Mathematical Solution for the Determination of Optimal Warehouse Location and Optimal Distribution Route

Abstract

In this paper, a procedure to determine the optimal location of a distribution warehouse, from which products are sent out to a group of companies has been studied. The goal was to minimize annual transportation distance between the warehouse and the customers. Fundamentals of mathematics have been used to formulate a virtual map showing the location of the present customers. Mathematical models and equations were developed making certain assumptions and an optimal location for the warehouse has been determined. Various factors that are involved in relocating the warehouse have been considered. Also a solution is given for the optimal location of a satellite or an auxiliary warehouse in addition to the existing one. A case study has been conducted on the model with the help of various numerical examples. Based on the optimal location of the relocated warehouse and the satellite warehouse obtained, the reductions in the transport costs were estimated. Once the optimal warehouse location has been found out, the next step was to find out an optimal route (least travel distance) for a practical case in which several companies have to be supplied with necessary products from one warehouse in a single trip. For this purpose, mathematical models were created and optimal routing algorithms were developed. Case studies have been conducted with the help of numerical examples. High amounts of savings in terms of travel distances, costs and time could be observed by the implementation of these algorithms.