Optimization of Products Transportation and Distribution Network

Optimization of Products Transportation and Distribution Network

1 Akpan, W. A . 2 Awaka- Ama, E.J. 3 Ikrang, E.G.

1 Mechanical and Aerospace Engineering Department, University of Uyo. Nigeria

2 Mechanical and Aerospace Engineering Department, University of Uyo. Nigeria

3 Agric/ Food Engineering Department, University of Uyo, Nigeria

Abstract:- This research work focuses on the problem of transportation and distribution of products by a manufacturing company. The aim of the study is to determine the least cost of transportation and distribution of products by a firm. A popular brand in the food and beverage industry in Nigeria was selected for a case study. Two of it plants in the southern part of the country were investigated. Distribution centres located at Umuahia, Awka and Asaba are the destinations. Data of the supply from the two plants to the three centres, demand per period from each of the destinations and the cost of transportation from plant to each destination were obtained from the data base of the company. The analysis of the data using Vogels linear programming model reveals a total savings of Nine million, seven hundred and sixty one thousand, nine hundred and eighty-five naira ( # 9,761,985.00). The research shows that Vogels approximation method is effective in solving practical products transportation and distribution problems.

Keywords.; Products transportation, distribution, network, optimization,Vogels method.

1. INTRODUCTION

   Transportation is the movement of people, animals and goods from one location to another. Distribution is the process of making a product or service available for use or consumption by a consumer or business user, using direct means or using indirect means with intermediaries.

   A product according is anything that can be offered to a customer for attraction, acquisition use or consumption that might satisfy a want or need.

   There are various modes of transportation of products depending on size and urgency. Road transport is cheap, convenient and one of the most flexible modes of transport. It is subject to heavy delays. It sets limit to and restrict the movement of certain heights, weights and lengths of products. Rail transport is speedy, environmentally friendly and not always subject to congestion or delays. However, it is inflexible. Airfreight is without doubt the fastest to transport products across distances but is expensive and not eco-friendly. Airfreight is carried by cargo airlines as well as scheduled passenger aircraft.

   Shipping by sea is relatively cheap, particularly if large volumes are sent. It is slow, and fairly inflexible with few ports and further arrangements must be made to move the products inland. Sea freight vessels are made up of cargo ships, bulk carriers, tankers for liquids, roll-on or roll-off vessels. There are two types of shipping: liner vessels which operate on fixed routes with fixed schedules and

   Tramp vessels which operate entirely according to the demand of the client.

   Couriers are business experts that operate fast, reliable and secured services. Couriers are expensive and only cost effective over short distances.

   Factors that influence the distribution network design include customers needs and the cost of meeting those needs.

   Goods and passengers movement in Nigeria are performed mainly by road with the railway and inland waterways playing significant, but less important roles. International freight movement is principally by sea while air transportation is mostly patronized by well placed individuals.

   The supply chain is the chain links to each element of the manufacturing and supply process, from raw materials to end users. The supply chain consists of all parties that are directly or indirectly involved in fulfilling customer demands. These include the manufacturer, supplier, transporter, wholesaler, retailers and customers [1]. The scope of supply chain can be defined in terms of the number of firms involved in the supply chain and the function involved. Dimension to consider include length of the supply chain and the numbers of suppliers and customers at each level. It is therefore clear that transportation and distribution are sub set of supply chain. This research work focuses on these two elements. The transportation model has been used in movement of goods from plant to warehouse, resource allocation, assignment of work to machines, capital budgeting and deployment of warship to locations [2].

   Linear programming model is a mathematical formulation in which the objective function is linear. Murthy [3] defined linear programming model as a formulation for the allocation of scarce or limited resources to competing products or activities under such assumption as certainty, linearity, fixed technology and constant profit per unit. The transportation model is a special class of linear transportation problem in which the objective is to transport a homogeneous commodity from various origins or factories to different destinations or markets at a minimum cost. There are few methods of solving transportation problems under linear programming. This include simplex method, North west corner Method, Least cost method and Vogels approximation method (VAM). According to Murthy [3] Vogel approximation method has the potential to give the most optimal solution and will be

   used in this study. Other researches on product transportation are found in: [4], [5], [6], [7], and [8].

2. METHODOLOGY

Two plants of a production company in food and beverages located in Rivers state and Imo state -Nigeria were selected for the case study and call sources. Each centre- Umuaha in Abia state, Awka in Anambra state and Asaba in Delta state were chosen and call destinations. Quantities of products supplied from these two plants to the three

X 11 X 21 B1 X 12 X 22 B2 X13 X 23 B3

demand centres were obtained. The costs of transportation

Where

X ij

is the quantity of products transported from

from the source to the destinations were also obtained and this data were inputs to Vogels approximation methodology for computation and the determination of the optimum product allocation to these centres.

1. Model Formulation

   supply point i to destination j

   ( i=1,2 are Port Harcourt and Owerri plant) and j=1,2.3 are Umuahia, Awka and Asaba demand centre points)

   A1 and A2 are Port Harcourt and Owerri supply

   Minimise the objective function Z

   Z ax11 bx12 cx13 dx21 ex22 fx23

   Where a, b, c, d, e and f are transportation costs and;

   x11, x12, x13 , x21, x22, x23 are quantities supplied.

   Subject to

   X11 X12 X13 A1 X21 X22 X23 A2

   capacities respectively.

   B1 and B2 are the demand requirements at one Umuahia, Awka and Asaba demand centre points

2. INPUT DATA

   Tables 1, 2, 3 and 4 show the input data to solve the Vogels algorithm.

   Table 1 Cost of transportation from Port Harcourt plant to each of the distribution centres

   Distribution Centre	Cost of Transport per truck x (N100)
   Asaba	623
   Awka	612
   Umuahia	578

   Table 2 Cost of transportation from Owerri plant to each of the distribution centres

   Distribution Centre	Cost of Transport per truck x (N 100)
   Asaba	578
   <>Awka	576
   Umuahia	576

   Table 3 Quantity of products supplied to the three centres

   Distribution Centre	Quantity demanded (Trucks)
   Asaba	565
   Awka	470
   Umuahia	525

   Table 4 Quantity of product demanded at centres

   Distribution Centre	Quantity demanded (Trucks)
   Asaba	623
   Awka	612
   Umuahia	578

   Table 5 shows a tableau representation prior to the solution of the problem.

   Table 5

   Distribution cost Plant and Demand	Umuahia (N 100)	Awka (N 100)	Asaba (#100)	Supply(trucks)
   Port Harcourt	578	619	623	936
   Owerri	576	576	578	624
   Demand	694	632	753	1,560 2,080

1. Vogels method and results

   Step 1 Creation of a dummy row to balance supply and demand as shown in table 6

   Table 6 Balance supply and demand by creating a dummy row

   Plants, Dummy and Demand	Umuahia	Awka	Asaba	Supply
   Port Harcourt	578	619	623	936
   Owerri	576	576	578	624
   Dummy	0	0	0	520
   Demand	694	632	754	Total=2080

   Step 2: The penalties for each row and column are written. This obtained by subtracting the least cost from the second least cost in each row and column. The column or row with the highest penalty will receive maximum allocation as shown in table 7.

   Table 7

   	Umuahia	Awka	Asaba	Supply	Penalty
   	578	619	623	936	41
   	576	576	578	624	0
   Dummy	0	0	0	520	0
   Demand	694	632	764	Total=2080
   Penalty	576	576	578

   Column 3 has the highest allocation with 578 and so the least cost cell (3.3) is satisfied with maximum allocation of 520. This eliminates row 3 and new penalties are taken resulting in the result of table 8

   Table 8

   	Umuahia	Awka	Asaba	Supply	Penalty
   	578	619	623	936	41
   	576	576	578	624	0
   Demand	694	632	234	Total=1.560
   Penalty	2	43	45

   Column 3 again has the highest penalty of 45. The least cot cell (3,2) is satisfied with allocation of 234 thereby eliminating column 3. It reduces to the results in table 9.

   Table 9

   	Umuahia	Awka	Supply	Penalty
   	578	619	936	41
   	576	576	390	0
   Demand	694	632	Total=1,326
   Penalty	2	43

   New penalties are taken and allocation made as previously done. This eliminates row 2 yielding the tabulation in table 10.

   Table 10

   	Umuahia	Awka	Supply	Penalty
   	578	619	936	41
   Demand	694	242	Total=936

   The cell with the least cost (1,1) is allocated maximum allocation (694) reducing it to the form shown in table 11.

   Table 11

   	Umuahia	Supply
   	619	242
   Demand	242	Total=242

   Step 3: Table 12 below presents a summary of the allocations made- indicated in brackets to the respective cost cells.

   Table 12

   	Umuahia	Awka	Asaba	Supply
   Port Harcourt	578(694)	619(242)	623	936
   Owerri	576	576(390)	578(234)	624
   dummy	0	0	0(520)754	520
   Demand	694	632		Total=2,080

   Step 4: The table of basic solution is drawn. Table 13 shows the optimal cost of transporting the products to their destinations with the creation of a dummy supply centre within these three centres of Port Harcourt, Umuahia and Asaba.

   Table 13

   From	To	Quantity( number of trucks)	Cost(x N 100)
   Port Harcourt	Umuahia	694	578x 694=401,132
   Port Harcourt	Awka	242	619×242=149,798
   Owerri	Awka	390	576×390=224,640
   Owerri	Awka	234	578×243=135,252
   Total(#)			91,0822

2. CONCLUSIONS AND RECOMMENDATIONS The cost of product transportation has been reduced from N 100,844,185 (One hundred million, eight hundred and forty-four thousand naira) to N 91,082,200 (Ninety one million, eighty two thousand, two hundred naira) with a saving of N 9,761,985 (Nine million, seven hundred and sixty-one thousand, nine hundred and eighty five naira) from two plants to three centres by using this method. Vogels approximation method is hereby recommended for application in these industries. The burden of computation can be reduced by using computer algorithm and is recommended for future work.

REFERENCES

1. Chopera, S. (2001) Designing the distribution Network in a supply Chain. Kellog School of Management, pp 1-42

2. Nyong, M.O. (2005) Management Science: An Operations Research Emphasis in Economics and Business. Clear Lines Publication, Calabar, Cross River State.

3. Murthy, P.R. (2007) Operation Research 2 Ed. New age internatonal limited. Pp 141-211

4. Kandekar, S. (2012): Optimizing the Distibution Channels-A Case Study of Timber Product Distribution Channel. Linkoping University, pp 37-59

5. Kerukoglu, S.(2010) An Improved Vogels Approximation Method for the Transportation Problem

6. Singh, S. Dubey, G.C. Shriivastava, R. (2012a) A Various Method to Solve the Optimality for the

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