Logistic Management

Abstract

This paper considers a two-stage distribution problem of a supply chain that is associated with a fixed charge. Two kinds of cost are

involved in this problem: a continuous cost that linearly increases with the amount transported between a source and a destination, and

secondly, a fixed charge, that incurs whenever there exists a transportation of a non-zero quantity between a source and a destination.

The objective criterion is the minimisation of the total cost of distribution. A genetic algorithm (GA) that belongs to evolutionary search

heuristics is proposed and illustrated. The proposed methodology is evaluated for its solution quality by comparing it with the approximate

and lower bound solutions. Thus, the comparison reveals that the GA generates better solution than the approximation method

and is capable of providing solution either equal or closer to the lower bound solution of the problem.

 2007 Elsevier B.V. All rights reserved.

Keywords: Fixed charge; Distribution problem; Supply chain; Genetic algorithm; Heuristics

1. Introduction

A supply chain (SC) is a network of firms that produce, sell, and deliver a product or service to a predetermined market

segment (Chopra and Meindl, 2001). It not only includes the manufacturers and suppliers, but also transporters, warehouses,

retailers and customers themselves. The term supply chain conjures up images of a product or a supply moving

from suppliers to manufacturers then distributors to retailers and then customers along a chain (Chopra, 2003). Customers

and their needs are the origin of the SC. The next stage of the SC is its distribution centres, which in turn, forward the needs

of the customers to the manufacturers. A constant flow of information, products, and funds takes place between the stages

concerned with the SC. The distribution of products all along the SC, that directly influences the supply chain cost, is a key

driver of the overall profitability of the firms. The cost of distribution accounts for about 30% of the cost of the product

and plays a vital role in the determination of its price. Hence, the problem of distribution is an important consideration for

industrial firms that have supply chain networks. In such problems, one of the strategic decisions is the allocation of transaction

quantities from production centres to terminal points in a cost effective manner. Often, unit transportation cost is

used to find the optimal distribution schedule. A basic assumption in any transportation problem is that the cost of transportation

is directly proportional to the number of units transported