LECTURES
IN
OPERATIONS PLANNING AND CONTROL
Prepared by:
MARLUNA LIM URUBIO, Ph. D Introduction to Operations Planning and Control
Production = Factories / Machines / Assembly
From
Production Management Manufacturing management which involves methods/techniques in factory operation.
Whereas,
Operations Responsible for Management management of production systems either for creation of goods or providing services.
Ex. For service oriented company, it involves managing food service, providing medical services, housekeeping etc.
Ex. Managing a factory that involves decisions on raw materials, equipment, etc.
Functions within Business Organizations
Operations
Finance Marketing Functions overlap and they do not exist independently, but they interact to achieve the goals and objective of the organization.
Marketing - includes promotion/selling of goods ( demand = supply )
Finance - ensuring funds are available for production requirement as well as product/ service promotions.
- includes budgeting, analysis of investment proposal, sales, allocation of funds.
Operation/Production - production of goods, services - it consists of all activities that are directly related to producing goods or providing service.
Industrial Engineering
Purchasing Maintenanc e
Operations
Public Accounting Relations
Personnel Accounting – provides data for cost of labor, materials, overhead, scraps, downtime, inventory
Purchasing – procurement of raw materials
Personnel –recruitment, training of personnel, labor relations, health, safety
Public Relations – building/maintaining image of the organization (sports fest/cultural events/tours of facilities, etc.)
Industrial Engineering – productivity/ quality improvement
Maintenance – general maintenance and repair of equipment and facilities
Operations Management Function
Main: guide the system thru decision making, especially day today operating decisions
1. Designing and operating production systems
System design – decisions on system capacity, location of facilities, arrangement of department, acquisition of equipment . usually involves decision that are for long-term use
System Operation- decision on management of personnel, inventory planning and control, scheduling, project management, quality control
Note: System design essentially determines many of the parameters of system operation. PRODUCTIVITY
Productivity - is one of the primary concern and responsibility of a manager, that is to achieve productive use of the organization’s resource.
- is an index that measures output ( goods or service ) relative to the input ( labor, materials, energy and other resources ).
PRODUCTIVITY = OUTPUT
INPUT
Productivity growth is the increase in productivity from 1 period to the next relative to the productivity in the preceding period.
Productivity Growth = Current Period Prod – Previous period Prod Previous Period Prod
Multifactor Productivity = Quality of production at standard price labor cost+ material cost + overhead
Classsifying Production Systems
1. Mass Production –there is large volume of standardized products/goods, produced by low skilled or semi skilled workers, using highly specialized and expensive equipment. 2. Lean production - uses minimal amount of resource to produce high volume of high quality goods with some variety.
3. Craft Production - uses highly skilled workers using simple, flexible tools to produce small quantities of customized goods
Efficiency - getting the most out of a fixed set of resources
PRODUCTIVITY Profitability - efficiency if a Increase in output per company or industry generates work hour or time earnings. expended
Profitability is expressed in terms of Labor productivity several popular number that measure measures output per hour one of two generic types of of labor performance - “ HOW MUCH THEY MAKE Multifactor productivity WITH WHAT THEY’VE GOT? “ measures output per unit and of combined input which “ HOW MUCH THEY MAKE consist of labor and capital FROM WHAT THEY TAKE IN? “ and in some cases, intermediate outputs
TO ATTAIN PRODUCTIVITY, INDUSTRIAL ENGINEERS MUST
Maximize Profit THROUGH EFFECTIVE and EFFICIENT MEANS Integration of MAN MACHINE MATERIALS METHODS
SAMPLE PROBLEM:
Given : output produced - 1,000 pcs Labor hours - 250 hrs
Solution : Productivity = units produced/ labor hours = 1,000 pcs / 250 hours = 4 pcs / hour
Multifactor Productivity = output / labor + materials + Energy + Capital + Misc.
Sample Problem:
Collins Title Company has a staff of 4 each working 8 hours per day for a payroll cost of USD 640/day and overhead expenses of USD 400/day. The company recently purchased a computerized title search system that will allow processing of 14 titles/day. Although the staff, their work hours and pay will be the same, the overhead expenses are now USD 800/day.
Given: Output : 8 titles / day Labor cost : USD 640/day Overhead : USD 400/day No. of Staff : 4 Available hours : 8 hours New output : 14 titles/day New Overhead Cost : USD 800/day
Solution:
Labor Productivity ( old system ) = 8 titles/ 4 8 = 0.125 titles/labor-hr
Labor Productivity ( new system ) = 14 titles/ 4 8 = 0.4375 titles/labor-hr
Multifactor Productivity ( old system ) = 8 titles/ USD 640 + USD 400 = 0.0077 titles / dollar
Multifactor Productivity ( new system ) = 14 titles/ USD 640 + USD 800 = 0.0097 titles / dollar Productivity Measures are useful to the following:
1. To track performance over time 2. To determine what has changed and then devise means of improving productivity in the subsequent periods. 3. To judge the performance of an entire industry or the productivity of a country as a whole.
Factors that Affect Productivity:
1. Methods ( Simple? Complicated ? ) Example: Bombing of IC in Helium Gas or FC 84
2. Capital Example: From manual packing to automated packing but requires capital investment for auto packer 3. Quality Example: will it be 100% inspection which is time consuming or just random sampling?
4. Technology Example: Embroidery which used to be manual can now be programmed
5. Management Example: A supportive management will boost morale of employees
6. Raw Materials Example: Will production be able to work if RM do not come on time?
7. Equipment Example: What will be the output if the machines are too old and experience downtime?
8. Working Condition/Environment Example: Will one produce more if the work area is too hot?
SAMPLE PROBLEMS FOR PRODUCTIVITY
A company that processes fruits and vegetables is able to produce 400 cases of canned peaches in one half hour with four workers. What is the labor productivity?
Solution :
Labor productivity = Quality Produced / Labors Hours
=400 cases (4 workers x 1/2 hours / workers)
=200 cases per labor hour A wrapping paper company produced 2,000 rolls of paper one day. Standard price is $ 1/roll. Labor cost was $ 160, material cost was $ 50, and overhead was $ 320. Determine the multifactor productivity.
Multifactor productivity = Quality produced at standard price/Labor cost + Material cost + Overhead
= 2,000 rolls x $ 1/ $160+ $ 50 + $320
= 3.77 rolls output per dollars
Sample Problem A. Find the productivity if four workers installed 720 square yards of carpeting in eight hours. B. Compute for the productivity of a machine which produced 68 usable pieces in two hours.
Solution: A) Productivity = yards of carpeting install Labors Hours worked
= 720 square yard 4 workers x8 hours / worker
= 720 yards 32 Hours
=22.5 yards/ hours
B) Productivity = Usable Pieces Production Time
= 68 Pieces 2 hours
= 34 pieces/ hours Sample Problem
Determine the multifactor productivity for the combined input of the labor and the machine time using the following data:
Input:
Labor: $ 1,000 Materials: $ 520 Overheads: $ 2,000
Solution:
Multifactor Productivity = Output / Labor + Materials + Overheads
= 1,760 Units / $ 1,000 + $ 520 + $ 2,000
= 0.50 units Sample Problem
Collins Little Company has a stuff of 4, each working 8 hours per day (for a payroll cost of $ 640 / day) and overhead expenses of $ 400 / day. Collins processes and closes on 8 titles each day. The company recently purchased a computerized title search system that will allow the processing of 14 titles per day. Although the staff, their works hours, and pay will be same, the overheads expenses are now $ 800 per day.
Solution:
Labor productivity with the old system:
= 8 titles per day/ 32 labor hours = 0.25 titles per hour
Labor productivity with the new system: =14 titles per day/ 32 labor hours = 0.44 title per labor hours
Multifactor productivity with the old system:
=8 titles per day / 640 + 400 = 0.0077 titles per dollars
Multifactor productivity with the new system:
=14 titles per day / 640 + 800 = 0.0097 titles per dollars
Sample Problem
At Modem Lumber, Inc., Art Binley, a president and a producer of an apple crates sold to growers, has been able, with his current equipment, to produces 400 crates per 100 logs. He currently purchases 100 logs per day, and each logs required 3 labor hours to process. He believes that he can hire a professional buyer who can buy a better quality log at the same cost. If this is the case, he increases his production to 260 crates per 100 logs. His labor hours will increase by 8 hours per day. What will be the impact on productivity (measured in crates per labor –hour) if the buyers is hired?
Solution: a) Current labor productivity = 240 crates / 100 logs (3 hours pert log)
= 240/ 300
= 0.8 create per labor hour b) Labor productivity with buyer = 260 crates / 100 logs (3 hours per logs) + 8 hours
= 260 / 308
= 0.844 crates per labor hours
Sample Problem
Art Binley has decided to look at his productivity from a multi factor (total factor productivity) perspective (to solve problem n0.5). To do so, he has determined his labor, capital, energy, material usage and decided to use dollars as the common denominator. His total labor hours are now 300 per day and will increase to 308 per day. His capital and energy cost will remain constant at $350 and $150 per day, respectively. Material costs for the 100 logs per day are $1000 and will remain the same. Because he will pay an average of $10 per hour (with fringes), Binley determine his productivity increase as follows:
Solution:
Current System System with Professional Buyer
Labor: 300 hrs at $ 10 = $ 3,000 308 hrs at $ 10 = $ 3,080 Material: 100 logs/day 1,000 1,000 Capital: 350 350 Energy: 150 150
Total Cost: $ 4,500 $ 4,500 Productivity of current system: Productivity of proposed system:
=240 crate/ 4,500 = 0.0533 = 260 crates/ 4,580 = 0.0567
Sample Problem
Calculate the productivity for the following operations: a) Three employees processed 600 insurance policies last week. They 8 hours per day, 5 days per week.
b) A team of workers made 400 units of product, which is valued by its standard cost of $10 each (before markups for other expenses and profit). That accounting department reported that for this job the actual cost were $ 400 per labor, $1000 for materials and 4300 for overhead:
Solution: a) Labor productivity = Policies processed Employee, hours
= 600 policies 3 (40)
= 5 policies per hours b) Multifactor productivity = Quality at standard cost Labor + Materials + Overheads
= 400units ($10/units) $400 + $1000 + $ 3000
= $4000 $1700
=2.35
Sample Problem
Student tuition at Boering University is $ 100 per semester credit hours. The states supplement school revenue by matching student tuition, dollars per dollars. Average class size for typical three credit course is 50 students. Labor costs are $4000 per class, material costs are $20 per student, and overhead cost are $25,000 per class.
Find: a) What is the multifactor productivity ratio? b) If instructors work an average, what is the labor productivity ratio?
Solution: a) Value of Output = ( 50 student )x (3 credit hours) x ($ 100 tuition + $ 100 state support) class student credit hours
= $ 30,000 per class
Value of Output = Labor + Materials + Overheads
= $ 4000 + ($20 per student x 50 students) + $25,000 Class
= $ 30,000 per class Multifactor productivity = Output/ Input
= $ 30,000 / class $ 30,000/ class
= 1.00 b) Labor productivity is the ratio of the value of output to the labor hours. The value of output is the same as in part (a), or $ 30,000 per class, so
Labor hours of input = 14 hours x 16 week weeks weeks
= 224hours per class
Labor productivity = Output/ Input
= $ 30,000 per class 224 hours per class
= $ 133.93 per hours
Sample Problem
A division of Miller chemicals produces water purification crystals for swimming pools. The major inputs used in the production process are labor, raw materials, and energy. The spreadsheets in the figure shown that amount of output produced and input used for 1994 and 1995. By dividing the pounds of the crystals produced by each input individually, we obtain the [partial productivity measured shown in a columns D through F. An example of multifactor productivity measure is output per non labor dollar.
For 1994 we have
= 100,000 $ 5,000 + $ 30,000
=2.86 lb/ non labor dollar
For 1995 we have
=150,00 $ 6,000 + $ 40,000
=3.261 lb/ non labor dollars
A B C D E F Miller 1 Chemicals 2 1994 1995 1994 1994 3 Outputs Pounds of 100,00 150,00 4 crystal 0 0 5 Productivity 6 Inputs measure 5 5.357 Direct labor Output direct 7 hours 20,000 28,000 labor hour 0.556 0.429 Direct labor $180,0 $350,0 Output direct 0.374 8 cost 00 00 labor dollar 0.286 5 Energy used 350,00 400,00 Output/kilowatt- 9 (kWh) 0 0 hour 20 25 Output/energy 0.833 10 Energy cost $5,000 $6,000 dollar 3 0.811 11 Raw material 120,00 185,00 Output/lb or raw 3.333 3.75 used (lb) 0 0 material Raw material $30,00 $40,00 Output/raw 12 cost 0 0 material dollar 13
For 1994:
Total productivity = 100,000 $ 180,000 + $ 5,000 = $ 30,000
=0.47 lb/ dollar
For 1995
Total productivity = 150,000 $ 350,000 + $ 6,000 + $ 40,000
=0.38 lb / dollar
DECISION PROCESS
Decision making can be done using the following :
1. Decision Tree 2. Forecasting 3. Capacity Planning
DECISION TREES
Decision Trees - schematic representation of the alternatives available to a decision maker and the possible consequences. This is composed of a number of nodes that have branches emanating from the stem. NOTE: Square nodes denote decision point and circular node denotes chance events. Decision trees are read from left to right.
Example of a Decision Tree
Left Right
Decision Point Chance Events 3 Basic Categories in Decision Making:
. Certainty It means that relevant parameters such as cost, capacity and demand have known values.
. Risk It means that certain parameters have probabilistic outcomes.
. Uncertainty It means that it is impossible to assess the likelihood of various possible future events. 4 Possible Decision Criteria Under Uncertainty:
1. Maximin - determines the worst possible pay off for each alternative and choosing the best among the worst.
2. Maximax - determines the best possible payoff and choose the best alternative from among the best.
3. Laplace - determines the average payoff for each alternative and choose the alternative with the best average.
Decision Making Under Risk
Expected monetary value criterion ( EMV ) - where the alternative with the highest expected value is selected.
Expected Value of Perfect Information ( EVPI )- difference between the expected payoff with perfect information and the expected payoff under risk.
FORECASTING
Forecast - statement about the future ( weather, demand, sales, etc )
Example: How much food should be prepared for the party? How many visitors will the venue accommodate? Will the person get the job?
Basis of Forecast:
1. Current factors or condition 2. Past experience in similar situation
Forecasting / Forecasts are basis for the following:
1. Capacity Planning 2. Budgeting 3. Sales Planning 4. Productions Inventory Planning 5. Manpower Planning 6. Purchasing Planning
Other uses of Forecasting:
1. Predict Profits 2. Revenues 3. Costs 4. Productivity Changes 5. Prices and availability of energy and raw materials 6. Interest Rater 7. Movement of key economic indications 8. Prices of stocks and bonds
Elements of Good Forecast:
1. Timely 2. Reliable 3. Accurate 4. Expressed in meaningful units Elements of Good Forecast:
5. Be in writing 6. Be simple and easy to understand Factors in Developing Useful Forecasts
1. Expertise 2. Judgment 3. Technical Expertise
6 Basic Steps in Forecasting:
1. Determine the purpose of the forecast 2. Establish time horizon 3. Select forecasting technique 4. Gather and analyze relevant data 5. Prepare the forecast 6. Monitor the forecast
Approaches to Forecasts
1. Judgmental Forecast - rely on analysis of subjective inputs obtained from sources like surveys, sales staff, marketing executive and panel of experts.
2. Historical Data/Time Series - attempts to project past experience into future. Assumption is that future will be like past.
3. Associative Model - uses equations that can be used to predict future demand. Example demand of paint might be related to variables such 3. Associative Models- use equations that can be used to predict future demand. Example demand of paint might be related to variables such as price/ gallon etc.
Approaches to Forecasting
1. Qualitative- consists of subjective inputs
2. Quantitative- Involves the use of historical data as basis Forecast Based on Judgment and Opinions 1. Executive Opinions
2. Sales force Opinions- sales staff or customer service opinion is believed to be a good source of information.
3. Consumer Surveys- the advantage is the ability to tap information that might be available. However, surveys can be expensive and time consuming.
4. Delphi Method- involves circulating a series of questionnaire among individuals who posses the knowledge and ability to contribute meaningfully. Responses are kept anonymous which tends to encourage honest responses.
Forecasts Based on Time Series Data
Time Series is a time ordered sequence of observation taken at regular intervals over a period of time.
Some Common Behaviors that Appear in Plotting Data
1. Trend- refers to a long term upward or downward movement. Example: population shifts, cultural changes
2. Seasonality-refers to short-term regular variations related to time. Example: restaurants and hotels are fully booked during Valentines Day while malls are peak during Christmas season.
3. Cycles- wavelike variations of more than 1 year duration. These are often related to a variety of economic and political conditions. 4. Irregular Variations- are due to unusual circumstances such as severe weather conditions, strikes, etc. These are not typical behavior.
5. Random Variations- are residual variations that remain after all other behavior have been accounted for.
Three Techniques for Averaging
1. Moving average 2. Weighted moving average 3. Exponential smoothing
Moving Average
Given: Period Demand( in pcs ) 1 42 2 40 3 43 4 40 5 41
To Find: Forecast for period 6 ( F6 ), using 3 period MA( moving average) Solution:
MA = F6 = 43+40+41 = 41.33 units ≈ 42 units 3
If F6 becomes actual demand:
F7 using MA = 40+41+42 = 41 units 3
Weighted Moving Average Given: Weights are as follows: 0.4, 0.3, 0.2, 0.1
Period Demand Weights 1 42 2 40 0.1 3 43 0.2 4 40 0.3 5 41 0.4 Find: Forecast for Period 6
Solution: F6 = 0.6(41)+0.3(40)+0.2(43)+0.1(40) = 41pcs
Exponential Smoothing CAPACITY PLANNING
Capacity planning refers to the upper limit or ceiling on the load that an operating unit can handle.
It enables manager to quantify production capability.
3 Basic Questions in Capacity Planning:
. What kind of capacity is needed? . How much is needed? . When is it needed?
Importance of Capacity Decision:
. capacity decisions have impact on the ability of the organization to meet future demands . it affects operating costs . it is a major determinant of initial cost . it affects competitiveness . it affects the ease of management
2 Useful Definitions of Capacity
. Design capacity - the maximum output that can possibly be attained. . Effective capacity - the maximum possible outputs given a product mix, scheduling difficulties, machine maintenance, quality factors, etc.
2 Measures of System Effectiveness:
. Efficiency is the rate of actual output to effective capacity.
. Utilization is the ratio of actual output to design capacity.
Efficiency = Actual Output
Effective capacity
Utilization = Actual Output
Design Capacity
Determinants of Effective Capacity:
1. Facilities 2. Product or Service 3. Processes- quality 4. Human Consideration - training 5. Operations - schedule 6. External Forces - product standards
Aggregate Planning It is an intermediate range capacity planning that covers a time horizon of 2 – 12 months.
3 Levels of Capacity Decisions in an Organization:
1. Long term - relate to product and service selection, facility size and location, equipment decision, lay out of facilities.
2. Intermediate term - relate to general level of employment, output and inventories.
3. Short term - consists scheduling of jobs, workers and equipment.
IMPORTANCE OF AGGREGATE PLANNING:
It helps synchronize flow throughout the supply chain, it affects costs, equipment, utilization, employment levels and customer satisfaction.
Demand Options in Aggregate Planning:
. Pricing . Promotion . Back Order . New Demand
Capacity Options in Aggregate Planning:
1. Hire and Lay off workers 2. Overtime/slack time 3. Part time workers 4. Inventories 5. Subcontracting
Strategies for Meeting Demand: 1. Maintain a level workforce 2. Maintain a steady output rate 3. Match demand period by period 4. Use a combination of options
General Procedure for Aggregate Planning consists of the following:
1. Determine demand for each period. 2. Determine capacities for each period. 3. Identify policies that are pertinent. 4. Determine units costs of regular time, overtime, subcon, holding of inventories, back orders , layoffs, etc. 5. Develop alternative plans and compute cost for each. 6. Select the alternative that satisfies objectives.
Some basic questions in capacity planning are the following:
1. What kind of capacity is needed? Depends on the products and services that management intends to produce or provide.
2. How much is needed?
3. When it is needed? Forecast is key units to answer the question.
CAPACITY DECISIONS ARE STRATEGIC
For a number of reasons, capacity decisions are among the most fundamental of all the design decisions that managers must make. In fact, capacity decisions can be critical for an organization:
1. Capacity decisions have a real impact on the ability of the organization to meet future demands for products and services; capacity essentially limits the rate of output possible. Having capacity to satisfy demand can allow a company to take advantage of tremendous opportunities.]
2. Capacity decisions affect operating costs. Ideally, capacity and demand requirements will be matched, which will tend to minimize operating costs. In practice, this is not always achieved because actual demand either differs from expected demand or trends to vary. In such cases, a decision might be made to attempt to balance the costs of over-and under capacity.
3. Capacity usually a major determinant of initial cost. Typically, the greater the capacity of a productive unit, the greater its cost. This does not necessarily imply a one-for-one- relationship; larger units tend to cost proportionately less than smaller units.
4. Capacity decisions often involved long-term commitment of resources and the fact that once they are implemented, it may be difficult or impossible to modify those decisions without incurring major cost.
5. Capacity decision can affect competitiveness. If a firm has excess capacity, or can quickly add capacity that may serve as a barrier to entry other firms. Then too, capacity can affect delivery speed which can be competitive advantage.
6. Capacity can affect the ease of the management, having appropriate capacity makes management easier then when the capacity is mismatched.
7. Globalization has increased the importance and the compellability of the capacity decisions, Fur-flung supply chains and distant markets add to the uncertainty about capacity needs.
8. Because capacity decisions often involve substantial financial and other resources, it is necessary to plan for them far in advance.
DEFINING AND MEASURING CAPACITY Capacity often refers to an upper limit on the rate of output.
Two useful definitions of capacity:
1. Design capacity: the maximum output rate or service capacity an operation, process, or facility is designed for.
2. Effective capacity: Design capacity minus allowances such as personal time, maintenance, and scrap.
- Actual output cannot exceed effective capacity and is often less because of machine breakdowns, absenteeism, shortages of materials, and equality problems as well as factors that are outside the control of the operating managers. - Efficiency is the ratio of actual output to effective capacity - Capacity utilization is the ratio of actual output to design capacity.
FORMULA TO REMEMBER IN CAPACITY PLANNING: Efficiency= actual output Effective capacity Utilization = actual output Design Capacity Business Inputs Outputs
Labor hours, machine per Auto manufacturing Number of cars per shift hours Steel mill Furnace size Tons of steel per day Oil refinery Refinery size Gallons of fuel per day Bushels of grains per Number of acres, number Farming acre per year gallons milk of cows per day Number of tables, sitting Number of milk served Restaurant capacity per day Number of tickets per Theater Number of seats performance Retail sails Square feet of floor Revenue generated per space day
DETERMINANTS OF EFFECTIVE CAPACITY
Facilities - Design of facilities, including size and provision for expansions is key. Location factors, such as transportation costs, distance to market, labor supply, energy sources, and room for expansion are also important. Likewise the layout of the work area often determines how smoothly work can be performed, and environmental factors such as heating, lighting, and ventilation also play a significant role in determining whether personnel can perform effectively or whether they must struggle to overcome poor design characteristics.
Product and services factors - in general the more the output is uniform, the more opportunities there are for standardization of methods and materials, which leads to a greater capacity. The particular mix of products or services rendered also must be considered since different items will have different rates of output.
Process factors - The quantity capability of the process is an obvious determinant of capacity. A more subtle determinant is the influence of output quality.
Human factors - the task that make up a job, the variety of activities involved, and the training, skill, and experience required to perform a job all have impact on the potential and actual output. In addition, employee motivation has a very relationship to capacity, as do absenteeism and labor turn- over.
Operational factors - Scheduling problems occurs when an organization has differences in equipment, capabilities among alternative pieces of equipment or differences in job requirements. Inventory stocking decisions, late deliveries, purchasing requirements, acceptability of purchased materials and parts, quality inspection and control procedures also can have an impact on effective capacity.
Supply chain factors - Must be taken into account capacity planning if substantial capacity changes are involved. Key question include: What impact will the changes have on the suppliers, warehousing, transportation, and distributors? If capacity will be increased, will these elements of the supply chain be able to handle increase? Conversely, if the capacity decreased, what impact will be loss in business have on these elements of the supply chain?
External factors - Product standards, especially minimum quality performance standards, can restrict management’s option for increasing and using capacity.
STRATEGY FORMULATION
An organization typically bases its capacity strategy on assumptions and predictions about long-term demand patterns, technological changes, and the behavior of its competitors. These typically involve: (1) the growth rate and variability of demand (2) the costs of building and operating facilities of various sizes (3) the rate direction of technological innovation (4) the likely behavior of the competitors, and (5) availability of capital and other inputs.
Key decisions of capacity planning relate to:
1. The amount of capacity needed
2. The timing of changes.
3. The need to maintain balance through out the system.
4. The extent of flexibility of facilities and the workforce.
Capacity cushion – extra demand intended to offset uncertainty.
STEPS IN THE CAPACITY PLANNING PROCESS
1. Estimate future capacity requirements. 2. Evaluate existing capacity and facilities and identify gaps. 3. Identify alternatives for meeting requirements. 4. Conduct financial analyses of each alternative. 5. Asses key qualitative issues for each alternative. 6. Select one alternative to pursue. 7. Implement the selected alternative. 8. Monitor results.
Determining Capacity Requirements
Capacity Planning Decisions involves; a. Long- term considerations- relate to overall level capacity. b. Short term considerations- relate to probable variations in capacity requirements
Factors/ reasons why companies buy product or services
1. Available capacity 2. Expertise 3. Quality considerations 4. The nature of Demand 5. Cost 6. Risk
Developing Capacity Alternatives
1. Design flexibility into systems
Example: Expand restaurant in the original design or remodel an existing structure.
Factors to be considered are layout of equipment, location, equipment , production planning, scheduling, and inventory policies.
1. Take stage of life cycle into account
Example
INTRODUCTION GROWTH MATURITY DECLINE Third generation Portable DVD Personal Computers Typewriters mobile phones Players E-conferencing Email Faxes Handwritten letters All-in-one racing skin- Breathable synthetic Cotton t-shirts Shell Suits suits fabrics iris-based personal Smart cards Credit cards Cheque books identity cards
3. Take a “big picture” approach to capacity changes
Example: A restaurant increases the number of chairs and tables, there’s a probable increase in demand of parking and maintenance.
4. Prepare to deal with capacity “chunks” – developing capacity alternatives may result to shortage or excess
Example: The desired number of units per hour is150, machines used for this operation are able to produce 100 units per hour each. One machine would be 50 units short to its desired number, but two machines will have an excess capacity of 50 units
5. Attempt to smooth out capacity requirements – The demand for the product/service changes occasionally. Expanding it may result to unevenness.
Example: When the storm came there’s an increase in demand on water, not like on normal days. Adding a water station would reduce the burden of heavy demands but it would add cost on other times
6. Identify the optimal operating level
Ideal level: cost per unit is lowest for that production unit Output rate < Optimal level: increase in output rate will result in decrease in average unit costs Output rate > Optimal level: average units costs would become increasingly larger
Figure.1 Production units have an optimal rate output for minimum cost Average per unit
Minimum cost
0 optimal rate Rate of output
Reasons for economies scale include;
a. Fixed costs are spread over more units, reducing the fixed cost per unit. b. Construction cost increase at a decreasing rate with respect to the size of the facilities to be built. c. Processing costs decrease as output rate increase because operations become more standardize which reduces unit costs.
Reasons for diseconomies scale include; a. Distribution costs increase due to traffic congestion and shipping from one large centralized facility instead of several smaller, decentralized facilities. b. Complexity increases costs; control and communication become more problematic. c. Inflexibility can be an issue. d. Additional levels of bureaucracy exist, slowing decision making and approvals for changes.
3 Important Factors in Planning Service Capacity
The need to be near customers.
Convenience for costumers is important aspect of service and service must be located near the costumers. Ex. Drug Store, were located near the hospitals.
The inability to store services.
The degree of volatility of demand.
Presents problems for capacity planners. Tends to higher the service than the goods not only in the timing of demands, but also in the amount of time required to service individual costumers.
Evaluating Alternatives
An organization needs to examine alternatives for future capacity from a number of perspectives. Most obvious are economic considerations:
. Will an alternative be economically feasible? . How much will it cost? . How soon can we have it? . What will operating and maintenance costs be? . What will its useful life be? . Will it be compatible with present personnel and operations?
IMPORTANT FACTORS IN EXAMINING ALTERNATIVES
1) Possible negative public opinion – any option that could disrupt lives and property is bound to generate hostile reactions.
2) Construction of new facilities – may necessitate moving personnel to a new location.
3) Embracing new technologies – may mean restraining some people and terminating some jobs.
4) Relocation – can cause unfavorable reactions, particularly if a town is about to lose a major employer.
5) Community pressure – may arise if the presence of the company is viewed unfavorably by noise, traffic and pollution.
TECHNIQUES USED FOR EVALUATING CAPACITY ALTERNATIVES
1) Cost-Volume Analysis 2) Financial Analysis 3) Decision Theory 4) Waiting-Line Analysis
Cost Volume Analysis – focuses on relationships between cost, revenue, and volume of output. The purpose of this analysis is to estimate the income of an organization under different operating conditions. It is particularly a useful tool for comparing capacity alternatives. Use of the technique requires identification of all costs related to the production of a given product. These costs are then designated as fixed costs or variable costs. Fixed costs tend to remain constant regardless of volume of output.
Examples of Fixed Costs
1) Rental costs 2) Property taxes 3) Equipment costs 4) Heating and Cooling Expenses 5) Administrative Costs
On the other hand, Variable costs vary directly with volume of output. The Two (2) Major components of Variable Costs
1) Materials 2) Labor Costs
The total cost associated with a given volume of output is equal to the sum of the fixed cost and the variable cost per unit times volume. Revenue per unit, like variable cost per unit, is assumed to be the same regardless of the quantity output. Hence, we could have the following formulas for solving problems related with Cost-Volume:
TC = FC + VC VC = Q x V TR = R x Q
Where: FC = Fixed Cost VC = Total Variable Cost v = Variable Cost per Unit TC = Total Cost TR = Total Revenue R = Revenue per unit Q = Quantity or Volume of Output QBEP = Break Even Quantity P = Profit
Total Profit can be computed using the formula:
P = TR-TC = R x Q – (FC + v x Q)
Rearranging terms, we could have:
P = Q(R – v) – FC
The required volume, Q, needed to generate a specified profit is:
Q = (P + FC)/(R-v)
A special case of this is the volume of output needed for total revenue to equal total cost. This is the Break-Even Point. We could compute it using the formula:
QBEP = FC/(R-v) SAMPLE PROBLEMS:
The owner of Old-Fashioned Berry Pies, S. Simon is contemplating adding new line of pies, which will require leasing new equipment for a monthly payment of $6000. Variable costs would be $2.00 per pie and pies would retail for $7.00 each.
a) How many pies must be sold in order to break even? b) What would the profit (loss) be if 1000 pies are made and sold in a month? c) How many pies must be sold to realize a profit of $4000? d) If 2000 can be sold, and a profit target is $5000, what price should be charged per pie?
Given:
FC = $6000 VC = $2.00 per pie Rev = $7.00 per pie
Solution:
a.) QBEP = FC/(Rev – VC) = ($6000)/($7 - $2) = 1200 pies per month
b.) For Q = 1000, P = Q(R – v) – FC = 1000($7 - $2) - $6000 = $1000
c.) P = $4000; Q = ($4000 + $6000)/($7 - $2) = 2000 pies
d.) Profit = Q(R – v) – FC
$5000 = 2000 (R - $2) - $6000
R = $7.50
SAMPLE PROBLEM # 2:
A manager has the option of purchasing one, two, or three machines. Fixed costs and Potential Volumes are as follows: Number of Machines Total Annual Fixed Costs Corresponding Range of Output 1 $ 9600 0 to 300 2 $ 15000 301 to 600 3 $ 20000 601 to 900
Variable Cost is $10 per unit, and revenue is $40 per unit:
a) Determine the break even point for each range b) If projected annual demand is between 580 and 600 units, how many machines should the manager purchase?
SOLUTIONS:
a.) For one machine;
QBEP = ($9600)/($40 per unit - $10 per unit) = 320units not in range For two machines = ($15000)/($40 per unit - $10 per unit) = 500 units For three machines = ($20000)/($40 per unit - $10 per unit) = 666.67 units
b.) Comparing the projected range of demand to the two ranges for which a break even point occurs, you can see that the break even point is 500, which is in the range 301 to 600.
Cost-Volume Analysis can be a valuable tool for comparing capacity alternatives if certain assumptions are satisfied: 1) One product is involved 2) Everything produced can be sold 3) The variable cost per unit is the same regardless of the volume 4) fixed costs do not change with volume changes, or they step changes 5) The revenue per unit is the same regardless of volume 6) Revenue per unit exceeds variable cost per unit
FINANCIAL ANALYSIS – a common approach is to use this to rank various investment proposals. Cash Flow – refers to the difference between the cash received from sales (of goods or services) and other sources, and the cash outflow for labor, materials, overhead and taxes.
Present Value – expresses in current value the sum of all future cash flows of an investment proposal.
THE THREE (3) MOST COMMONLY USED METHODS OF FINANCIAL ANALYSIS ARE PAYBACK, PRESENT VALUE AND INTERNAL RATE OF RETURN.
Payback – is a crude but widely used method that focuses on the length of time it will take for an investment to return its original cost.
Present Value – summarizes the initial cost of an investment, its estimated annual cash flows, and any expected salvage value in a single value cslled the equivalent current value.
Internal Rate of Return – summarizes the initial cost, expected annual cash flows, and estimated future salvage values of an investment proposal in an equivalent interest rate.
DECISION THEORY - is a helpful tool for financial comparison of alternatives under conditions of risk and uncertainty. It is suited to capacity decisions and to a wide range of other decisions mangers must take.
WAITING-LINE ANALYSIS - is useful in helping managers choose a capacity level that will be cost effective through balancing the cost of having customers wait with the cost of providing additional capacity. It can be an aid in the determination of the expected costs for various levels of service capacity.
SUMMARY Capacity – refers to a system’s potential for producing goods or delivering services over a specified time interval.
Capacity decisions – are important because capacity is a ceiling on output and a major determinant of operating costs.
Capacity planning decision - is one of the most important decisions that managers make. The capacity decision is strategic and long – term in nature, often involving a significant initial investment of capital.
Capacity planning is particularly difficult in cases where returns will accrue over a lengthy period and risk is a major consideration.
FACTORS THAT CAN INTERFERE EFFECTIVE CAPACITY:
Facilities Design and layout Human factors Product/service design Equipment failures Scheduling problems Quality considerations
Capacity planning – involves Long - term and Short - term considerations.
Long- term considerations – relate to the overall level of capacity.
Short – term considerations – relate to variations in capacity requirements due to seasonal, random, and irregular fluctuations in demand. Program Evaluation and Review Technique / Critical Path Method ( P E R T C P M )
Advantages of using PERT / CPM
1. This shows the graphical display of project activities. 2. This shows an estimate of how long the project will take. 3. This serves as an indication of which activities are most critical to timely project completion. 4. This serves as an indication of how long any activity can be delayed without lengthening the project.
Precedence Diagram
2 Ways of Constructing a Diagram
1. AOA or Activity – on Arrow
A B C
2. AON or Activity on Node
A B C
Sample Problem : Precedes Activity Time Crash Time Cost/day to Crash
- a 6 wks 6 Php 500 a b 10 wks 8 Php 300 - c 5 wks 4 Php 700 c d 4 wks 1 Php 600 d e 9 wks 1 Php 800 b/e f 2 wks 1 Php 200
B = 10 A = 6 F = 2
E = 9 C = 5
D = 4
Find : 1. The CPM 2. Improve the completion time by doing the necessary crashing if applicable. Solution:
1. Determine the CPM
ABF = 6 + 10 + 2 = 18 CDEF = 5 + 4 + 9 + 2 = 20 Longest path is CDEF, therefore, this is the CPM
2. Rank the CPM activities in order of lowest crashing cost and determine the number of days each can be crashed. Activity Cost Days Available for Crashing Time F Php 500 1 2 D Php 600 1 4 C Php 700 4 5 E Php 800 1 9
C D E F 5 + 4 + 9 + 2 = 20 Critical Path
Choose the lowest crashing cost which is f, therefore, 5 + 4 +9 + 1 = 19 days 1 day can still be crashed , 5 + 3 + 9 + 1 = 18 days, New Cost is + Php 1,100.
INVENTORY MANAGEMENT
Introduction to Inventory Management
Inventory is a stock or store of goods. It includes raw materials or stock incoming suppliers. Two types of Demand: 1. Dependent Demand These are items that are typically subassemblies or component parts that will be used in the production of a final or finished product. Subassemblies and component a part is derived from the number of finished units that will be produced. Example: Demand for wheels for new cars.
2. Independent Demand These are items that are the finished goods or other end items. These items are sold or at least shipped out rather than used in making another product.
The Nature and Importance of Inventories
TYPES OF INVENTORIES Raw materials and purchased parts Partially completed goods Finished-goods inventories or merchandise Replacement parts, tools, and suppliers Goods-in-transit to warehouses or customers Functions of Inventory
1. To meet anticipated customer demand. These inventories are referred to as anticipation stocks because they are held to satisfy planned or expected demand. 2. To smooth production requirements. Firms that experience seasonal patterns in demand often build up inventories during off-season to meet overly high requirements during certain seasonal periods. Companies that process fresh fruits and vegetable deal with seasonal inventories.
3. To decouple operations. The buffers permit other operations to continue temporarily while the problem is resolved. Firms have used buffers of raw materials to insulate production from disruptions in deliveries from suppliers, and finished goods inventory to buffer sales operations from manufacturing disruptions. 4. To protect against stock-outs. Delayed deliveries and unexpected increases in demand increase the risk of shortages. The risk of shortages can be reduced by holding safety stocks, which are stocks in excess of anticipated demand. 5. To take advantage of order cycles. Inventory storage enables a firm to buy and produce in economic lot sixes without having to try to match purchases or production with demand requirements in short run. 6. To hedge against price increase. The ability to store extra goods also allows a firm to take advantage of price discounts for large orders. 7. To permit operations. Production operations take a certain amount of time means that there will generally be some work- in-process inventory.
Inadequate control of inventories can result into two categories:
1. Under stocking results in missed deliveries, lot sales, dissatisfied customers and production bottlenecks 2. Overstocking unnecessarily ties up funds that might be more productive
Two Main Concerns of Inventory Management
1. Level ofObjectives customer service of Inventory to have theManagement right goods, in sufficient Generalquantities, in the right place, and at the right time. 2. CostTo of achieve ordering satisfactory and carrying levels inventories. of customer service while keeping inventory costs within reasonable bounds. Specific Decision maker tries to achieve a balance in stocking Fundamental decision must be made related to the timing and size of orders Requirements for Effective Inventory Management
To be effective, management must have the following:
1. A system to keep track of the inventory on the hand on order. 2. A reliable forecast of demand that includes an indication of possible forecast error. 3. Knowledge of lead times and lead time variability. 4. Reasonable estimates of inventory holding costs, ordering costs, and shortage costs. 5. A classification system for inventory items.
Inventory Counting Systems Inventory counting systems can be either 1. periodic 2. perpetual. Periodic System This is a physical count of items in inventory is made at periodic intervals (e.g. weekly, monthly) in order to decide how much to order of each item.
Advantage Orders for many items occur at the same time, which can result in economies in processing and shipping orders
Disadvantages 1. Lack of control between reviews. 2. The need to protect against shortages between review periods by carrying extra stock. 3. The need to make a decision on order quantities at each review.
Major users: Supermarkets, discounts stores, and department stores.
Universal Product Code (UPC) bar code printed on a label that has information about the item to which it is attached. Bar coding represents an important development for other sectors of business besides retailing. In manufacturing, bar codes attached to parts, subassemblies, and finished goods greatly facilitate counting and monitoring activities.
Perpetual Inventory System (also known as a continual system) This keeps track of removals from inventory on a continuous basis, so the system can provide information on the current level of inventory for each item.
Advantages 1. The control provided by the continuous monitoring of inventory withdrawals. 2. The fixed-order quantity; management can identify an economic order size.
Disadvantage 1. The added cost of record keeping.
Two-bin-system is two containers of inventory; reorder when the first is empty. The advantage of this system is that there is no need to record each withdrawal from inventory; the disadvantage is that the reorder card may not be turned in for a variety of reasons. Demand Forecast and Lead time Information Managers need to know the extent to which demand and lead time might vary; the greater the potential variability, the greater the need for additional stock to reduce the risk of a shortage between deliveries.
Lead time is time interval between ordering and receiving the order.
Cost Information
Three Basic Costs
1. Holding or Carrying Cost is costs to carry an item in inventory for a length of time usually a year. Cost includes interest, insurance, taxes, depreciation, obsolescence, deterioration, spoilage, pilferage, breakage, etc.
2. Ordering Cost is cost of ordering and receiving inventory. These include determining how much is needed, preparing invoices, inspecting goods upon arrival for quality and quantity, and moving the goods to temporary storage.
3. Storage Cost is cost resulting when demand exceeds the supply of inventory on hand. These costs can include the opportunity cost of not making a sale, loss of customer goodwill, late charges, and similar costs.
Classification System
An important aspect of inventory management is that items held in inventory are not of equal importance in terms of dollars invested, profit potential, sales or usage volume, or stock-out penalties. Example:
A producer of electrical equipment might have electric generators, coils of wire, and miscellaneous nuts and bolts among the items carried in inventory. It would be unrealistic to devote equal attention to each of these items.
A-B-C Approach classifies inventory items according to some measure of importance, usually annual dollar usage, and then allocates control efforts accordingly.
Three Classes of Items Used:
A (very important) B ( moderately important) A-B-C Concept
High
Annual dollar- Volume of items
Low
Few Number of Items Many A typical A-B-C breakdown in relative annual dollar value of items and number of items by category
Cycle Counting is a physical count of items in inventory. The purpose of cycle counting is to reduce discrepancies between the amounts indicated by inventory records and the actual quantities of inventory on hand.
The key questions concerning cycle counting for management are: 1. How much accuracy is needed? 2. When should cycle counting be performed? 3. Who should do it?
Economic Order Quantity Models
Economic Order Quantity (EOQ) is the order size that minimizes total cost. EOQ models identify the optimal order quantity in terms of minimizing the sum of certain annual costs that vary with order size.
Three (3) Order Size 1. The economic order quantity model. 2. The economic order quantity model with non instantaneous delivery. 3. The quantity discount model. Basic Economic Order Quantity (EOQ) Model EOQ models identify the optimal order quantity in terms of minimizing the sum of certain annual costs that vary with order size.
Inventory Cycles begins with the receipt of an order of Q units, which are withdrawn at instant rate over time. When the quantity on the hand is just sufficient to satisfy demand during lead time, an order for Q units is submitted to the supplier.
Assumption of the Basic EOQ Model 1. Only one product is involved. 2. Annual demand requirements are known. 3. Demand is spread evenly throughout the year so that the demand rate is reasonably constant. 4. Lead time does not vary. 5. Each order is received in a single delivery. 6. There are quantity discounts. Annual Carrying Cost is computed by multiplying the average amount of inventory hand by the cost to carry one unit for one year. The average inventory is simply half of the order quantity.
Annual Carrying Cost = Q H 2 where: Q = Order quantity in units H = Holding (carrying) cost per unit
Carrying Cost, Ordering Cost, and Total Cost curve
A. Carrying costs are linearly Annual Q H related to order size. Cost 2
Order Quantity B. Ordering costs are inversely Annual and nonlinearly related to Cost D S order size Q
Order Quantity
C. The total-cost curve is Annual TC= Q H + D S U-shaped Coast 2 Q
Order Quantity
Annual Ordering Cost is a function of the number of orders per year and the ordering cost per order.
Annual Ordering Cost = D S Q where: D = Demand, usually in unit per year S = Ordering cost
Total Annual Cost is associated with carrying and ordering inventory when Q unit are ordered each time.
TC = Annual Carrying Cost + Annual Ordering Cost TC = Q H + D S 2 Q
The length of an order cycle (Ex. The time between orders) is:
Length of Order Cycle = Qо D
EOQ with Non instantaneous Replenishment
When a firm is both a producer and a user or deliveries are spread over time, inventories tend to build up gradually instead of instantaneously.
If usage production (or delivery) rates are equal, there will be no inventory buildup since all output will be used immediately and the issue of lot size doesn’t come up. In the more typical case, the production or delivery rate exceeds the usage rate. In the production case, production occurs over only a portion of each cycle because the production rate is greater than the usage rate, and usage occurs over the entire cycle.
Equations:
TCmin = Carrying cost + setup cost
= (Imax / 2) H + ( D/ Q0)S Where
Imax = Maximum inventory
Q0 = √2DS/H √p/ p – u
Where
P = Production or delivery rate u = usage rate
Example: A toy manufacturer uses 48000 rubber wheels per year for its popular dump truck series. The firm makes its own wheels, which it can produce at a rate of 800 per day. The toy trucks are assembled uniformly over the entire year. Carrying cost is $1 per wheel a year. Setup cost for production run of the wheels is $45. The firm operates 240 days per year. Determine each of the following. a. Optimal run size b. Minimal total annual cost for carrying and setup c. Cycle time for the optimal run size Solution: D = 48000 wheels per year S = $ 45 H = $1 per wheel per year P = 800 wheels per day U = 48000 wheels per 240 days, or 200 wheels per day
a. Q0 = √2DS/H √p/ p – u = √2(48000)45/1 √800 /(800 – 200)
= 2400 wheels b. TCmin = Carrying cost + setup cost = (Imax / 2) H + ( D/ Q0)S
Imax = 1800 wheels
TC = (1800/2) * 1 + (48000/2400) *45 = $1800
c. Cycle time = 2400/ 200 = 12 days
d. run time = 2400/ 800 = 3 days
Quantity Discounts are price reductions for large orders offered to customers to induce them to buy in large quantities. If quantity discounts are offered, the customer must weigh the potential benefits of reduced purchase price and fewer orders that will result from buying in large quantities against the increase in carrying costs caused by higher average TC = carrying cost + Ordering cost + Purchasing Cost = (Q/2)H + (D/Q)s + PD
where: P = Unit price
Cost
TC with PD
TC without PD
PD
EDQ
Quantity * Adding PD doesn’t change the EOQ TC @ 2.00 each
TC @ 1.70 each
TC @ 1.40 each PD @ 2.00 PD @ 1.70 PD @ 1.40
45 70 Quantity
* The total cost curve with quantity discounts is composed of a portion of the total cost curve for each price
Example:
The maintenance department of a large hospital uses about 816 cases of liquid cleanser annually. Ordering costs are $12, carrying costs are $4 per case a year, and the new schedule indicates that orders of less than 50 cases will cost $20 per case, 50 to 79 will cost $18 per case, 80 to 99 cases will cost $17 per case, and larger orders will cost $16 per case. Determine the optimal order quantity and total cost.
Solution:
D= 816 cases per year S = $12 H = $4 per year
Range Price 1 to 49 $20 50 to 79 18 80 to 99 17 100 or more 16
EDQ = √2DS/H= √ 2(816)12 /4 = 70 cases
TC70 = Carrying cost + Order cost + Purchase cost = (Q/2) H + (D/Q0) +PD = (70/2) 4 + (816/70)12 +18(816) = $14968
TC80 = $14154
TC100 = $13354 When to Reorder with EOQ Ordering
Reorder Point it occurs when the quantity on hand drops to a predetermined amount. That amount generally includes expected demand during lead time and perhaps an extra cushion of stock, which serves to reduce the probability of experiencing a stock out during lead time. 4 Determinants of the Reorder Point Quantity: 1. The rate of demand 2. The length of lead time 3. The extent of demand and/or lead time variability 4. The degree of stock out risk acceptable to management
If demand and lead time are both constant , the reorder point is simply ROP = d*LT where: d = Demand per day or week LT = Lead time in days or weeks
Example:
Tingly Two – a Day vitamins which are delivered to his home by a routman seven days after an order is called in. At what point should tingly telephone his order in?
Usage = 2 per day Lead time = 7 days ROP = Usage * Lead time = 2 vitamins per day * 7 days = 14 vitamins
Tingly should reorder when 14 vitamin tablets are left
Safety stock is when variability is present in demand or lead time, the possibility that actual demand will exceed expected demand created. Consequently, it is very necessary to carry additional inventory.
ROP = Expected demand during lead time + Safety
Service Level Because it costs money to hold safety stock, a manager must carefully weigh the cost of carrying safety stock against the reduction in stock – out risk it provides, since the service level increases as the risk of stock out decreases. The probability that demand will not exceed supply during lead time
Service Level = 100% - stock out risk
The amount of safety sock that is appropriate for a given situation depends on the following factors: 1. The average demand rate and the average demand time. 2. Demand and time variability. 3. The desired service level.
For a given order cycle service level, the greater the variability in either demand rate or lead time, the greater the amount of safety stock that will be needed to achieve that service level. Several models will be described that can be used in cases when variability is present. The first model can be used if an estimate of expected demand during lead time and its standard deviation are available.
Reorder Point Formula ROP = Expected demand during lead time + zσdLT
where:
z = Number of standard variations
σdLT = The standard deviation of lead time demand
The ROP Based on normal distribution of lead time demand: Risk of a Service Level stock out (Probability of no Blackout)
Expected Demand ROP quantity.
Safety stock
0 z
Example:
Suppose a manager of a construction supply house determined from historical records that the lead time demand for sand averages 50 tons. In addition, suppose the manager determined that demand during lead time could be described by a normal distribution that has a mean of 50 tons and a standard deviation of 5 tons. Answer these questions assuming that the manager is willing to accept a stock – out risk of no more than 3 percent.
a. What value of z is appropriate? b. How much safety stock should be held? c. What reorder point should be used? Expected lead time demand = 50 tons σdLT = 5 tons Risk = 3% Solution: a. from z table, using a service level of 1 - .03 = .9700, you obtain a value of z = + 1.88 b. Safety stock = zσdLT
=1.88(5) =9.40 tons c. ROP = expected time of demand + safety stock = 50 + 9.40 = 59.40 tons.
If only demand is available, then σdLT = √LTσd, and the reorder point is
ROP = đ * LT + z √LTσd where:
đ = Average daily or weekly demand σd = standard deviation of demand per day or week LT = Lead time in days or weeks
Shortages and Service Levels The ROP computation does not reveal the expected amount of shortage for a given lead time service level. The expected number of units can, however, be very useful to a manager. This quantity can easily be determined from the same information used to compute the ROP, with one additional piece of information. (Table 11 – 3; Operation Production Management Fifth Edition by William Stevenson).
Formula: E(n) = E(z)σdLT where: E(n) = Expected number of units short per order cycle E(z) = Standard number of units short obtained from table 11 – 3 σdLT = Standard deviation of lead time demand
Example:
Suppose the standard deviation of lead time demand is known to be 20 units. Lead time demand is approximately normal
a. For a lead time service level of 90%, determine the expected number of units short o any order cycle. b. What lead time service would an expected shortage of 20 units imply?
Solution:
a. Lead time service level = .90. From table 11 – 3 (Stevenson), E(z) = 0.048. E(n) = 0.048(20 units) = 0.96, or about 1 unit b. For the case where E(n) =2, you must solve for E(z) and then use table 11 – 3 (Stevenson) to determine the lead time service level that implies. Thus, E(n) = E(z) σdLT, so E(z) = E(n) / σdLT = 2/20 = .100. From table 11 – 3, this implies a service level of approximately 81.5 percent (interpolating).
Fixed-Order interval Model
The Annual service level and the lead time service level can be related using the following formula:
SL annual = 1 - E (N) D Using the previous formula: E (N) = E (π) D/Q = E(z) σdLT D/Q Thus, SL annual = 1 - E( z ) σdLT Q How Much to Order: Fixed-Order-Interval Model
Fixed-Order-Interval (FOI) model is used when orders must be placed at fixed time intervals (weekly, twice a month, etc.). The question to be answered at each order point is: How much should be ordered for the next (fixed) interval? Fixed-interval recorder, requires only periodic checks of inventory levels.
Determining the Amount to Order Both the demand rate and lead time are constant, the fixed- interval model and the fixed-quantity model function identically. In the fixed-quantity arrangement, orders are triggered by a quantity (ROP), while in the fixed-interval arrangement orders are triggered by a time. Order size in the fixed-interval model is determined by the following computation: Expected demand Amount = during protection + Safety - Amount on hand to order interval stock at recorder time
= d(OI + LT) + zσd(OI+LT)^ ½ - A where: OI = Order interval (length of time between orders) A = Amount on hand at recorder time
As in previous models, we assume that demand during the protection interval is normally distributed.
The SINGLE – PERIOD MODEL
Single-period is used to handle ordering of perishable (fresh, fruits, vegetables, seafood, cut flowers) and items that have a limited useful life (newspaper, magazines, spare parts for specialized equipment. The period for spare parts is the life of the equipment, assuming that the parts cannot be used for other equipment.) Shortage cost includes a charge for loss of customer goodwill as well as opportunity cost of lost sales. Shortage cost is simply unrealized profit.
C shortage = Cs = Revenue per unit – Cost per unit The shortage or stock out relates to an item used in production or to spare part for a machine, then shortage cost refers to the actual cost of lost production.
Excess cost pertains to items left over at the end of the period. In effect, excess cost the difference between purchase costs and salvage value. That is,
C excess = C s = Original cost per unit – Salvage value per unit
The goal of the single-period model is to identify the order quantity, or stocking that will minimize the long run excess and shortage costs.
Ce Cs
Service level
Se Quantity
So = Optimum Stoking quantity Continuous Stoking Levels The concept of identifying an optimal stocking level is perhaps easiest to visualize when demand is uniform. The service level is the probability that demand will not exceed the stocking level and computation of the service level is the key to determining the optimal stocking level.
Cs Service level =
C + Cs
Where
Cs = Shortage cost per unit
Ce = Excess cost per unit
Example Sweet cider is delivered weekly to Cindy’s Cider bar. Demand varies uniformly between 300 liters and 500 liters per week. Cindy pays 20 cents per liter for the cider and charge 80 cents per liter for it. Unsold cider has no salvage value and cannot be carried over into the next week due to spoilage. Find the optimal stocking level and its stock out risk for that quantity;
Ce = Cost per unit – Salvage value per unit = $0.20 - $0 = $0.20 per unit
Cs = Revenue per unit – Cost per unit = $0.80 - $0.20 = $0.60 per unit
SL = Cs = $0.60 = .75
Cs+ Ce $0.60+$0.20
So = 300 + 0.75(500- 300) = 450 liters 75%
300 450 500
Stock out risk is 1.00 - .75 = .25
Discrete Stocking Levels
Then stocking levels are discrete rather than continuous, the service level computed using the ratio Cs/( Cs + Ce) usually does not coincide with a feasible stocking level.
Example Historical records on the use of spare parts for several large hydraulics presses are to serve as an estimate of usage for spares of a newly installed press. Stock out cots involves downtime expenses and special ordering costs. There average $4,200 per unit short rates cost $800 each, and unused parts have zero salvage. Determine the optimal level.
0 1 2 3 4 5 6 7 8 stoking
level
Cs
Cs + Ce
Number of spares Relative Frequency Cumulative used Frequency 0 .20 .20 1 .40 .60 2 .30 .90 3 .10 1.00 4 or more .00 1.00
Cs = $4.20 Ce = $800 SL = Cs = $ 4,200 = .84
Cs+ Ce $ 4,200+$ 800
Operations Strategy
Inventories are necessary part of doing business, but having too much inventory is not good. One reason is that inventories tend to hide problems; they make it easier to live a problem rather than eliminate them. Another reason is that inventories are costly maintain.
Revised CC
CC
Qlo Qo OC
Revised (increased) carrying costs results in a smaller EOQ
Revised CC
Improve OC CC
QIIo Qlo Qo OC
Reductions in both ordering/setup cost and carrying cost results in much smaller lot sizes.