking ties
arbitrary. Allocate as much as possible to the cell with the least unit cost in the
selected row or column
C. Adjust the supply and demand and cross out the satisfied row or column by
the allocation made in step B. If a row and a column are satisfied
simultaneously, only one of them is crossed out and the remaining row or
column is assigned a zero (0) supply or demand.
D. Recompute the penalties for the uncrossed out rows and columns and go to
step B
E. If exactly one row or column remains uncrossed out stop and determine the
basic variable in the row or column by the least cost method. The uncrossed
out row or columns with zero (0) supply or demand are allocated by the Least
Cost method.
[19]
Example
Find the initial BFS for the following transportation problems using the NWCR, LCM and
VAM
(a) Table 2: Transportation tableau
Supply
6 7 9 5 40
3 2 4 1 30
7 3 9 5 25
Demand: 30 20 25 20
(b) Table 3: Transportation tableau
Supply 9 5 8 25
6 8 4 35
7 9 40
Demand: 35 25 45
Solution
(a) The given transportation tableau has:
The total supply = (40 + 35 + 25) = 100
The total demand = (35 + 20 + 25 + 20) =100
Hence the tableau is balanced.
[20]
We now find the initial BFS as follows:
(i) Using the NWCR we obtain the allocations as shown in the tableau below:
Table 4: Transportation tableau displaying allocations under NWCR
6 5 7 9
40 30 10
3 2 4 1 30 10 20
7 3 9 5
25 5 20
30 20 25 20
The allocations made by the method is BFS since (m+n-1) = 3 + 4 - 1 = 6, which equals the number of allocations made. There is also no circuit among the allocated cells. The total cost of transportation,
C = 6(30) + 5(10) + 2(20) + 4(20) + 9(5) + 5(20) = 495 units of money.
(ii) By the LCM we obtain the solution as given below
Table 5: Transportation tableau displaying allocations under LCM
6 5 7 9
40 30 10
3 2 4 1 30 10 20
7 3 9 5
25 10 15
30 20 25 20
[21]
The initial allocations made do not form BFS since they are fewer than (m+n-1). In order words, the solution is degenerate and so zero (0) is allocated to cell (3,2) to make the solution non-degenerate. The required total cost,
C = 6(30) + 7(10) + 2(10) + 1(20) +3(10) + 9(15) = 455 units of money.
The LCD has obtained a better result than the one obtained by the NWCR.
(iii) Using the VAM, we obtain the following allocations
Table 6: Transportation tableau displaying allocations under VAM
Row Penalty 6 5 7 9
40 1 1 1 1 15 25
3 2 4 1 30 1 1 1 - 10 20
7 3 9 5
25 2 4 2 2 5 20
30 20 25 20
The solution obtained by the VAM is BFS since we have (m+n-1) = 6 allocations. The total transportation cost,
C = 6(15) + 7(25) + 3(10) + 1(20) + 7(5) + 3(20) = 410 units of money which is also
better than the two total costs obtained by the NWCR and LCM
(b) The given transportation is balanced since the total supply equals the total demand.
We now apply the initial BFS solution methods as follows.
[22]
(i) By NWCR. We obtain the solution,
Table 7: Transportation tableau displaying solution under NWCR
5 9 8 25 25
6 8 4 35 5 25 5
7 6 9 40 40
30 25 45
There are exactly (m+n-1) = (3 + 3 –1) = 5 allocated cells and so the solution is non- degenerate and also BFS. The total transportation cost,
C = 9(25) + 6(5) + 8(25) + 4(5) + 9(40) = 835
(ii) By the LCM, we obtain the solution,
Table 8: Transportation tableau displaying solution under LCM
5 9 8 25 15 10
6 8 4 35 35
7 6 9 40 15 25
30 25 45
The total transportation cost,
C = 9(15) + 5(10) + 4(35) + 7(15) + 6(25) = 580
[23]
(iii) By the VAM, we obtain the following solutions,
Table 9: Transportation tableau displaying allocations under VAM
5 9 8 25 3 - - - 25
6 8 4 35 2 2 2 2 15 20
7 6 9 40 1 1 1 1 15 25
30 25 45 Column 1 2 1 Penalty 1 2 5
The total transportation cost,
C = 5(25) + 6(15) + 4(20) + 7(15) + 6(25) = 125 + 90 + 80 + 105 + 150 = 550
The total transportation cost for the NWCR, LCM and VAM are respectively 835, 580 and
550 units of money and these show that the cost as given by the VAM for the same inputs into the three type of solution or methods, the VAM is the best of all the tree.
[24]
(β) Optimal Solution Methods
The methods for obtaining the solution to transportation model are the Stepping-Stone method (SSM) and Modified Distribution method (MODI).
(i) Steppingstone Method
The Steppingstone Method, being a variant of the Simplex method, requires an initial basic feasible solution which is then improved to optimality. Such an initial basic feasible solution may be obtained by the use of the North West Corner Rule, the Least Cost Method or the
Vogel‘s Approximation Method.
Let us consider the balanced transportation problem shown below:
Table 10: A balanced transportation model table
W W W 1 2 n
S a 1 11 12 1n 1
a S 21 2 2 22 2n
S m2 mn a m m
b 2 b n
Suppose that we have an initial basic feasible solution of this problem consisting of non- negative allocations in (m+n-1) cells. Let us call the cells which are not in the basic feasible solution unoccupied cells.
It can be shown that for each unoccupied cell, there is a unique circuit beginning and ending in that cell, consisting of that unoccupied cell and other cells all of which are occupied such that each row or column in the tableau either contains two or more of the cells of the circuit.
[25]
(ii) Circuit
A circuit made up of cells of the tableau of a balanced transportation problem is a sequence of cells such that:
(a) it starts and ends with the same cell
(b) each cell in the sequence can be connected to the next member of the sequence by a
horizontal and vertical line in the tableau.
An example is as shown below:
Table 11: Connected cells in a balanced transportation tableau
1 2 3 4
1
2
3
4
(iii) Test for Optimality
To test the current basic feasible solution for optimality, we take each of the unoccupied cells in turn and place one unit allocation in it. This is indicated by just the sign (+). Following the unique circuit containing this cell as described above, we place alternatively the sign (-) and
(+) until all the cells of the circuit are covered. Knowing the unit cost of the each cell, we compute the total change in cost produced by the allocation of one unit in the unoccupied cell and the corresponding placements in the other unoccupied cells.
This total cost explained above is known as the improvement index of that unoccupied cell under consideration. If the improvement index of each unoccupied cell in the basic feasible solution is non-negative then the current basic feasible solution is optimal since every re-
[26] allocation increases the cost. If there is at least one unoccupied cell with a negative improvement index then a re-allocation to produce a new basic feasible solution with lower cost is possible and so the current basic feasible solution is not optimal.
Thus the current basic feasible solution is optimal if and only if each unoccupied cell has a non-negative improvement index.
(iv) Improvement to Optimality
As it has been stated above, if there exists at least one unoccupied cell in a given basic feasible solution which has a positive improvement index then the basic feasible solution is not optimal. To improve this solution, we find the unoccupied cell with the most positive improvement index N say. Using the circuit that was used in the calculation of its improvement index, we find the smallest allocation in the cells of the circuit with the sign ‗-‗.
Call this smallest allocation m. We then subtract m from the allocation in all the cells of the circuit with the sign ‗-‗and add m to all the allocations in the cells in the circuit with the sign
‗+‘. This has the effect of satisfying the constraints on demand and supply in the transportation tableau. Since the cell which carried the allocation m now has a zero allocation, it is deleted from the solution and is replaced by the cell in the circuit which was originally unoccupied and now has allocation m. The result of this reallocation is a new basic feasible solution. The cost of this new basic feasible solution is less than the cost of the previous basic feasible solution. This new basic feasible solution is tested for optimality, and if each unoccupied cell has a non-negative improvement index then the current feasible solution is optimal, .The whole process is repeated until an optimal solution is obtained.
The Stepping Stone Method is summarized as follows:
A. select an empty cell
B. identify a circuit beginning and ending in that cell
[27]
C. insert alternating signs in the corner cells of the closed circuit starting with a
positive (+) sign in the empty cell
D. determine the sum of the cost of positive cells and negative cells.
E. if the difference of the sum is positive, do not move into empty cell but if it is
negative move maximum number of units to empty cell without violating
constraints and alternatively subtract the same number of units from cells with
positive sign.
F. if it is zero, an alternate solution exists.
G. repeat the procedure until all empty cells are evaluated.
3.3 Solving the Transportation Model Using Simplex Method
It is also possible to use the simplex method to solve the transportation problem. The difference between the simplex method and the methods of the transportation problem is in the details of implementing the optimality and feasibility conditions.
The basic steps in the application of the simplex method to the transportation problem are;
(i) determine the starting feasible solution
(ii) determine an entering variable from among the non-basic variables if all such
variables satisfy the optimality conditions, otherwise go to step(iii).
(iii) determine the leaving variable from all the variables of the current basic solution.
(iv) then find the new basic solution. Otherwise return to step (ii).
[28]
3.4.1 Overview of Domestic – Type Refuse Management In The Kumasi Metropolis
The Kumasi Metropolis is divided into 4 sub metros namely Bantama, Manhyia, Subin and
Asokwa. Kumasi, which is the second largest city in the country, is also, the second most commercially active in the country.
Figure 1: Map of Kumasi Metropolitan Area
For the past twenty four years, the Kumasi Metropolis has seen a tremendous increase in its population and this may be attributed to rural – urban migration or migration from the less endowed deficits regions and city in the country and also international immigration in search of better life and living. The population rose from four hundred and eighty seven thousand five hundred and four (487,504) in 1984 to one million one hundred and seventy thousand two hundred and seventy in 2000 and a floating population of about three hundred and fifty thousand (350,000), (Ghana Statistical Service, 2000). This increase has resulted in an over whelming increase in waste generation in the metropolis due to the numerous unauthorized structures for both commercial and domestic activities leading to waste generation which far
[29] outstrips the resources available for collection operation. Refuse management has always been a public good and that has been the task of the Waste Management Department of the
Kumasi Metropolitan Assembly.
The department had contracted six waste management companies namely Zoomlion Ghana
Limited, Mesk World Limited (MWL), Kumasi Waste Management Limited (KWML) and
Kumasi Metropolitan Assembly as waste management companies. The bulk of the refuse collection and disposal are done by these companies and institutions like Kumasi Brewery
Limited, Ghana Police Kumasi central police station, KNUST and some few Timber firms attend to their own generated refuse. Street and drain cleaning are handled by the various town councils under the supervision and funding from KMA.
3.4.2 Refuse Collection Equipment
Equipment used in the metropolis for waste collection by the various contracted companies is
Skips, Compactors, tractors with trailers, ERFs and Tricycles with back-built buckets. The
KMA has 2 skip load trucks and 4 tractors with trailers, KWML has 3 skips loader trucks, 2 compactors and 6 ERFs trucks. Zoomlion Ghana Limited has 2 compactors and 4 skip loader trucks and 8 tricycles. MWL has 12 skip loader trucks and 4 compactors. WGGL has 4 skip loader trucks and 7 compactors and ABC limited has 5 skip loader trucks and 2 compactors.
Therefore there 28 skip loader trucks, 17 compactor trucks or compactors, 4 tractors with trailers. There are 15 loader trucks which are 23 cubic metres and the rest are 13 cubic metres trucks.ABC has skip loader trucks and 2 compactors.
3.4.3 Structure of the Waste Management Problem to Solve
Despite this number of containers there are always heaps of refuse left uncollected from previous days and weeks. These heaps of refuse are the cause of environmental pollution and
[30] epidemic breakout (such as cholera and typhoid) in the metropolis. This health havoc and environmental eye saws are likely to result in revenue loss to the metropolis and the country as a whole sine they scare investors and tourists. In this way, there is a need to put in a mechanism or a system that can efficiently help collect the hugely generated refuse in the metropolis using the available resource employed.
3.4.4 Storage
Domestic-type refuse storage in the metropolis is by both primary and secondary storage.
Primary storage is by the use of cardboards, plastics, woven, baskets, aluminum or galvanized metal bins, wooden boxes. These bins are of varying sizes depending on the waste generation. Secondary storage is by the use of large skips containers, which are shared by a community. The size of the container depends on the size of the community and the dominant commercial activity (Market).
3.4.5 Collection
The type of collection system used in any particular area or in any given locality will depend to a large extent on the allocation of responsibility for collection. In other words the Waste
Management Department of the Kumasi Metropolitan Assembly is the deciding factor in the design and planning of the collection system. Refuse collection involves the collection of refuse from the generation point to the disposal site by the use of collection vehicles. The collection time or period in the time a collection vehicle arrives at the refuse area until the vehicle finishes the collection routine. The frequency of collection could be twice a week, thrice a week, daily, every other day or otherwise depending on the size of the bin and the rate of refuse generation.
The six (6) companies contracted provide a thirteen (13) and twenty-three (23) cubic meter container operations to all the four (4) sub metros. The container services are carried out by
[31] the 28 roll-on-off trucks and 17 compactor trucks handles the direct haul which forms the remaining. The metropolis generates between 1000 and 1100 tones of solid waste a day and the KMA is able to collect an average of 800 tones daily which represents 80% of the total waste generated. The container collection service handles 99% of the waste collection in the metropolis and this covers 792 tones of the total waste generation in the metropolis. The bulk of refuse generated in the metropolis is mostly of domestic-type, this form 98% of waste generation in the metropolis.
3.4.6 Transportation
The mode of refuse transport in the metropolis is by direct haul and waste transfer. Direct haul is affected by the compact trucks (compactors) and waste transfer by the roll-on-off container trucks. Waste transfer handles about 99% of waste for disposal in the metropolis.
Figure 2: A ERF truck on a weighing bridge
3.5 Treatment of Domestic-Type Refuse In the Metropolis
With the exception of hospital and clinical specifics that are wrapped in special black polyethylene bags for easy identification at disposal site and on-site burial, no category of solid waste generated in the metropolis is subjected to any kind of treatment prior to disposal.
[32]
3.6 Material Recovery/Recycling
Some members of communities in the Kumasi Metropolis (usually the very poor groups) pick up copious quantities of materials from the curb before and after they enter the waste stream; this is known as SCANVENGING. Solid wastes generated in the metropolis consist of a large proportion of recoverable components that can be retrieved before final disposal.
Scavenging in the metropolis is very pronounced in high income areas where residents can afford to discard partially damaged items that can still be used by some other people. The scavenger population usually recovers a large quantity of mostly cans and containers of metal, glass, plastic and rubber (tsale-wate) waste for re-use or back to the market or the production cycle. When a number of the scavenger populate was interested to find out whether they would like to form themselves into co-operative groups that would provide opportunities for co-operation with the metropolitan assemblies, since their activities are a waste reduction strategy, their reaction was full of suspicion. They thought that if they did the municipal authorities would find ways to initiate tax payment or even take over their business thus rendering them jobless.
3.7 Refuse Disposal
The Dompoase Sanitation Landfill is a World Bank funded project under the Urban
Environmental Sanitation Project (popularly known as Urban-4). Operation started at this site in February 2004 and it has a lifespan fifteen (15) years. There are three (3) phases each with a lifespan of five (5) years. The site covers a total land of 100 acres. It is about seven (7)
Kilometers from Kumasi. Open-controlled dumping is being practiced by the Waste
Management Department-KMA. At the time of data collection, there were two disposal sites in the Kumasi metropolis namely, Dompoase and Bohyen Landfill sites. The Bohyen landfill site has far exceeded its receiving capacity and it will be abandoned in March 2007. It therefore means that all the generated refuse in the metropolis are dumped in these sites and
[33] this depends on how far the collection point is from the dump site. As mentioned before, the objective of the model is to determine the quantity of refuse to be transported from a collection point to a disposal site such that the total transportation cost is minimized.
Figure 3: A Skip and a ERF truck offloading at Dompoase landfill site
3.8 Data Collection Methods
During the data collection the entire trip routines were timed to measure the distance covered by the trucks in the collection routine. They also helped in determining the quantity of fuel used to access the various collection points. Weights of refuse collected were made at the disposal site weigh bridge in kilograms; the weights were then converted from kilograms to tones by the metric standard in which 1000kg is equivalent to 0.9482ton.
The following are the manual calculations of quantity refuse of refuse generated at the various collection points, the number of trips embarked on by the various types of trucks and the cost involved in the using that truck. Total truck capacity for skip = 4500kg = 4.5ton,
Total truck capacity for ERF = 10500kg = 10.3ton. Though the capacities of the trucks are in cubic meters the weight in kilograms for the refuse is taken. This is because the trucks are
[34] not loaded in such a way that one can just take the capacity of the vehicle to be the volume of refuse lifted. The average weight of refuse lifted by a skip truck is 4.6ton and the average weight of refuse lifted by an ERF truck is 11.3ton.The total amount of refuse generated at a
푚 collection point i denoted by 1 푎푖 where i = 1...... m is given by the total amount of refuse gathered at the collection point i within the time horizon for the data collection period of three (3) months. Places like Aboabo, Sawaba, Dechemso, Suame, Ayigya, Adum,
Bantama, Krofrom, Tafo, Patasi, Amakom, Atonsu, Kejetia, Central Market, Asafo, etc have their refuse lifted on daily bases whiles the average lifting for the rest of the areas is 3. The
푚 total numbers of trips of refuse generated in an area 1 푎푖 shown in the table below. Also
푛 shown in the table is the total number of trips of refuse 푗 푏푗 conveyed by truck j from collection point i.
Due to the fact that KMA-WMD pays the contractors by the per ton method, the quantity of refuse that the trucks can convey per trip must also be in tons. On the average the 13 meter cube skip conveys 4500kg of refuse which is equivalent to 4.5ton and the 12 meter cube skip conveys 4100kg of refuse which is 4.1ton. The ERF conveys 10300kg which is equivalent to
10.3ton. The table below shows the quantity of refuse conveyed by the various trucks per trip.
Table 12: Quantity (in tons) of refuse conveyed by the trucks per trip
Truck Type Quantity(ton), bj Skip(12m3) 4.1 Skip(13m3) 4.5 ERF 10.3
Data collection though recorded the quantity of refuse conveyed by each of the trucks but because the trucks were not assigned to particular collection point(s) the data collection considered the amount of refuse conveyed from the collection point irrespective of the trucks visiting the point. The table below shows the quantity of refuse conveyed from the various
[35] collection points (ai, where i= 1...... 243), the number of trips a vehicle type can convey, the quantity of refuse generated at a collection point i, and the cost involved in using that type of vehicle for the collection. This was over a time horizon of ten days.
[36]
CHAPTER 4
MODELING AND DATA ANALYSIS
4.1 Introduction
This chapter considers the modeling of the transportation problem for waste collection in the metropolis, taking in to consideration the cost of hauling the refuse from the various collection points by the types of vehicles used in the collection of waste in the metroplis. By so doing, the number of trips of waste generated at the collection point, the total number of trips of waste that a vehicle type can convey and the number of trips a vehicle type can embark on in a day.
4.2 Explicit Model Formulation
The waste allocation problem can be formulated as follows;
Let the collection point/source be denoted by i.
Let the vehicle type be denoted by j.
Also, let Cij= the cost of hauling from collection point/source i by vehicle type j.
Let ai be the total number of trips of refuse generated at collection point i.
Let bj be the total number of trips of refuse that can be conveyed by vehicle type j.
Let Nij be the number of trips from collection point/source i by vehicle type j.
If the total cost for hauling a trip of refuse is to be minimized, then the objective function
should be.
m n
Minimize: Z = Cij N ij i1 j1
[37]
Subject to,
n N j ai , i = 1, 2, 3…, m …………. (1) j1
n Ni b j , j = 1, 2, 3…, n………….. (2) i1
Where Nij 0, for all i and j………………… (3)
Where Z be the total cost of hauling of refuse (load) from collection point/source i by vehicle
j
Because there are two landfill sites at Dompoase and Bohyen landfill sites, let‘s distinguish the general linear programming problem for the two sites by using subscript p and h for the
Dompoase and Bohyen sites respectively, then for Dompoase
m n Maximize: Zp = Cij N ij i1 j1
Subject to,
n Nij ai , i = 1, 2, 3…, m …………. (1) j1
n Nij b j , j = 1, 2, 3…, n………….. (2) i1
Where Nij 0, for all i and j…… (3)
Where Zp is the total cost of hauling the refuse (load) from collection point/source i by vehicle j to the Dompoase landfill site.
For the Bohyen site;
[38]
m n
Maximize: Zh = X ij N ij i1 j1
Subject to,
n Nij ai , i = 1, 2, 3…, m …………. (1) j1
n Nij b j , j = 1, 2, 3…, n………….. (2) i1
Where Nij 0, for all i and j………………… (3)
Where Zh is the total cost of hauling the refuse (load) from collection point/source i by vehicle j to the Bohyen landfill site.
The general linear programming problem when put in the above form is referred to as canonical form. The first set of constraints suggests that the sum of refuse transported from a collection point must at least equal the quantity generated. In the same way, the second suggests that the sum of refuse transported to the disposal site must not exceed its receiving limit or capacity.
From equations (1) and (2) it can be deduced that the total quantity of refuse transported from all the collection points must at least be equal to the collective total capacity of collection trucks in operation at any given time.
m n When the total supply equals the total demand, which is ai b j, , the resulting i1 j1 transportation model is said to be balanced, otherwise, the model is unbalanced. An unbalanced transportation model can always be converted to an equivalent balanced model.
[39]
Table 13: Parameters of the model (Manual calculation of the quantity of refuse lifted from the collection points to the Dompoase Landfill site)
Collection Weight Trips/Month Cost/Trip Cost(GH¢)/ Point Lifted (Nij) (GH¢) month(Cij) (i) (ton), (ai) Skip ERF Skip ERF Skip ERF Abattoir 64 14 6 5 9 71 53 Aboabo 410 91 40 12 20 1066 803 Abrem 19 4 2 9 15 36 27 Adabraka 54 12 5 12 20 142 106 Adoato 84 19 8 13 22 243 182 Adompom 29 6 3 12 20 75 56 Adukrom 21 5 2 13 23 62 47 Adum 180 40 18 9 15 358 268 Adwaase 126 28 12 9 15 250 187 Ahafo Kenyase 26 6 2 5 9 31 23 Ahensan 575 128 56 6 10 712 533 Ahodwo 74 17 7 10 17 165 123 Airport Int. School 62 14 6 13 23 185 139 Akrom 16 4 2 13 23 49 37 Akwatia-Line 61 13 6 8 14 111 83 Amakom 256 57 25 8 13 447 335 Anglican 44 10 4 9 15 86 64 Anlorga 28 6 3 10 17 64 48 Anomangye 54 12 5 13 23 162 122 Anwomaso 37 8 4 8 13 64 48 Apino 13 3 1 8 13 22 17 Appiadu 15 3 1 2 4 8 6 Apramang 9 2 1 9 15 18 13 Apre 12 3 1 9 16 24 18 Arizona 14 3 1 10 18 33 25 Asafo 186 41 18 9 15 368 275 Asawase 137 30 13 13 22 388 291 Asebi 9 2 1 13 22 27 20 Ash-Foam 5 1 0 10 17 11 8 Ash-Towm 132 29 13 10 17 297 222 Asokore Mampong 16 4 2 14 25 51 38 Asokwa 215 48 21 7 11 315 236 Asuoyeboah 87 19 8 12 21 240 180 Atasemanso 119 27 12 11 19 289 217 Atonsu 140 31 14 5 8 151 113 Ayigya 158 35 15 8 14 294 220
[40]
Table 13 continued Trips/Month Cost/Trip Cost(GH¢)/ Weight (N ) (GH¢) month(C ) Collection Lifted ij ij Point(i) (ton), (ai) Skip ERF Skip ERF Skip ERF Boadi 22 5 2 10 17 47 35 Bomso 82 18 8 8 14 148 111 Bremang 228 51 22 9 15 458 343 Bremang West 18 4 2 12 21 49 36 Buokrom 116 26 11 12 21 311 233 C.P.C 25 6 2 13 22 70 52 Central Market 125 28 12 9 15 247 185 Chiriapatre 41 9 4 7 11 60 45 Collegiate 14 3 1 9 15 28 21 Consar 8 2 1 7 11 12 9 Daban 48 11 5 8 14 89 67 Daniel Sawmill 5 1 0 4 7 4 3 Danyame 31 7 3 8 13 53 40 Darkwadwom 72 16 7 8 14 131 98 Denkyemmuoso 16 4 2 11 19 41 31 Depot 4 1 0 8 15 8 6 Dichemso 76 17 7 11 20 192 144 Fankyenebra 18 4 2 9 15 36 27 Fante New Town 32 7 3 9 16 69 51 Gee Qnts 24 5 2 10 17 52 39 Holy Family 13 3 1 9 16 26 19 I.P.T 52 11 5 13 23 152 114 K. O/Dr Mensah 77 17 7 10 18 178 133 Kaase 55 12 5 7 12 83 62 Kejetia 102 23 10 9 16 211 158 Kentinkrono 35 8 3 12 20 91 68 Kotei 69 15 7 9 15 138 103 Kromase 28 6 3 11 19 70 52 Kronom 84 19 8 13 22 239 179 Kwaadaso S.D.A 13 3 1 15 25 43 32 Manhyia 132 29 13 11 18 317 237 Mary Akuamoah 72 16 7 13 22 204 153 Mbrom 92 20 9 12 21 252 189 Moshie Zongo 66 15 6 14 24 204 153 N.Suntreso 53 12 5 11 19 128 96 New Tafo 174 39 17 12 21 462 346 Oduom 48 11 5 10 17 108 81
[41]
Table 13 continued Weight Trips/Month Cost/Trip Cost(GH¢)/ Collection Lifted (Nij) (GH¢) month(Cij) Point(i) (ton), (ai) Skip ERF Skip ERF Skip ERF Ofori-Krom 113 25 11 12 20 296 222 Pankrono 152 34 15 13 23 447 335 Pankrono Adabraka 33 7 3 15 25 108 81 Pankrono Dome 32 7 3 15 26 110 82 Papa J 29 6 3 12 21 77 58 Patase 96 21 9 11 19 241 181 Prempeh College 10 2 1 13 22 27 20 Salvation 12 3 1 11 19 30 23 Santase 271 60 26 9 15 519 389 Sepe 102 23 10 13 22 289 216 Sobolo 129 29 12 9 16 259 194 Sokoban 41 9 4 4 8 40 30 South Suntreso 42 9 4 10 17 95 71 Stadium 153 34 15 9 15 290 218 T & E 12 3 1 10 18 28 21 Tafo 180 40 18 14 23 546 409 Takyeman 28 6 3 14 25 91 68 Tanoso 50 11 5 14 24 154 115 Tech 96 21 9 10 17 210 158 Wamase 18 4 2 11 18 43 32
[42]
Table 14: Parameters of the model (Manual calculation of the quantity of refuse lifted from the collection points from the collection points to the Bohyen Landfill site) Weight Collection Point Lifted Trips/Month(Nij) Cost/Trip(GH¢) Cost(GH¢)/month(Cij) (i) (ton), (ai) Skip ERF Skip ERF Skip ERF 2 B.N 19 4 2 8.98 15.40 38.55 28.87 4 B.N 18 4 2 8.26 14.16 32.42 24.28 Aboabo 70 15 7 11.25 19.29 174.11 130.40 Abrepo 114 25 11 5.58 9.56 141.20 105.75 Abuakwa 86 19 8 13.42 23.01 257.77 193.06 Aburaeso 28 6 3 11.56 19.82 71.99 53.92 Adoato Adumanu 43 10 4 11.77 20.18 112.29 84.10 Aduman 22 5 2 14.25 24.43 70.83 53.05 Agric Care 6 1 1 12.39 21.24 17.79 13.32 Ahodwo 22 5 2 8.67 14.87 41.46 31.05 Akem 21 5 2 6.71 11.51 31.50 23.59 Akurem 10 2 1 6.20 10.62 13.82 10.35 Ampabame 12 3 1 4.85 8.32 13.09 9.80 Aprabon 12 3 1 13.84 23.72 37.84 28.34 Ash-Foam 3 1 0 9.29 15.93 6.84 5.12 Asuoyeboah 47 11 5 10.84 18.59 114.21 85.54 Atafoa 16 3 2 10.33 17.70 36.00 26.96 Atwima Takyeman 11 2 1 13.84 23.72 33.03 24.74 Ayarewa 22 5 2 13.42 23.01 66.24 49.61 Bantama 161 36 16 8.26 14.16 296.41 222.00 Bebre 8 2 1 9.60 16.46 16.19 12.13 Bohyen 19 4 2 4.13 7.08 17.63 13.21 C.P.C 6 1 1 8.26 14.16 11.01 8.24 Edwenase 11 2 1 12.80 21.95 30.53 22.87 Kejetia 10 2 1 9.81 16.82 22.30 16.70 Kronom 14 3 1 13.22 22.66 41.88 31.37 Kwaadaso 146 32 14 12.39 21.24 402.54 301.48 Kwantwima 21 5 2 10.33 17.70 47.31 35.43 Kwapra 17 4 2 11.36 19.47 43.74 32.76 Moshie Zongo 12 3 1 13.42 23.01 34.60 25.92 Mpatasie 22 5 2 5.68 9.74 27.71 20.75 N.Suntreso 25 5 2 10.33 17.70 56.60 42.39 Nzema 97 22 9 11.15 19.12 241.01 180.50 Ohwim 31 7 3 5.58 9.56 38.84 29.09 S. Suntreso 68 15 7 9.09 15.58 137.34 102.86
[43]
Table 14 Continued
Weight Collection Lifted Trips/Month(Nij) Cost/Trip(GH¢) Cost(GH¢)/month(Cij) Point (ton), (i) (ai) Skip ERF Skip ERF Skip ERF Suame 192 43 19 7.64 13.10 325.55 243.82 Tafo 145 32 14 13.63 23.36 440.52 329.94 Tanoso 96 21 9 10.53 18.05 224.37 168.04 Yennyawoso 210 47 20 7.23 12.39 337.14 252.50
5.0 DISCUSION
The table below shows the comparison of the real situation of the refuse generation at the various collection points, the rate at which the containers are conveyed after they have been filled. To the waste collection contractors a day refers to the day the container was placed at the collection point. About one day therefore refers to a situation where filling takes more than the day the container was placed. Some containers take more than two days to fill up and that may be so full in the third day to the extent that refuse would be left on the side of the container.
Below is the quantity of refuse generated at each collection point and the number of trips when using the ERF vehicle, the rate of refuse generation at the collection point, the number of days taken to lift the container and the recommended number of days the containers must be lifted. Below is those refuse taken to the Dompoase landfill site.
[44]
Table 15: Optimal number of trips, Dompoase
No. of Weight Trips/10 Days, Collection Point (i) Collection Lifted(ton) ERF Trips/Day Points (ai) (Nij) Abattoir 2 64 6 1 Aboabo 7 410 40 4 Abrem 2 19 2 0 Adabraka 2 54 5 1 Adoato 4 84 8 1 Adompom 3 29 3 0 Adukrom 1 21 2 0 Adum 3 180 18 2 Adwaase 4 126 12 1 Ahafo Kenyase 1 26 2 0 Ahensan 4 575 56 6 Ahodwo 3 74 7 1 Airport Int. School 2 62 6 1 Akrom 1 16 2 0 Akwatia-Line 11 61 6 1 Amakom 9 256 25 2 Anglican 2 44 4 0 Anlorga 1 28 3 0 Anomangye 1 54 5 1 Anwomaso 1 37 4 0 Apino 13 1 0 Appiadu 1 15 1 0 Apramang 1 9 1 0 Apre 1 12 1 0 Arizona 1 14 1 0 Asafo 5 186 18 2 Asawase 4 137 13 1 Asebi 1 9 1 0 Ash-Foam 1 5 0 0 Ash-Town 4 132 13 1 Asokore Mampong 2 16 2 0 Asokwa 8 215 21 2 Asuoyeboah 3 87 8 1 Atasemanso 5 119 12 1 Atonsu 4 140 14 1 Ayigya 4 158 15 2
[45]
Table 15 continued No. Weight Trips/10 Days, Collection Point (i) Collection Lifted(ton) ERF Trips/Day Points (ai) (Nij) Boadi 1 22 2 0 Bomso 5 82 8 1 Bremang 5 228 22 2 Bremang West 1 18 2 0 Buokrom 4 116 11 1 C.P.C 1 25 2 0 Central Market 4 125 12 1 Chiriapatre 2 41 4 0 Collegiate 1 14 1 0 Consar 1 8 1 0 Daban 2 48 5 0 Daniel Sawmill 1 5 0 0 Danyame 2 31 3 0 Darkwadwom 2 72 7 1 Denkyemmuoso 1 16 2 0 Depot 1 4 0 0 Dichemso 3 76 7 1 Fankyenebra 1 18 2 0 Fante New Town 2 32 3 0 Gee Quarters 1 24 2 0 Holy Family 1 13 1 0 I.P.T 2 52 5 1 K. O/Dr Mensah 2 77 7 1 Kaase 2 55 5 1 Kejetia 3 102 10 1 Kentinkrono 2 35 3 0 Kotei 4 69 7 1 Kromase 1 28 3 0 Kronom 2 84 8 1 Kwaadaso S.D.A 1 13 1 0 Manhyia 4 132 13 1 Mary Akuamoah 2 72 7 1 Mbrom 3 92 9 1 Moshie Zongo 2 66 6 1 N.Suntreso 2 53 5 1 New Tafo 5 174 17 2 Oduom 2 48 5 0
[46]
Table 15 continued No. Weight Trips/10 Days, Collection Point (i) Collection Lifted(ton) ERF Trips/Day Points (ai) (Nij) Ofori-Krom 3 113 11 1 Pankrono 4 152 15 1 Pankrono Adabraka 1 33 3 0 Pankrono Dome 1 32 3 0 Papa J 1 29 3 0 Patase 4 96 9 1 Prempeh College 1 10 1 0 Salvation 1 12 1 0 Santase 7 271 26 3 Sepe 3 102 10 1 Sobolo 4 129 12 1 Sokoban 2 41 4 0 South Suntreso 2 42 4 0 Stadium 4 153 15 1 T & E 1 12 1 0 Tafo 6 180 18 2 Takyeman 1 28 3 0 Tanoso 3 50 5 0 Tech 3 96 9 1 Wamase 1 18 2 0
Areas whose number of trips are made zero are the areas that take too long to fill the ERF container and thus it will be economically advisable to send skip vehicles for the collection of the refuse in those areas. These areas are Abrem, Apino, Akrom, Adukrom, Appiadu,
Apramang, Apre, Arizona, Asebi, Ash-Foam, Asokore-Mampong, Boadi, Bremang West,
Collegiate, Consar, Daniel-Sawmill, Fankyenebra, Holy Family, Kwaadaso S.D.A, Prempeh
College, Salvation, T & E, and Wamase.
When waste takes so long to dispose of it leads to decays. This makes residents around those collection points suffer airborne disease and other related diseases that results from bad waste control and management like malaria, typhoid fever, intestinal worms etc. The rate of generation of the refuse at the various collection points is in respect to the kind of container
[47] used at the point. Therefore where it is clear that the use of a kind of container can lead to environmental inconsistencies with the rules and regulations of W.H.O, M.o.H, and the EPA then other type of vehicles can be used. It is therefore recommended that places like Akwatia- line, Tanoso, Apre etc and the collections points must be accessed using the skip vehicle which is small as compared to the ERF vehicle.
It can be noted from the final result (Table…) that, to meet the demand at all the collection points at a minimal cost of GH¢ 19014.68 the whole available space from the skip must be used, while the ERF uses a fraction of its available space. The skip should serve 94 out of the
131 collection points in full; both the ERF and skip should partly serve Santase. The following collection points should be served fully by the ERF; Ahafo-Kenyase, Apramang,
Atonsu, Ahensan, Amakom, Anwomaso, Apino, Appiadu, Asokwa, Atonsu, Ayigya, Bomso,
Danyame, Chiriapatre, Daban, Daniel Sawmill, Abattoir, Sokoban Kaase, and Stadium, it is economically prudent to access the various collection points by the vehicles assigned to them by the excel solver. In areas like Adum, Aboabo, Akwati-Line, Kejetia, Central Market and
Tech where there are two containers serving each of the points, the points should be accessed by a ERF container to check the rate at which collection vehicles would have to visit the points.
From table 4.1.2 (constraint table), constraint 2 is not binding or has the shadow price of zero
(0), an indication that the size of ERF space in use is below the total capacity available. This means that at this level of demand the company will still have an excess of ERF space.
Therefore holding all other constraints constant the company can serve any additional collection point without incurring any additional cost of transportation. That is without changing the current optimal cost of transportation, GH¢ 19014.68 per month instead of GH¢
229500 per month used by the KMA-WMD.
[48]
With this change, the allowable increase is about 1E+30 and the allowable decrease is about
GH¢ 1609.00. Some constraints are not binding but a careful look into those constraint reveals that their shadow prices are all positive. These indicate that a deliberate attempt to increase the space of the truck sent there from the current size indicated in the answer report will cost the company some amount of cost. Almost all the demand constraints are binding, an indication that demands at all these collection points are met. The shadow prices of these constraints are all positives an indication that an increase in the space of truck sent to any of these points will cause an increase in the cost of running such vehicles, it is therefore advisable to keep the same capacity of vehicles running in such places. To see to a more efficient cost effect system in which the Assembly can maximize the use of the little resources the contracted companies have it very prudent management concentrate on the use of the Skip trucks rather than the ERF.
Below is the quantity of refuse generated at each collection point and the number of trips when using the ERF vehicle, the rate of refuse generation at the collection point, the number of days taken to lift the container and the recommended number of days the containers must be lifted. Below is those refuse taken to the Bohyen landfill site.
[49]
Table 16: Optimal number of trips, Bohyen
Weight Trips/10 Collection Point No. Collection Lifted(ton) Days, ERF Trips/Day (i) Points (ai) (Nij) 2 B.N 1 19 2 0 4 B.N 1 18 2 0 Aboabo 2 70 7 1 Abrepo 3 114 11 1 Abuakwa 2 86 8 1 Aburaeso 1 28 3 0 Adoato Adumanu 1 43 4 0 Aduman 1 22 2 0 Agric Care 1 6 1 0 Ahodwo 1 22 2 0 Akem 1 21 2 0 Akurem 1 10 1 0 Ampabame 1 12 1 0 Aprabon 1 12 1 0 Ash-Foam 1 3 0 0 Atafoa 1 16 2 0 Atwima Takyeman 1 11 1 0 Ayarewa 1 22 2 0 Bantama 3 161 16 2 Bebre 1 8 1 0 Bohyen 1 19 2 0 C.P.C 1 6 1 0 Edwenase 1 11 1 0 Kejetia 1 10 1 0 Kronom 1 14 1 0 Kwaadaso 3 146 14 1 Kwapra 1 17 2 0 Kwantwima 1 21 2 0 Tafo 5 145 14 1 Mpatasie 1 22 2 0 Moshie Zongo 1 12 1 0 N.Suntreso 1 25 2 0 Nzema 3 97 9 1 Ohwim 2 31 3 0 S. Suntreso 2 68 7 1
[50]
Table 16 continued Weight Collection Point No. Collection Trips/10 Lifted(ton) Trips/Day (i) Points Days, ERF (ai) Asuoyeboah 2 47 5 0 Suame 4 192 19 2 Tanoso 3 96 9 1 Yennyawoso 4 210 20 2
Agric-care is a company that deals in agro chemical and farming feeds which rot easily and pollute the air with its scent and hazardous gases into the environment thus it needs to be disposed of at most within three days after dumping. Because these are not so much in quantity it could be kept in various containers such as polythene bags rather than to assigning a skip or ERF container for such purpose. I commend that the company be made to transport the waste they accumulate in the shortest possible time to the landfill.
Other collection points such as Asuoyeboah, Ohwim, N.Suntreso, Moshie Zongo, Mpatasie,
Kwantwima, Kwapra, Kronom, Kejetia, Edwenase, C.P.C, Bohyen, Ayarewa, Bebre,
Takyeman, Atwima, Atafoa, Ash-Foam, Aprabon, Ampabame, Akurem, Akem, Ahodwo,
Agric Care, Aduman, Adoato Adumanu, Aburaeso, 2 B.N,4 B.N generate small quantity of refuse and thus smaller containers (e.g. those conveyable by tricycles and tractors) must be sent to such areas to check some of these diseases that can be caused by the decay of the putrescible component of the refuse. If the skip vehicle is used to access these collection points their case will be as shown in the table below.
[51]
CHAPTER 5
SUMMARY, CONCLUSION AND RECOMMENDATION
5.1 Summary
The rate at which the population in the metropolis is increasing has led a subsequent increase in waste generation which needs to be tackled scientifically. Thus this study is a good step to improve the transportation problems related to waste management caused by the alarming rate of waste generation in the metropolis.
5.2 Conclusion
The KMA as at the time of data collection was spending about two hundred and twenty nine thousand five hundred Ghana cedis (GH¢ 229,500.00) per month. By the research, the KMA would be spending about nineteen thousand and fourteen Ghana cedis sixty eigth pesewa
(GH¢19014.68) per month. Thus by implementing the findings of this research the KMA will reduce the cost on waste collection in the metropolis by about 88%.
5.3 Recommendation
It is recommended that the KMA-WMD follow the solution above to attain the operational values and a minimum cost of GH¢19014.68 per month instead of GH¢ 229,500.00 per month. With the increase in population and means of transportation, we recommend that drivers and their mates are well motivated to see to a continual running of the trucks for the assigned jobs. Because drivers and their mates are not well motivated they most of the time end up parking the vehicle for a very long time in their name of breaking and sometimes buy of food as this take precious time for working away from the time management of the contracted companies has assigned to the drivers in terms of the number of trips to embark on. We therefore recommend also that collection and transportation of the refuse be done in
[52] the night when vehicular traffic is less to ensure an uninterrupted refuse collection and transportation.
Decision makers in the metropolis must be responsive to the problems posed by solid waste disposal as a result of increased population and map up refuse management strategies such as our Transportation Model and other researches by students to efficiently handle the resulting increasing amount of refuse.
The following recommendations are very necessary for the various collection points
1. Care must be taking on the areas that take more than 5 days to fill their containers,
because refuse may rot if left for a long period. In the case of refuse rot, kids who
come to dispose refuse end up throwing waste around the container, this due to the
stench from the rotten refuse. Others do not bring the garbage at all to the collection
points and thus throw them into gutters and other unapproved places for waste
disposal.
2. It is not economically advisable to allow trucks that has been assigned zero final value
to collect refuse from the areas(towns) they were assigned zero final value
3. Areas like Appiadu, Apramang, Apre, Arizona, Asebi, Asokore Mampong, Holy
family, etc that generate less than 4 trips of skip‘s capacity per month must be
accessed by tricycles in about every three days to prevent long staying of the refuse in
the containers to prevent rotting.
4. Because the abattoir generates wastes which are mainly from the left over of animal
feeds, animal faeces, remains from butchered meat, tyre, etc. It is hygienically
advisable to dispose the wastes at most every two days so to prevent the
inconvenience of stench from the waste and gems been carried by flies to the
[53]
butchered meat. It would therefore be very good to allow a skip to collect the waste
and on daily bases.
5. Containers serving in Kejetia, Moshie Zongo and Mbrom must be lifted every
evening instead of morning, to prevent spillage of refuse as a result of over dumping
around the container because the container may be full. There should therefore be a
standby container to collect refuse whenever the current is filled.
5.4 Suggestion for Future Research
It is suggested that further research(s) be conducted in this field taking into consideration the administration cost per company involved in the waste collection and management. This could not be captures because the companies were very reluctant on giving out information on the administration cost. Though a lot of efforts were made and all to no avail.
Each collection point in this research may refer to a town or a village and this may contain one or more actual collection points, consideration should therefore be giving to the number of collection points in each town or village.
[54]
REFFERENCES
Cairncrose, S. Feachem, R., (1988). Environmental Health Engineering in the Tropics, John Wiley &
Son's. Baffin‘s lane Chichester England, pp 196-202
Ceril, L., Smith, W., Pike, Paul W., Murrill (1970) Formulation and Optimization of Mathematical
Models Copyright by International Textbook Company Louisiana State University, pp554-575
Feachem, R., Mara, D., McGarry, M.,(1983) Water, Waste and Health in Hot Climate John
Wiley and Sons New York, Reprinted pp 320 - 327
Gass and Saul I., (1958) Linear Programming Methods and Application McGraw- Hill Book
Company, Inc., New York pp 74 – 76
Green, D. W., Perry, H. R.., (1997) Perry's Chemical Engineering Handbook McGraw-Hill Companies
Inc. U.S.A
Hagerty, D. J., Pavani, J. L., Heer, Jr. J. E., (1973) Solid Waste Management Littan
Educational Publishing Inc. New York pp 44-47
Hardman, D. J., Me Eldewney, S., Waite, S., (1993). Pollution, Ecology and Biotreatment
John Wiley & Sons Inc., New York pp 48-50
Ivor, H., Seeley. (1992) Public Works Engineering The Macmillan Press Ltd London pp 220-22
Kreith, F., (1994.) Handbook of Solid Waste Management Copyright by McGraw - Hill Inc. U.S.A
Kumasi Metropolitan Assembly-Waste Management Department. (2006) Data and 2005 Annual Report
Ralph E, Stever, (1986) Multiple Criteria Optimization, theory, Computation and application John
Wiley and sons. New York pp31, 66-70
[55]
APPENDIX I
ANSWER REPORT, DOMPOASE
Answer report to the excel solution on the Dompoase Landfill site is as shown below
Table A 1: Real cost of transporting waste from parts of the metropolis to the Dompoase landfill site Trivial Cost Real Cost Total Cost[¢] 27628.56 11836.62
Table A 2: Values from EXCEL transportation solution Cell Name Original Value Final Value $E$108 ai=704 91 0 $F$108 b2=704 40 40 $E$109 ai=704 19 0 $F$109 b2=704 8 8 $E$110 ai=704 4 0 $F$110 b2=704 2 2 $E$111 ai=704 12 0 $F$111 b2=704 5 5 $E$112 ai=704 27 0 $F$112 b2=704 12 12 $E$113 ai=704 19 0 $F$113 b2=704 8 8 $E$114 ai=704 6 0 $F$114 b2=704 3 3 $E$115 ai=704 5 0 $F$115 b2=704 2 2 $E$116 ai=704 28 0 $F$116 b2=704 12 12 $E$117 ai=704 6 0 $F$117 b2=704 2 2 $E$118 ai=704 128 0 $F$118 b2=704 56 56 $E$119 ai=704 17 0 $F$119 b2=704 7 7 $E$120 ai=704 14 0 $F$120 b2=704 6 6 $E$121 ai=704 4 0 $F$121 b2=704 2 2
[56]
Table A 2: Continued Cell Name Original Value Final Value $E$122 ai=704 13 0 $F$122 b2=704 6 6 $E$123 ai=704 57 0 $F$123 b2=704 25 25 $E$124 ai=704 10 0 $F$124 b2=704 4 4 $E$125 ai=704 6 0 $F$125 b2=704 3 3 $E$126 ai=704 12 0 $F$126 b2=704 5 5 $E$127 ai=704 8 0 $F$127 b2=704 4 4 $E$128 ai=704 3 0 $F$128 b2=704 1 1 $E$129 ai=704 3 0 $F$129 b2=704 1 1 $E$130 ai=704 2 0 $F$130 b2=704 1 1 $E$131 ai=704 3 0 $F$131 b2=704 1 1 $E$132 ai=704 3 0 $F$132 b2=704 1 1 $E$133 ai=704 41 0 $F$133 b2=704 18 18 $E$134 ai=704 30 0 $F$134 b2=704 13 13 $E$135 ai=704 2 0 $F$135 b2=704 1 1 $E$136 ai=704 1 0 $F$136 b2=704 0 0 $E$137 ai=704 29 0 $F$137 b2=704 13 13 $E$138 ai=704 4 0 $F$138 b2=704 2 2 $E$139 ai=704 48 0 $F$139 b2=704 21 21 $E$140 ai=704 19 0 $F$140 b2=704 8 8 $E$141 ai=704 31 0 $F$141 b2=704 14 14 $E$142 ai=704 35 0 $F$142 b2=704 15 15 $E$143 ai=704 40 0 [57]
Table A 2: Continued Cell Name Original Value Final Value $F$143 b2=704 18 18 $E$144 ai=704 2 0 $F$144 b2=704 1 1 $E$145 ai=704 5 0 $F$145 b2=704 2 2 $E$146 ai=704 18 0 $F$146 b2=704 8 8 $E$147 ai=704 51 0 $F$147 b2=704 22 22 $E$148 ai=704 4 0 $F$148 b2=704 2 2 $E$149 ai=704 26 0 $F$149 b2=704 11 11 $E$150 ai=704 6 0 $F$150 b2=704 2 2 $E$151 ai=704 9 0 $F$151 b2=704 4 4 $E$152 ai=704 7 0 $F$152 b2=704 3 3 $E$153 ai=704 28 0 $F$153 b2=704 12 12 $E$154 ai=704 9 0 $F$154 b2=704 4 4 $E$155 ai=704 3 0 $F$155 b2=704 1 1 $E$156 ai=704 11 0 $F$156 b2=704 5 5 $E$157 ai=704 1 0 $F$157 b2=704 0 0 $E$158 ai=704 16 0 $F$158 b2=704 7 7 $E$159 ai=704 4 0 $F$159 b2=704 2 2 $E$160 ai=704 1 0 $F$160 b2=704 0 0 $E$161 ai=704 17 0 $F$161 b2=704 7 7 $E$162 ai=704 4 0 $F$162 b2=704 2 2 $E$163 ai=704 7 0 $F$163 b2=704 3 3 $E$164 ai=704 5 0 $F$164 b2=704 2 2 [58]
Table A 2: Continued Cell Name Original Value Final Value $E$165 ai=704 3 0 $F$165 b2=704 1 1 $E$166 ai=704 11 0 $F$166 b2=704 5 5 $E$167 ai=704 17 0 $F$167 b2=704 7 7 $E$168 ai=704 14 0 $F$168 b2=704 6 6 $E$169 ai=704 12 0 $F$169 b2=704 5 5 $E$170 ai=704 23 0 $F$170 b2=704 10 10 $E$171 ai=704 8 0 $F$171 b2=704 3 3 $E$172 ai=704 15 0 $F$172 b2=704 7 7 $E$173 ai=704 6 0 $F$173 b2=704 3 3 $E$174 ai=704 3 0 $F$174 b2=704 1 1 $E$175 ai=704 29 0 $F$175 b2=704 13 13 $E$176 ai=704 16 0 $F$176 b2=704 7 7 $E$177 ai=704 20 0 $F$177 b2=704 9 9 $E$178 ai=704 15 0 $F$178 b2=704 6 6 $E$179 ai=704 12 0 $F$179 b2=704 5 5 $E$180 ai=704 39 0 $F$180 b2=704 17 17 $E$181 ai=704 11 0 $F$181 b2=704 5 5 $E$182 ai=704 25 0 $F$182 b2=704 11 11 $E$183 ai=704 7 0 $F$183 b2=704 3 3 $E$184 ai=704 7 0 $F$184 b2=704 3 3 $E$185 ai=704 34 0 $F$185 b2=704 15 15 $E$186 ai=704 6 0 [59]
Table A 2: Continued Cell Name Original Value Final Value $F$186 b2=704 3 3 $E$187 ai=704 21 0 $F$187 b2=704 9 9 $E$188 ai=704 2 0 $F$188 b2=704 1 1 $E$189 ai=704 3 0 $F$189 b2=704 1 1 $E$190 ai=704 60 0 $F$190 b2=704 26 26 $E$191 ai=704 23 0 $F$191 b2=704 10 10 $E$192 ai=704 29 0 $F$192 b2=704 12 12 $E$193 ai=704 9 0 $F$193 b2=704 4 4 $E$194 ai=704 34 0 $F$194 b2=704 15 15 $E$195 ai=704 3 0 $F$195 b2=704 1 0 $E$196 ai=704 40 0 $F$196 b2=704 18 18 $E$197 ai=704 6 0 $F$197 b2=704 3 3 $E$198 ai=704 11 0 $F$198 b2=704 5 5 $E$199 ai=704 21 0 $F$199 b2=704 9 9 $E$200 ai=704 4 0 $F$200 b2=704 2 2
[60]
CONSTRAINTS TABLE, DOMPOASE
Table A 3: Values from EXCEL transportation solution showing constraints and slack Cell Name Cell Value Status Slack $H$108 ERF 40 Binding 0 $H$109 ERF 8 Binding 0 $H$110 ERF 2 Binding 0 $H$111 ERF 5 Binding 0 $H$112 ERF 12 Binding 0 $H$113 ERF 8 Binding 0 $H$114 ERF 3 Binding 0 $H$115 ERF 2 Binding 0 $H$116 ERF 12 Binding 0 $H$117 ERF 2 Binding 0 $H$118 ERF 56 Binding 0 $H$119 ERF 7 Binding 0 $H$120 ERF 6 Binding 0 $H$121 ERF 2 Binding 0 $H$122 ERF 6 Binding 0 $H$123 ERF 25 Binding 0 $H$124 ERF 4 Binding 0 $H$125 ERF 3 Binding 0 $H$126 ERF 5 Binding 0 $H$127 ERF 4 Binding 0 $H$128 ERF 1 Binding 0 $H$129 ERF 1 Binding 0 $H$130 ERF 1 Binding 0 $H$131 ERF 1 Binding 0 $H$132 ERF 1 Binding 0 $H$133 ERF 18 Binding 0 $H$134 ERF 13 Binding 0 $H$135 ERF 1 Binding 0 $H$136 ERF 0 Binding 0 $H$137 ERF 13 Binding 0 $H$138 ERF 2 Binding 0 $H$139 ERF 21 Binding 0 $H$140 ERF 8 Binding 0
[61]
Table A 3: Continued Cell Name Cell Value Status Slack $H$141 ERF 14 Binding 0 $H$142 ERF 15 Binding 0 $H$143 ERF 18 Binding 0 $H$144 ERF 1 Binding 0 $H$145 ERF 2 Binding 0 $H$146 ERF 8 Binding 0 $H$147 ERF 22 Binding 0 $H$155 ERF 1 Binding 0 $H$156 ERF 5 Binding 0 $H$157 ERF 0 Binding 0 $H$158 ERF 7 Binding 0 $H$159 ERF 2 Binding 0 $H$160 ERF 0 Binding 0 $H$161 ERF 7 Binding 0 $H$162 ERF 2 Binding 0 $H$163 ERF 3 Binding 0 $H$164 ERF 2 Binding 0 $H$165 ERF 1 Binding 0 $H$166 ERF 5 Binding 0 $H$167 ERF 7 Binding 0 $H$168 ERF 6 Binding 0 $H$169 ERF 5 Binding 0 $H$170 ERF 10 Binding 0 $H$171 ERF 3 Binding 0 $H$172 ERF 7 Binding 0 $H$173 ERF 3 Binding 0 $H$174 ERF 1 Binding 0 $H$175 ERF 13 Binding 0 $H$176 ERF 7 Binding 0 $H$177 ERF 9 Binding 0 $H$178 ERF 6 Binding 0 $H$179 ERF 5 Binding 0 $H$180 ERF 17 Binding 0 $H$181 ERF 5 Binding 0 $H$182 ERF 11 Binding 0 $H$183 ERF 3 Binding 0 $H$184 ERF 3 Binding 0 $H$185 ERF 15 Binding 0
[62]
Table A 3: Continued Cell Name Cell Value Status Slack $H$186 ERF 3 Binding 0 $H$187 ERF 9 Binding 0 $H$188 ERF 1 Binding 0 $H$189 ERF 1 Binding 0 $H$190 ERF 26 Binding 0 $H$191 ERF 10 Binding 0 $H$193 ERF 4 Binding 0 $H$192 ERF 12 Binding 0 $H$194 ERF 15 Binding 0 $H$195 ERF 0 Binding 0 $H$196 ERF 18 Binding 0 $H$197 ERF 3 Binding 0 $H$198 ERF 5 Binding 0 $H$199 ERF 9 Binding 0 $H$200 ERF 2 Binding 0
[63]
SENSITIVITY REPORT TABLE, DOMPOASE
Table A 4: Values from EXCEL transportation solution for sensitivity analysis Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $E$108 ai=704 0 3 11.7 1.00E+30 2.88437 $F$108 b2=704 40 0 20.178 6.601999904 20.178 $E$109 ai=704 0 3 12.8 1.00E+30 3.21107 $F$109 b2=704 8 0 21.948 7.349777701 21.948 $E$110 ai=704 0 2 8.7 1.00E+30 2.20427 $F$110 b2=704 2 0 14.868 5.045332998 14.868 $E$111 ai=704 0 3 11.7 1.00E+30 2.9617 $F$111 b2=704 5 0 20.001 6.778999906 20.001 $E$112 ai=704 0 3 10.9 1.00E+30 2.70301 $F$112 b2=704 12 0 18.762 6.18688859 18.762 $E$113 ai=704 0 3 13.0095 1.00E+30 3.26591 $F$113 b2=704 8 0 22.302 7.475299745 22.302 $E$114 ai=704 0 3 11.7705 1.00E+30 2.95487 $F$114 b2=704 3 0 20.178 6.763366639 20.178 $E$115 ai=704 0 3 13.3192 1.00E+30 3.34367 $F$115 b2=704 2 0 22.833 7.653283242 22.833 $E$116 ai=704 0 2 8.93112 1.00E+30 2.24207 $F$116 b2=704 12 0 15.3105 5.131852388 15.3105 $E$117 ai=704 0 1 5.47225 1.00E+30 1.37375 $F$117 b2=704 2 0 9.381 3.144372008 9.381 $E$118 ai=704 0 1 5.5755 1.00E+30 1.39967 $F$118 b2=704 56 0 9.558 3.203699831 9.558 $E$119 ai=704 0 3 9.96362 1.00E+30 2.50127 $F$119 b2=704 7 0 17.0805 5.725130259 17.0805 $E$120 ai=704 0 3 13.4225 1.00E+30 3.36959 $F$120 b2=704 6 0 23.01 7.71261106 23.01 $E$121 ai=704 0 3 13.4225 1.00E+30 3.36959 $F$121 b2=704 2 0 23.01 7.712611068 23.01 $E$122 ai=704 0 2 8.26 1.00E+30 2.07359 $F$122 b2=704 6 0 14.16 4.746222126 14.16 $E$123 ai=704 0 2 7.87281 1.00E+30 1.97639 $F$123 b2=704 25 0 13.4963 4.523742873 13.4963 $E$124 ai=704 0 2 8.77625 1.00E+30 2.20319 $F$124 b2=704 4 0 15.045 5.042860854 15.045
[64]
Table A 4: Continued Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $F$125 b2=704 3 0 17.346 5.814122213 17.346 $E$126 ai=704 0 3 13.4225 1.00E+30 3.36959 $F$126 b2=704 5 0 23.01 7.712611058 23.01 $E$127 ai=704 0 2 7.847 1.00E+30 1.96991 $F$127 b2=704 4 0 13.452 4.508910815 13.452 $E$128 ai=704 0 2 7.74375 1.00E+30 1.94399 $F$128 b2=704 1 0 13.275 4.449582995 13.275 $E$129 ai=704 0 1 2.2715 1.00E+30 0.57024 $F$129 b2=704 1 0 3.894 1.305210983 3.894 $E$130 ai=704 0 2 8.77625 1.00E+30 2.20319 $F$130 b2=704 1 0 15.045 5.042860869 15.045 $E$131 ai=704 0 2 9.2925 1.00E+30 2.33279 $F$131 b2=704 1 0 15.93 5.3395 15.93 $E$132 ai=704 0 3 10.325 1.00E+30 2.59199 $F$132 b2=704 1 0 17.7 5.932777457 17.7 $E$133 ai=704 0 2 8.8795 1.00E+30 2.22911 $F$133 b2=704 18 0 15.222 5.102188681 15.222 $E$134 ai=704 0 3 12.7514 1.00E+30 3.20111 $F$134 b2=704 13 0 21.8595 7.326980381 21.8595 $E$135 ai=704 0 3 12.9062 1.00E+30 3.23999 $F$135 b2=704 1 0 22.125 7.415971932 22.125 $E$136 ai=704 1 3 10.1185 1.00E+30 2.54015 $F$136 b2=704 0 0 17.346 5.814122225 17.346 $E$137 ai=704 0 3 10.1529 1.00E+30 2.54879 $F$137 b2=704 13 0 17.405 5.833897874 17.405 $E$138 ai=704 0 4 14.455 1.00E+30 3.62879 $F$138 b2=704 2 0 24.78 8.305888942 24.78 $E$139 ai=704 0 2 6.608 1.00E+30 1.65887 $F$139 b2=704 21 0 11.328 3.796977701 11.328 $E$140 ai=704 0 3 12.4932 1.00E+30 3.13631 $F$140 b2=704 8 0 21.417 7.178661017 21.417 $E$141 ai=704 0 1 4.82694 1.00E+30 1.21176 $F$141 b2=704 14 0 8.27475 2.773573386 8.27475 $E$142 ai=704 0 2 8.36325 1.00E+30 2.09951
[65]
Table A 4: Continued Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $E$143 ai=704 0 2 8.92375 1.00E+30 2.24022 $F$143 b2=704 18 0 15.2979 5.127614894 15.2979 $E$144 ai=704 0 2 6.608 1.00E+30 1.65887 $F$144 b2=704 1 0 11.328 3.796977704 11.328 $E$145 ai=704 0 2 9.7055 1.00E+30 2.43647 $F$145 b2=704 2 0 16.638 5.576810896 16.638 $E$146 ai=704 0 2 8.15675 1.00E+30 2.04767 $F$146 b2=704 8 0 13.983 4.686894297 13.983 $E$147 ai=704 0 2 9.03438 1.00E+30 2.26799 $F$147 b2=704 22 0 15.4875 5.191180633 15.4875 $E$148 ai=704 0 3 12.39 1.00E+30 3.11039 $F$148 b2=704 2 0 21.24 7.119333195 21.24 $E$149 ai=704 0 3 12.0389 1.00E+30 3.02226 $F$149 b2=704 11 0 20.6382 6.917618655 20.6382 $E$150 ai=704 0 3 12.6998 1.00E+30 3.18815 $F$150 b2=704 2 0 21.771 7.297316678 21.771 $E$151 ai=704 0 3 10.1185 1.00E+30 2.54015 $F$151 b2=704 4 0 17.346 5.814122209 17.346 $E$152 ai=704 0 2 7.74375 1.00E+30 1.94399 $F$152 b2=704 3 0 13.275 4.449583399 13.275 $E$153 ai=704 0 2 8.8795 1.00E+30 2.22911 $F$153 b2=704 12 0 15.222 5.102188682 15.222 $E$154 ai=704 0 2 6.608 1.00E+30 1.65887 $F$154 b2=704 4 0 11.328 3.796977702 11.328 $E$155 ai=704 0 2 8.8795 1.00E+30 2.22911 $F$155 b2=704 1 0 15.222 5.102188683 15.222 $E$156 ai=704 0 2 8.26 1.00E+30 2.07359 $F$156 b2=704 5 0 14.16 4.746222128 14.16 $E$157 ai=704 1 1 4.13 1.00E+30 1.0368 $F$157 b2=704 0 0 7.08 2.373111086 7.08 $E$158 ai=704 0 2 8.15675 1.00E+30 2.04767 $F$158 b2=704 7 0 13.983 4.686894298 13.983 $E$159 ai=704 0 3 11.151 1.00E+30 2.79935 $F$159 b2=704 2 0 19.116 6.407400089 19.116
[66]
Table A4 : Continued Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $F$160 b2=704 0 15 14.514 1.00E+30 14.514 $E$161 ai=704 0 3 11.4091 1.00E+30 2.86415 $F$161 b2=704 7 0 19.5585 6.555719441 19.5585 $E$162 ai=704 0 2 8.77625 1.00E+30 2.20319 $F$162 b2=704 2 0 15.045 5.042860854 15.045 $E$163 ai=704 0 2 9.499 1.00E+30 2.38463 $F$163 b2=704 3 0 16.284 5.458155658 16.284 $E$164 ai=704 0 2 9.80875 1.00E+30 2.46239 $F$164 b2=704 2 0 16.815 5.636138723 16.815 $E$165 ai=704 0 2 9.2925 1.00E+30 2.33279 $F$165 b2=704 1 0 15.93 5.339500005 15.93 $E$166 ai=704 0 3 13.216 1.00E+30 3.31775 $F$166 b2=704 5 0 22.656 7.593955401 22.656 $E$167 ai=704 0 3 10.3766 1.00E+30 2.60495 $F$167 b2=704 7 0 17.7885 5.962441572 17.7885 $E$168 ai=704 0 1 5.03344 1.00E+30 1.2636 $F$168 b2=704 6 0 8.62875 2.892229042 8.62875 $E$169 ai=704 0 2 6.8145 1.00E+30 1.71071 $F$169 b2=704 5 0 11.682 3.915633357 11.682 $E$170 ai=704 0 2 9.2925 1.00E+30 2.33279 $F$170 b2=704 10 0 15.93 5.339499996 15.93 $E$171 ai=704 0 3 11.564 1.00E+30 2.90303 $F$171 b2=704 3 0 19.824 6.64471098 19.824 $E$172 ai=704 0 2 9.01717 1.00E+30 2.26367 $F$172 b2=704 7 0 15.458 5.181292593 15.458 $E$173 ai=704 0 3 11.3575 1.00E+30 2.85119 $F$173 b2=704 3 0 19.47 6.526055326 19.47 $E$174 ai=704 0 4 14.5583 1.00E+30 3.65471 $F$174 b2=704 1 0 24.957 8.365216768 24.957 $E$175 ai=704 0 3 10.7587 1.00E+30 2.70085 $F$175 b2=704 13 0 18.4434 6.181954495 18.4434 $E$176 ai=704 0 3 12.6998 1.00E+30 3.18815 $F$176 b2=704 7 0 21.771 7.297316675 21.771 $E$177 ai=704 0 3 12.39 1.00E+30 3.11039 $F$177 b2=704 9 0 21.24 7.11933319 21.24 $E$178 ai=704 0 3 13.8355 1.00E+30 3.47327
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Table A 4: Continued Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $E$179 ai=704 0 3 10.8412 1.00E+30 2.72159 $F$179 b2=704 5 0 18.585 6.229416593 18.585 $E$180 ai=704 0 3 11.977 1.00E+30 3.00671 $F$180 b2=704 17 0 20.532 6.88202229 20.532 $E$181 ai=704 0 3 10.1185 1.00E+30 2.54015 $F$181 b2=704 5 0 17.346 5.814122205 17.346 $E$182 ai=704 0 3 11.7705 1.00E+30 2.95487 $F$182 b2=704 11 0 20.178 6.763366634 20.178 $E$183 ai=704 0 4 14.7648 1.00E+30 3.70655 $F$183 b2=704 3 0 25.311 8.483872415 25.311 $E$184 ai=704 0 4 15.281 1.00E+30 3.83615 $F$184 b2=704 3 0 26.196 8.780511149 26.196 $E$185 ai=704 0 3 13.216 1.00E+30 3.31775 $F$185 b2=704 15 0 22.656 7.593955402 22.656 $E$186 ai=704 0 3 12.1835 1.00E+30 3.05855 $F$186 b2=704 3 0 20.886 7.000677955 20.886 $E$187 ai=704 0 3 11.3575 1.00E+30 2.85119 $F$187 b2=704 9 0 19.47 6.526055735 19.47 $E$188 ai=704 0 3 12.803 1.00E+30 3.21407 $F$188 b2=704 1 0 21.948 7.356644497 21.948 $E$189 ai=704 0 3 11.3575 1.00E+30 2.85119 $F$189 b2=704 1 0 19.47 6.526055734 19.47 $E$190 ai=704 0 2 8.61105 1.00E+30 2.16172 $F$190 b2=704 26 0 14.7618 4.94793666 14.7618 $E$191 ai=704 0 3 12.7772 1.00E+30 3.20759 $F$191 b2=704 10 0 21.9038 7.341812442 21.9038 $E$192 ai=704 0 2 9.05158 1.00E+30 2.27231 $F$192 b2=704 12 0 15.517 5.201068673 15.517 $E$193 ai=704 0 1 4.43975 1.00E+30 1.11456 $F$193 b2=704 4 0 7.611 2.55109455 7.611 $E$194 ai=704 0 2 8.56975 1.00E+30 2.15135 $F$194 b2=704 15 0 14.691 4.924205612 14.691 $E$195 ai=704 1 10 10.325 1.00E+30 10.325 $F$195 b2=704 0 18 17.7 1.00E+30 17.7 $E$196 ai=704 0 3 13.629 1.00E+30 3.42143 $F$196 b2=704 18 0 23.364 7.831266715 23.364
[68]
Table A 4: Continued Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $F$197 b2=704 3 0 24.78 8.30588893 24.78 $E$198 ai=704 0 3 13.9388 1.00E+30 3.49919 $F$198 b2=704 5 0 23.895 8.009250204 23.895 $E$199 ai=704 0 2 9.912 1.00E+30 2.48831 $F$199 b2=704 9 0 16.992 5.69546655 16.992 $E$200 ai=704 0 3 10.6347 1.00E+30 2.66975 $F$200 b2=704 2 0 18.231 6.110760931 18.231
[69]
SENSITIVITY, CONSTRAINTS TABLE, DOMPOASE
Table A 5: Values from EXCEL transportation solution showing sensitivity output constraint Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $H$108 ERF 40 20 39.8151899 2.477490938 39.8151899 $H$109 ERF 8 22 8.142105049 2.477490938 8.142105049 $H$110 ERF 2 15 1.811055405 2.477490939 1.811055405 $H$111 ERF 5 20 5.291110162 2.477490938 5.291110162 $H$112 ERF 12 19 11.58903463 2.477490938 11.58903463 $H$113 ERF 8 22 8.171089579 2.477490938 8.171089579 $H$114 ERF 3 20 2.776463236 2.477490938 2.776463236 $H$115 ERF 2 23 2.043887184 2.477490938 2.043887184 $H$116 ERF 12 15 12.20535405 2.477490938 12.20535405 $H$117 ERF 2 9 2.490758576 2.477490938 2.490758576 $H$118 ERF 56 10 55.77897761 2.477490938 55.77897761 $H$119 ERF 7 17 7.214600065 2.477490938 7.214600065 $H$120 ERF 6 23 6.037063689 2.477490938 6.037063689 $H$121 ERF 2 23 1.595104725 2.477490938 1.595104725 $H$122 ERF 6 14 5.888000388 2.477490938 5.888000388 $H$123 ERF 25 13 24.82827644 2.477490938 24.82827644 $H$124 ERF 4 15 4.259451974 2.477490938 4.259451974 $H$125 ERF 3 17 2.748434239 2.477490938 2.748434239 $H$126 ERF 5 23 5.281873333 2.477490938 5.281873333 $H$127 ERF 4 13 3.559045566 2.477490938 3.559045566 $H$128 ERF 1 13 1.253979094 2.477490939 1.253979094 $H$129 ERF 1 4 1.47152233 2.477490938 1.47152233 $H$130 ERF 1 15 0.884187443 2.477490938 0.884187443 $H$131 ERF 1 16 1.124663495 2.477490938 1.124663495 $H$132 ERF 1 18 1.403679417 2.477490938 1.403679417 $H$133 ERF 18 15 18.09558401 2.477490938 18.09558401 $H$134 ERF 13 22 13.29466278 2.477490938 13.29466278 $H$135 ERF 1 22 0.899794498 2.47749094 0.899794498 $H$136 ERF 0 17 0.489870421 2.477490937 0.052977217 $H$137 ERF 13 17 12.7719857 2.477490938 12.7719857 $H$138 ERF 2 25 1.543824401 2.477490938 1.543824401 $H$139 ERF 21 11 20.84975146 2.477490938 20.84975146 $H$140 ERF 8 21 8.399143689 2.477490938 8.399143689 $H$141 ERF 14 8 13.63419586 2.477490938 13.63419586 $H$142 ERF 15 14 15.36116427 2.477490938 15.36116427 $H$143 ERF 18 15 17.50824913 2.477490938 17.50824913 $H$144 ERF 1 11 0.766656764 2.477490938 0.766656764 $H$145 ERF 2 17 2.107907961 2.477490938 2.107907961 $H$146 ERF 8 14 7.950998252 2.477490938 7.950998252
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Table A 5: Continued Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $H$148 ERF 2 21 1.711042848 2.477490939 1.711042848 $H$149 ERF 11 21 11.29791528 2.477490938 11.29791528 $H$150 ERF 2 22 2.404442006 2.477490938 2.404442006 $H$151 ERF 4 17 4.112618252 2.477490938 4.112618252 $H$152 ERF 3 13 3.010887573 2.477490938 3.010887573 $H$153 ERF 12 15 12.13814816 2.477490938 12.13814816 $H$154 ERF 4 11 3.978206472 2.477490938 3.978206472 $H$155 ERF 1 15 1.3947611 2.477490938 1.3947611 $H$156 ERF 5 14 4.704412298 2.477490938 4.704412298 $H$157 ERF 0 7 0.44878246 2.477490938 0.011889256 $H$158 ERF 7 14 6.998330874 2.477490938 6.998330874 $H$159 ERF 2 19 1.597971327 2.477490937 1.597971327 $H$160 ERF 0 0 0.418205372 0.018687832 1E+30 $H$161 ERF 7 20 7.351241424 2.477490938 7.351241424 $H$162 ERF 2 15 1.787167055 2.477490938 1.787167055 $H$163 ERF 3 16 3.150714045 2.477490938 3.150714045 $H$164 ERF 2 17 2.306659029 2.477490938 2.306659029 $H$165 ERF 1 16 1.223720518 2.477490937 1.223720518 $H$166 ERF 5 23 5.023879159 2.477490938 5.023879159 $H$167 ERF 7 18 7.478645955 2.477490938 7.478645955 $H$168 ERF 6 9 6.180393786 2.477490938 6.180393786 $H$169 ERF 5 12 5.297161877 2.477490938 5.297161877 $H$170 ERF 10 16 9.937553398 2.477490938 9.937553398 $H$171 ERF 3 20 3.436418706 2.477490938 3.436418706 $H$172 ERF 7 15 6.676315922 2.477490938 6.676315922 $H$173 ERF 3 19 2.675176634 2.477490938 2.675176634 $H$174 ERF 1 25 1.291881942 2.477490939 1.291881942 $H$175 ERF 13 18 12.86371696 2.477490938 12.86371696 $H$176 ERF 7 22 7.030182006 2.477490938 7.030182006 $H$177 ERF 9 21 8.891243689 2.477490938 8.891243689 $H$178 ERF 6 24 6.435521359 2.477490938 6.435521359 $H$179 ERF 5 19 5.148417087 2.477490938 5.148417087 $H$180 ERF 17 21 16.85370835 2.477490938 16.85370835 $H$181 ERF 5 17 4.643895146 2.477490938 4.643895146 $H$182 ERF 11 20 10.99724058 2.477490938 10.99724058 $H$183 ERF 3 25 3.193394563 2.477490938 3.193394563 $H$184 ERF 3 26 3.1325589 2.477490938 3.1325589 $H$185 ERF 15 23 14.78211068 2.477490938 14.78211068 $H$186 ERF 3 21 2.77741877 2.477490937 2.77741877 $H$187 ERF 9 19 9.283968155 2.477490938 9.283968155 $H$188 ERF 1 22 0.933238188 2.477490938 0.933238188 $H$189 ERF 1 19 1.170529126 2.477490938 1.170529126
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Table A 5: Continued Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $H$191 ERF 10 22 9.867480906 2.477490938 9.867480906 $H$193 ERF 4 8 3.950814498 2.477490938 3.950814498 $H$192 ERF 12 16 12.49838447 2.477490938 12.49838447 $H$194 ERF 15 15 14.80822861 2.477490938 14.80822861 $H$195 ERF 0 0 0 0 1E+30 $H$196 ERF 18 23 17.50251592 2.477490938 17.50251592 $H$197 ERF 3 25 2.748115728 2.477490938 2.748115728 $H$198 ERF 5 24 4.823535534 2.477490938 4.823535534 $H$199 ERF 9 17 9.274731327 2.477490938 9.274731327 $H$200 ERF 2 18 1.759775081 2.477490938 1.759775081 $E$201 ai=704 4 0 1613 1E+30 1609 $F$201 b2=704 702 0 704.4237911 1E+30 2.477490938
[72]
LIMITS REPORT TABLE, DOMPOASE
Table A 6: Final cost as displayed by EXCEL transportation solution Target Name Cost Total Cost[¢] 11852.92
Table A 7: Values from EXCEL transportation solution showing upper limits Adjustable Value Lower Target Result Upper Target Name Limit Limit ai=704 0 0 11853 1609 30678 b2=704 40 40 11853 42 11903 ai=704 0 0 11853 1609 32448 b2=704 8 8 11853 11 11907 ai=704 0 0 11853 1609 25851 b2=704 2 2 11853 4 11890 ai=704 0 0 11853 1609 30678 b2=704 5 5 11853 8 11902 ai=704 0 0 11853 1609 29391 b2=704 12 12 11853 14 11899 ai=704 0 0 11853 1609 32785 b2=704 8 8 11853 11 11908 ai=704 0 0 11853 1609 30792 b2=704 3 3 11853 5 11903 ai=704 0 0 11853 1609 33284 b2=704 2 2 11853 5 11909 ai=704 0 0 11853 1609 26223 b2=704 12 12 11853 15 11891 ai=704 0 0 11853 1609 20658 b2=704 2 2 11853 5 11876 ai=704 0 0 11853 1609 20824 b2=704 56 56 11853 58 11877 ai=704 0 0 11853 1609 27884 b2=704 7 7 11853 10 11895 ai=704 0 0 11853 1609 33450 b2=704 6 6 11853 9 11910 ai=704 0 0 11853 1609 33450 b2=704 2 2 11853 4 11910 ai=704 0 0 11853 1609 25143 b2=704 6 6 11853 8 11888 ai=704 0 0 11853 1609 24520 b2=704 25 25 11853 27 11886
[73]
Table A 7: Continued Adjustable Lower Upper Name Value Limit Target Result Limit Target ai=704 0 0 11853 1609 25974 b2=704 4 4 11853 7 11890 ai=704 0 0 11853 1609 28134 b2=704 3 3 11853 5 11896 ai=704 0 0 11853 1609 33450 b2=704 5 5 11853 8 11910 ai=704 0 0 11853 1609 24479 b2=704 4 4 11853 6 11886 ai=704 0 0 11853 1609 24313 ai=704 0 0 11853 1609 15508 b2=704 1 1 11853 4 11863 ai=704 0 0 11853 1609 25974 b2=704 1 1 11853 3 11890 ai=704 0 0 11853 1609 26805 b2=704 1 1 11853 4 11892 ai=704 0 0 11853 1609 28466 b2=704 1 1 11853 4 11897 ai=704 0 0 11853 1609 26140 b2=704 18 18 11853 21 11891 ai=704 0 0 11853 1609 32370 b2=704 13 13 11853 16 11907 ai=704 0 0 11853 1609 32619 b2=704 1 1 11853 3 11908 ai=704 1 1 11853 1610 28134 b2=704 0 0 11853 3 11896 ai=704 0 0 11853 1609 28189 b2=704 13 13 11853 15 11896 ai=704 0 0 11853 1609 35111 b2=704 2 2 11853 4 11914 ai=704 0 0 11853 1609 22485 b2=704 21 21 11853 23 11881 ai=704 0 0 11853 1609 31955 b2=704 8 8 11853 11 11906 ai=704 0 0 11853 1609 19619 b2=704 14 14 11853 16 11873 ai=704 0 0 11853 1609 25309 b2=704 15 15 11853 18 11888 ai=704 0 0 11853 1609 26211 b2=704 18 18 11853 20 11891 ai=704 0 0 11853 1609 22485 b2=704 1 1 11853 3 11881 ai=704 0 0 11853 1609 27469 b2=704 2 2 11853 5 11894 ai=704 0 0 11853 1609 24977
[74]
Table A 7: Continued Adjustable Value Lower Target Result Upper Target Name Limit Limit b2=704 8 8 11853 10 11888 ai=704 0 0 11853 1609 26389 b2=704 22 22 11853 25 11891 ai=704 0 0 11853 1609 31788 b2=704 2 2 11853 4 11906 ai=704 0 0 11853 1609 31224 b2=704 11 11 11853 14 11904 ai=704 0 0 11853 1609 32287 b2=704 2 2 11853 5 11907 ai=704 0 0 11853 1609 28134 b2=704 4 4 11853 7 11896 ai=704 0 0 11853 1609 24313 b2=704 3 3 11853 5 11886 ai=704 0 0 11853 1609 26140 b2=704 12 12 11853 15 11891 ai=704 0 0 11853 1609 22485 b2=704 4 4 11853 6 11881 ai=704 0 0 11853 1609 26140 b2=704 1 1 11853 4 11891 ai=704 0 0 11853 1609 25143 b2=704 5 5 11853 7 11888 ai=704 1 1 11853 1610 18498 b2=704 0 0 11853 2 11870 ai=704 0 0 11853 1609 24977 b2=704 7 7 11853 9 11888 ai=704 0 0 11853 1609 29795 b2=704 2 2 11853 4 11900 ai=704 1 1 11853 1610 25476 b2=704 0 0 11853 2 11889 ai=704 0 0 11853 1609 30210 b2=704 7 7 11853 10 11901 ai=704 0 0 11853 1609 25974 b2=704 2 2 11853 4 11890 ai=704 0 0 11853 1609 27137 b2=704 3 3 11853 6 11893 ai=704 0 0 11853 1609 27635 b2=704 2 2 11853 5 11895 ai=704 0 0 11853 1609 26805 b2=704 1 1 11853 4 11892 ai=704 0 0 11853 1609 33117 b2=704 5 5 11853 8 11909 ai=704 0 0 11853 1609 28549
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Table A 7: Continued Adjustable Value Lower Target Result Upper Target Name Limit Limit b2=704 7 7 11853 10 11897 ai=704 0 0 11853 1609 19952 b2=704 6 6 11853 9 11874 ai=704 0 0 11853 1609 22817 b2=704 5 5 11853 8 11882 ai=704 0 0 11853 1609 26805 b2=704 10 10 11853 12 11892 ai=704 0 0 11853 1609 30459 ai=704 0 0 11853 1609 26362 b2=704 7 7 11853 9 11891 ai=704 0 0 11853 1609 30127 b2=704 3 3 11853 5 11901 ai=704 0 0 11853 1609 35277 b2=704 1 1 11853 4 11915 ai=704 0 0 11853 1609 29164 b2=704 13 13 11853 15 11899 ai=704 0 0 11853 1609 32287 b2=704 7 7 11853 10 11907 ai=704 0 0 11853 1609 31788 b2=704 9 9 11853 11 11906 ai=704 0 0 11853 1609 34114 b2=704 6 6 11853 9 11912 ai=704 0 0 11853 1609 29296 b2=704 5 5 11853 8 11899 ai=704 0 0 11853 1609 31124 b2=704 17 17 11853 19 11904 ai=704 0 0 11853 1609 28134 b2=704 5 5 11853 7 11896 ai=704 0 0 11853 1609 30792 b2=704 11 11 11853 13 11903 ai=704 0 0 11853 1609 35609 b2=704 3 3 11853 6 11916 ai=704 0 0 11853 1609 36440 b2=704 3 3 11853 6 11918 ai=704 0 0 11853 1609 33117 b2=704 15 15 11853 17 11909 ai=704 0 0 11853 1609 31456 b2=704 3 3 11853 5 11905 ai=704 0 0 11853 1609 30127 b2=704 9 9 11853 12 11901 ai=704 0 0 11853 1609 32453 b2=704 1 1 11853 3 11907
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Table A 7: Continued Adjustable Value Lower Target Result Upper Target Name Limit Limit ai=704 0 0 11853 1609 30127 b2=704 1 1 11853 4 11901 ai=704 0 0 11853 1609 25708 b2=704 26 26 11853 29 11889 ai=704 0 0 11853 1609 32411 b2=704 10 10 11853 12 11907 ai=704 0 0 11853 1609 26417 b2=704 12 12 11853 15 11891 b2=704 4 4 11853 6 11872 ai=704 0 0 11853 1609 25642 b2=704 15 15 11853 17 11889 ai=704 1 1 11853 1610 28466 b2=704 0 0 11853 2 11897 ai=704 0 0 11853 1609 33782 b2=704 18 18 11853 20 11911 ai=704 0 0 11853 1609 35111 b2=704 3 3 11853 5 11914 ai=704 0 0 11853 1609 34280 b2=704 5 5 11853 7 11912 ai=704 0 0 11853 1609 27801 b2=704 9 9 11853 12 11895 ai=704 0 0 11853 1609 28964 b2=704 2 2 11853 4 11898
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APPENDIX II
Answer report as displayed by the Excel Solver for Bohyen Landfill site is as shown in the tables below.
ANSWER REPORT, BOHYEN
Table B 1: Real cost of transporting waste in parts of the metropolis to the Bohyen Landfill site Trivial Cost Real Cost Total Cost[GH¢] 7178.06 7178.06
Table B 2: Values from EXCEL transportation solution Cell Name Original Value Final Value $E$54 b1=421 0 0 $F$54 ai=184 0 0 $E$55 b1=421 0 0 $F$55 ai=184 2 2 $E$56 b1=421 0 0 $F$56 ai=184 2 2 $E$57 b1=421 0 0 $F$57 ai=184 7 7 $E$58 b1=421 0 0 $F$58 ai=184 11 11 $E$59 b1=421 0 0 $F$59 ai=184 8 8 $E$60 b1=421 0 0 $F$60 ai=184 3 3 $E$61 b1=421 0 0 $F$61 ai=184 4 4 $E$62 b1=421 0 0 $F$62 ai=184 2 2 $E$63 b1=421 0 0 $F$63 ai=184 1 1 $E$64 b1=421 0 0 $F$64 ai=184 2 2 $E$65 b1=421 0 0 $F$65 ai=184 2 2 $E$66 b1=421 0 0
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Table B 2: Continued Cell Name Original Value Final Value $F$66 ai=184 1 1 $E$67 b1=421 0 0 $F$67 ai=184 1 1 $E$68 b1=421 0 0 $F$68 ai=184 1 1 $E$69 b1=421 0 1 $F$69 ai=184 0 0 $E$70 b1=421 0 0 $F$70 ai=184 2 2 $E$71 b1=421 0 0 $F$71 ai=184 1 1 $E$72 b1=421 0 0 $F$72 ai=184 2 2 $E$73 b1=421 0 0 $F$73 ai=184 16 16 $E$74 b1=421 0 0 $F$74 ai=184 1 1 $E$75 b1=421 0 0 $F$75 ai=184 2 2 $E$76 b1=421 0 0 $F$76 ai=184 1 1 $E$77 b1=421 0 0 $F$77 ai=184 1 1 $E$78 b1=421 0 0 $F$78 ai=184 1 1 $E$79 b1=421 0 0 $F$79 ai=184 1 1 $E$80 b1=421 0 0 $F$80 ai=184 14 14 $E$81 b1=421 0 0 $F$81 ai=184 2 2 $E$82 b1=421 0 0 $F$82 ai=184 2 2 $E$83 b1=421 0 0 $F$83 ai=184 14 14 $E$84 b1=421 0 0 $F$84 ai=184 2 2 $E$85 b1=421 0 0 $F$85 ai=184 1 1 $E$86 b1=421 0 0 $F$86 ai=184 2 2 $E$87 b1=421 0 0 $F$87 ai=184 9 9 [79]
Table B 2: Continued Cell Name Original Value Final Value $E$88 b1=421 0 0 $F$88 ai=184 3 3 $E$89 b1=421 0 0 $F$89 ai=184 7 7 $E$90 b1=421 0 0 $F$90 ai=184 5 5 $E$91 b1=421 0 0 $F$91 ai=184 19 19 $E$92 b1=421 0 0 $F$92 ai=184 9 9 $E$93 b1=421 0 0 $F$93 ai=184 20 20
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CONSTRAINTS TABLE, BOHYEN
Table B 3: Values from EXCEL transportation solution showing constraints and slack Name Cell Value Status Slack ERF 2 B.N 4 Binding 0 ERF 4 B.N 4 Binding 0 ERF Aboabo 15 Binding 0 ERF Abrepo 25 Binding 0 ERF Abuakwa 19 Binding 0 ERF Aburaeso 6 Binding 0 ERF Adoato Adumanu 10 Binding 0 ERF Aduman 5 Binding 0 ERF Agric Care 1 Binding 0 ERF Ahodwo 5 Binding 0 ERF Akem 5 Binding 0 ERF Akurem 2 Binding 0 ERF Ampabame 3 Binding 0 ERF Aprabon 3 Binding 0 ERF Ash-Foam 1 Binding 0 ERF Atafoa 3 Binding 0 ERF Atwima Takyeman 2 Binding 0 ERF Ayarewa 5 Binding 0 ERF Bantama 36 Binding 0 ERF Bebre 2 Binding 0 ERF Bohyen 4 Binding 0 ERF C.P.C 1 Binding 0 ERF Edwenase 2 Binding 0 ERF Kejetia 2 Binding 0 ERF Kronom 3 Binding 0 ERF Kwaadaso 32 Binding 0 ERF Kwapra 4 Binding 0 ERF Kwantwima 5 Binding 0 ERF Tafo 32 Binding 0 ERF Mpatasie 5 Binding 0 ERF Moshie Zongo 3 Binding 0 ERF N.Suntreso 5 Binding 0 ERF Nzema 22 Binding 0 ERF Ohwim 7 Binding 0 ERF S. Suntreso 15 Binding 0 ERF Asuoyeboah 11 Binding 0 ERF Suame 43 Binding 0 ERF Tanoso 21 Binding 0 ERF Yennyawoso 47 Binding 0 Skip Using ERF 1263.126654 Not Binding 2048.873 ERF Using ERF 0 Not Binding 5603.472
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SENSITIVITY REPORT TABLE, BOHYEN
Table B 4: Values from EXCEL transportation solution for sensitivity analysis
Cell Name Final Value Reduced Gradient $E$54 b1=421 0 0 $F$54 ai=184 0 0 $E$55 b1=421 0 0 $F$55 ai=184 2 0 $E$56 b1=421 0 0 $F$56 ai=184 2 0 $E$57 b1=421 0 0 $F$57 ai=184 7 0 $E$58 b1=421 0 0 $F$58 ai=184 11 0 $E$59 b1=421 0 0 $F$59 ai=184 8 0 $E$60 b1=421 0 0 $F$60 ai=184 3 0 $E$61 b1=421 0 0 $F$61 ai=184 4 0 $E$62 b1=421 0 0 $F$62 ai=184 2 0 $E$63 b1=421 0 0 $F$63 ai=184 1 0 $E$64 b1=421 0 0 $F$64 ai=184 2 0 $E$65 b1=421 0 0 $F$65 ai=184 2 0 $E$66 b1=421 0 0 $F$66 ai=184 1 0 $E$67 b1=421 0 0 $F$67 ai=184 1 0 $E$68 b1=421 0 0 $F$68 ai=184 1 0 $E$69 b1=421 1 0 $F$69 ai=184 0 0 $E$70 b1=421 0 0 $F$70 ai=184 2 0 $E$71 b1=421 0 0 $F$71 ai=184 1 0 $E$72 b1=421 0 0 $F$72 ai=184 2 0
$E$73 b1=421 0 0
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Table B 4: Continued Cell Name Final Value Reduced Gradient $E$74 b1=421 0 0 $F$74 ai=184 1 0 $E$75 b1=421 0 0 $F$75 ai=184 2 0 $E$76 b1=421 0 0 $F$76 ai=184 1 0 $E$77 b1=421 0 0 $F$77 ai=184 1 0 $E$78 b1=421 0 0 $F$78 ai=184 1 0 $E$79 b1=421 0 0 $F$79 ai=184 1 0 $E$80 b1=421 0 0 $F$80 ai=184 14 0 $E$81 b1=421 0 0 $F$81 ai=184 2 0 $E$82 b1=421 0 0 $F$82 ai=184 2 0 $E$83 b1=421 0 0 $F$83 ai=184 14 0 $E$84 b1=421 0 0 $F$84 ai=184 2 0 $E$85 b1=421 0 0 $F$85 ai=184 1 0 $E$86 b1=421 0 0 $F$86 ai=184 2 0 $E$87 b1=421 0 0 $F$87 ai=184 9 0 $E$88 b1=421 0 0 $F$88 ai=184 3 0 $E$89 b1=421 0 0 $F$89 ai=184 7 0 $E$90 b1=421 0 0 $F$90 ai=184 5 0 $E$91 b1=421 0 0 $F$91 ai=184 19 0 $E$92 b1=421 0 0 $F$92 ai=184 9 0 $E$93 b1=421 0 0 $F$93 ai=184 20 0
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SENSITIVITY, CONSTRAINT REPORT TABLE, BOHYEN
Table B 5: Values from EXCEL transportation solution showing sensitivity output constraint Shadow Constraint Allowable Allowable Cell Name Final value Price R.H Side Increase Decrease $E$32 4 B.N 11.77322 8.26 11.77322 2048.873 11.77322 $F$32 Aboabo 46.4105 11.25425 46.4105 2048.873 46.4105 $G$32 Abrepo 75.97587 5.5755 75.97587 2048.873 75.97587 $H$32 Abuakwa 57.61288 13.4225 57.61288 2048.873 57.61288 $I$32 Aburaeso 18.67574 11.564 18.67574 2048.873 18.67574 $J$32 Adoato Adumanu 28.62054 11.7705 28.62054 2048.873 28.62054 $K$32 Aduman 14.91391 14.2485 14.91391 2048.873 14.91391 $L$32 Agric Care 4.306422 12.39 4.306422 2048.873 4.306422 $M$32 Ahodwo 14.34089 8.673 14.34089 2048.873 14.34089 $N$32 Akem 14.08062 6.71125 14.08062 2048.873 14.08062 $O$32 Akurem 6.69256 6.195 6.69256 2048.873 6.69256 $P$32 Ampabame 8.090124 4.85275 8.090124 2048.873 8.090124 $Q$32 Aprabon 8.206041 13.8355 8.206041 2048.873 8.206041 $R$32 Ash-Foam 2.208982 9.2925 2.208982 2048.873 2.208982 $S$32 Atafoa 10.46095 10.325 10.46095 2048.873 10.46095 $T$32 Atwima Takyeman 7.162789 13.8355 7.162789 2048.873 7.162789 $U$32 Ayarewa 14.80456 13.4225 14.80456 2048.873 14.80456 $V$32 Bantama 107.654 8.26 107.654 2048.873 107.654 $W$32 Bebre 5.058788 9.60225 5.058788 2048.873 5.058788 $X$32 Bohyen 12.80772 4.13 12.80772 2048.873 12.80772 $Y$32 C.P.C 3.998039 8.26 3.998039 2048.873 3.998039 $Z$32 Edwenase 7.15404 12.803 7.15404 2048.873 7.15404 $AA$32 Kejetia 6.8216 9.80875 6.8216 2048.873 6.8216 $AB$32 Kronom 9.507372 13.216 9.507372 2048.873 9.507372 $AC$32 Kwaadaso 97.46642 12.39 97.46642 2048.873 97.46642 $AD$32 Kwapra 11.55232 11.3575 11.55232 2048.873 11.55232 $AE$32 Kwantwima 13.74599 10.325 13.74599 2048.873 13.74599 $AF$32 Tafo 96.96776 13.629 96.96776 2048.873 96.96776 $AG$32 Mpatasie 14.63833 5.67875 14.63833 2048.873 14.63833 $AH$32 Moshie Zongo 7.733625 13.4225 7.733625 2048.873 7.733625 $AI$32 N.Suntreso 16.44489 10.325 16.44489 2048.873 16.44489 $AJ$32 Nzema 64.8391 11.151 64.8391 2048.873 64.8391 $AK$32 Ohwim 20.89785 5.5755 20.89785 2048.873 20.89785 $AL$32 S. Suntreso 45.34756 9.086 45.34756 2048.873 45.34756 $AM$32 Asuoyeboah 31.60376 10.84125 31.60376 2048.873 31.60376 $AN$32 Suame 127.8235 7.6405 127.8235 2048.873 127.8235 $AO$32 Tanoso 63.91395 10.5315 63.91395 2048.873 63.91395 $AP$32 Yennyawoso 139.9401 7.2275 139.9401 2048.873 139.9401
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LIMITS REPORT TABLE, BOHYEN
Table B 6: Values cost limits for using ERF trucks Target Name Value Total Cost[¢] Using ERF 7178.06
Table B 7: Values from EXCEL transportation solution showing upper limits
Cell Adjustable Name Value Lower Limit Target Result Upper Limit Target Result $E$54 b1=421 0 #N/A #N/A #N/A #N/A $F$54 ai=184 0 #N/A #N/A #N/A #N/A $E$55 b1=421 0 #N/A #N/A 420 7178.058 $F$55 ai=184 2 #N/A #N/A 2 7178 $E$56 b1=421 0 #N/A #N/A 420 7178.058 $F$56 ai=184 2 #N/A #N/A 2 7178 $E$57 b1=421 0 #N/A #N/A 420 7178.058 $F$57 ai=184 7 #N/A #N/A 7 7178 $E$58 b1=421 0 #N/A #N/A 420 7178.058 $F$58 ai=184 11 #N/A #N/A 11 7178 $E$59 b1=421 0 #N/A #N/A 420 7178.058 $F$59 ai=184 8 #N/A #N/A 8 7178 $E$60 b1=421 0 #N/A #N/A 420 7178.058 $F$60 ai=184 3 #N/A #N/A 3 7178 $E$61 b1=421 0 #N/A #N/A 420 7178.058 $F$61 ai=184 4 #N/A #N/A 4 7178 $E$62 b1=421 0 #N/A #N/A 420 7178.058 $F$62 ai=184 2 #N/A #N/A 2 7178 $E$63 b1=421 0 #N/A #N/A 420 7178.058 $F$63 ai=184 1 #N/A #N/A 1 7178 $E$64 b1=421 0 #N/A #N/A 420 7178.058 $F$64 ai=184 2 #N/A #N/A 2 7178
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Table B 7: Continued Cell Adjustable Name Value Lower Limit Target Result Upper Limit Target Result $E$66 b1=421 0 #N/A #N/A 420 7178.058 $F$66 ai=184 1 #N/A #N/A 1 7178 $E$67 b1=421 0 #N/A #N/A 420 7178.058 $F$67 ai=184 1 #N/A #N/A 1 7178 $E$68 b1=421 0 #N/A #N/A 420 7178.058 $F$68 ai=184 1 #N/A #N/A 1 7178 $E$69 b1=421 1 1 7178.058 421 7178.058 $F$69 ai=184 0 #N/A #N/A 0 7178 $E$70 b1=421 0 #N/A #N/A 420 7178.058 $F$70 ai=184 2 #N/A #N/A 2 7178 $E$71 b1=421 0 #N/A #N/A 420 7178.058 $F$71 ai=184 1 #N/A #N/A 1 7178 $E$72 b1=421 0 #N/A #N/A 420 7178.058 $F$72 ai=184 2 #N/A #N/A 2 7178 $E$73 b1=421 0 #N/A #N/A 420 7178.058 $F$73 ai=184 16 #N/A #N/A 16 7178 $E$74 b1=421 0 #N/A #N/A 420 7178.058 $F$74 ai=184 1 #N/A #N/A 1 7178 $E$75 b1=421 0 #N/A #N/A 420 7178.058 $F$75 ai=184 2 #N/A #N/A 2 7178 $E$76 b1=421 0 #N/A #N/A 420 7178.058 $F$76 ai=184 1 #N/A #N/A 1 7178 $E$77 b1=421 0 #N/A #N/A 420 7178.058 $F$77 ai=184 1 #N/A #N/A 1 7178 $E$78 b1=421 0 #N/A #N/A 420 7178.058 $F$78 ai=184 1 #N/A #N/A 1 7178 $E$79 b1=421 0 #N/A #N/A 420 7178.058 $F$79 ai=184 1 #N/A #N/A 1 7178 $E$80 b1=421 0 #N/A #N/A 420 7178.058 $F$80 ai=184 14 #N/A #N/A 14 7178 $E$81 b1=421 0 #N/A #N/A 420 7178.058 $F$81 ai=184 2 #N/A #N/A 2 7178 $E$82 b1=421 0 #N/A #N/A 420 7178.058 $F$82 ai=184 2 #N/A #N/A 2 7178 $E$83 b1=421 0 #N/A #N/A 420 7178.058 $F$83 ai=184 14 #N/A #N/A 14 7178 $E$84 b1=421 0 #N/A #N/A 420 7178.058 $F$84 ai=184 2 #N/A #N/A 2 7178 $E$85 b1=421 0 #N/A #N/A 420 7178.058 $F$85 ai=184 1 #N/A #N/A 1 7178 $E$86 b1=421 0 #N/A #N/A 420 7178.058 $F$86 ai=184 2 #N/A #N/A 2 7178
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Table B 7: Continued Adjustable Target Cell Name Value Lower Limit Result Upper Limit Target Result $E$87 b1=421 0 #N/A #N/A 420 7178.06 $F$87 ai=184 9 #N/A #N/A 9 7178 $E$88 b1=421 0 #N/A #N/A 420 7178.06 $F$88 ai=184 3 #N/A #N/A 3 7178 $E$89 b1=421 0 #N/A #N/A 420 7178.06 $F$89 ai=184 7 #N/A #N/A 7 7178 $E$90 b1=421 0 #N/A #N/A 420 7178.06 $F$90 ai=184 5 #N/A #N/A 5 7178 $E$91 b1=421 0 #N/A #N/A 420 7178.06 $F$91 ai=184 19 #N/A #N/A 19 7178 $E$92 b1=421 0 #N/A #N/A 420 7178.06 $F$92 ai=184 9 #N/A #N/A 9 7178 $E$93 b1=421 0 #N/A #N/A 420 7178.06 $F$93 ai=184 20 #N/A #N/A 20 7178
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