OPTIMAL SCHEDULING OF PETROLEUM PRODUCTS DISTRIBUTION IN NIGERIA By M.N Eke and, S.O. Enibe Department of Mechanical Engineering University of Nigeria, Nsukka ABSTRACT One major problem in Nigeria is the persistent scarcity and inequitable distribution of petroleum products even with the establishment of three refineries, many storage depots and pipelines interconnecting them. This paper is applied to the situation in the downstream petroleum sector in order to determine an efficient and equitable distribution of three blends of petroleum products, namely; Premium motor spirit (PMS) Dual purpose kerosene (DPK) and Automotive Gasoline (AGO). For effective distribution, three refineries and seventeen storage depots were considered because of their interconnections with pipelines. The model was formulated as a linear programming problem with 20 constraints and 51 variables and was solved using LINDO Optimization software which uses simplex approach. Post-optimality analysis was performed investigating the effect of varying supply from refineries and demand at storage depots. The optimal solution was obtained for each of the product in the target year “2010” and the result was compared with the result of optimal solution obtained during uncertainty period say “2015”. The study reveals that any variation in supply, demand and transportation cost changes the optimal solution. Keyword: Distribution, petroleum products, refineries, storage depots, linear programming. NOMENCLATURE AGO – Automotive Gasoline MT – Metric tonne BPD(B/D) – Barrel per day NNPC – Nigeria National Cij – Cost of transporting a unit Petroleum Corporation metric tonne of the product PMS – Premium motor Spirit from the supply point i to the PPMC – Pipeline and Product demand point j. Marketing Company Dj – Demand point requirement j. Si – Supply point availability i. DPK – Dual purpose kerosene 67 68 M.N. Eke and S.O. Enibe INTRODUCTION to consumers such as petrol stations) by The production and distribution of lorry tankers are represented as a linear petroleum products in Nigeria is an programming problem by Mehring and important factor in her domestic economy. Gutherman [3] in which total cost of From 1970 to date, the nation has invested delivery are minimized (or profit substantially in refineries, storage depots, contribution is maximized). Supply and pipelines etc. The total pipeline network is distribution models are apparently of the about 4500Km [1]. Unfortunately, within few model in the oil industry that integrates the past few years, the supply of these several functional areas [4, 5]. petroleum product blends to storage depots Dantizig [6] formulated the and then to consumers have not been transportation problem as linear enough to meet the increasing demand. The programming problem and then developed areas of demand include: Domestic sector, the simplex algorithm for solving such Industrial sector, Transport and Agricultural problems. The simplex algorithm is an sectors [2]. iterative procedure, that is, one that repeats Proper schedule of the distribution the same steps over and over again, through pipeline networks can facilitate the producing a sequence of “basic feasible” economical integration of refinery locations solutions where each solution improves on and storage depots for easy shipment of the the preceding one until no further products from refineries to depot locations improvement is possible. The solution and then to consumers at minimum delivery finally arrived at is the desired optimal cost. solution. The refineries are situated in Port Chen et al [7] developed a primal- Harcourt, Warri and Kaduna; and storage dual simplex algorithm for the general depots are located in Aba, Enugu, Makurdi, linear programming problem and applied it Yola, Benin, Ore, Mosimi, Satellite town in to cost reduction problems. Lagos, Ibadan, Ilorin, Suleja, Minna, Jos, HU [8] and HU and Johnson [9] Gombe, Maiduguri, Kano and Gusau. developed a primal-dual simplex algorithm The objective of the study is to that is designed to take advantage of both develop a transportation model based on the primal and dual feasible solutions. Klabjan linear programming technique that will [10] developed an algorithm known as schedule the distribution which minimizes parallel primal-dual simplex which is the cost of delivery of these blends of capable of solving linear programs with products from refineries to storage depots. thousands of rows and millions of columns. The system should be robust yet simple to support routine scheduling of monthly and 2.0 MODEL AND PROBLEM annual distribution of petroleum products. FORMULATION The supply model, the demand In formulating the model, the model, primary distribution (moving objective is to minimize the cost of delivery products from refineries or other supply of these blends of petroleum products from sources to depots) at least cost, perhaps refineries to storage depots through pipeline continuously by pipeline and secondary network. distribution (moving products from depots The objective function of the model is NIGERIAN JOURNAL OF TECHNOLOGY, VOL. 26 NO.1, MARCH 2007 OPTIMAL SCHEDULING OF PETROLEUM PRODUCTS DISTRIBUTION IN NIGERIA 69 m n The equation (1) of the model is the Minimize Z C X (1) ij ij objective function which expresses the goal i1 j1 of the problem. Subject to the constraints n Equation (2) in the model is the supply availability. This indicates that the Xij Si all source nodes i (2) i1 quantities of final blended products leaving i = 1,2,3, …, n, n = 17 the refineries are less than or equal to the n quantities being produced by the refineries. Xij Dj all demand nodes j (3) i1 Equation (3) of the model is the i = 1,2, …, m, m = 3 demand requirement. The demand model X 0 (4) indicates that the quantities of blended ij products leaving the refineries to storage Where Xij = quantity of product transported depots are greater than or equal to the from supply point i to demand demand of each depot. point j Equation (4) of the model is the non- Cij = Cost of transporting each unit negativity constraint which explains that the product from supply point i to quantity of each final blended product demand point j. transported from refineries to the depots Si = Supply point availability must be greater than or equal to zero. Dj = Demand point requirement There are several assumptions that 2.1 Problem formulation accompany the above model Formulation of cost minimization 1) It is assumed that multiple sourcing is problem for distribution of petroleum allowed. This occurs when a particular products must begin with identification of demand point requirements is met by decision variables. There are 51 decision more than one supply point. variables which are defined as follows Xij = 2) The model assumes that the quantity of PMS, DPK or AGO transported transportation cost on a given route is from supply point i (refineries) at unit cost directly proportional to direct distance (cij) to demand point j (storage depots). between supply points and demand Table 1 show the decision variables used for points. the three refineries and seventeen storage depots. NIGERIAN JOURNAL OF TECHNOLOGY, VOL. 26 NO.1, MARCH 2007 70 M.N. Eke and S.O. Enibe Table 1: Decision variables used for the three refineries and seventeen storage depots. Storage Depots/Refineries Port Harcourt Warri Kaduna Aba X1,1 X2,1 X3,1 Enugu X1,2 X2,2 X3,2 Makurdi X1,3 X2,3 X3,3 Yola X1,4 X2,4 X3,4 Benin X1,5 X2,5 X3,5 Ore X1,6 X2,6 X3,6 Mosimi X1,7 X2,7 X3,7 Satellite X1,8 X2,8 X3,8 Ibadan X1,9 X2,9 X3,9 Ilorin X1,10 X2,10 X3,10 Suleja X1,11 X2,11 X3,11 Minna X1,12 X2,12 X3,12 Jos X1,13 X2,13 X3,13 Gombe X1,14 X2,14 X3,14 Maiduguri X1,15 X2,15 X3,15 Kano X1,16 X2,16 X3,16 Gusau X1,17 X2,17 X3,17 3.0 METHODOLOGY Xdi is the actual demand or supply of each 3.1 Data Collection product in a particular depot or refinery. Six years‟ data on products demand, Xdt is the total demand or supply of each supply and consumptions were obtained product in all the depots or refinery from the NNPC‟s data bank in Port throughout the country. Harcourt and PPMC. The average demand or supply over the period is then given by 3.2 Statistical Analysis b Projections of the products demand, supply K (6) and consumption were made based on the n above data. Where K is the average demand over the For the period (1994-1999), the period actual percentage depot demand and b is the summation of actual refinery supply for each product is given by percentage demand or supply of the equation each product at each depot or refinery for n years. Xdi b% x 100% (5) n is the number of years (n = 6) Xdt Where b% is the actual percentage demand Using the projected quantity or supply of each product at each consumed (Cp) from data available from depot or refinery in a particular NNPC and population size(Pt) from the year National Population Commission ( NPC), NIGERIAN JOURNAL OF TECHNOLOGY, VOL. 26 NO.1, MARCH 2007 OPTIMAL SCHEDULING OF PETROLEUM PRODUCTS DISTRIBUTION IN NIGERIA 71 the projected per capita consumption of the consumption of each product; and Pt is the blends of petroleum products(Y) will be population in a particular year. The C projected per capita consumption against Y p (9) p year for the blends of petroleum products is t shown in figure 1. Where, Cp is the projected consumption of each product; Y is the per capita 0.09 0.08 0.07 0.06 PMS DPK AGO 0.05 Per capita consumption, x1000kg Per capita consumption, 0.04 0.03 Per capita consumption, 1000kg x 0.02 0.01 0 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 Year Figure 1: Projected per capita consumption against year for the blends of petroleum product The demand of each product in a particular The unit transportation cost (Cij ) for each depot can be estimated by the relationship: route is obtained.