Mathematical Programming Model for the Two-Level Facility Location Problem: The Case of Tanzanian Emergence Maize Distribution Network for 2004–2010 Maize Data

Abstract

A two-level facility location problem (FLP) has been studied in the transportation network of emergence maize crop in Tanzania. The facility location problem is defined as the optimal location of facilities or resources so as to minimize costs in terms of money, time, distance and risks with the relation to supply and demand points. Distribution network design problems consist of determining the best way to transfer goods from the supply to the demand points by choosing the structure of the network such that the overall cost is minimized. The three layers, namely production centres (PCs), distribution centres (DCs) and customer points (CPs) are considered in the two-level FLP. The flow of maize from PCs to CPs through DCs is designed at a minimum cost under deterministic mathematical programming model. The four decisions to be made simultaneously are: to determine the locations of DCs (including number of DCs), allocation of CPs to the selected DCs, allocation of selected DCs to PCs, and to determine the amount of maize crop transported from PCs to DCs and then from DCs to CPs. The modelled problem generated results through optimization with respect to optimal location-allocation strategies. The results of the optimized network shows the improvement in costs saving compared to the manually operated existing network. The results show the costs saving of up to 18% which is equivalent to $2,910 thousand (TZS 2.9 billion).

Keywords:    Optimization, Maize crop, Transportation network, Deterministic model, Facility location.