Abstract
This contribution deals with a distribution system design problem, in which the located facilities satisfy all customer demands under limited abilities. The objective is to minimize the total costs, including both fixed charges and service costs. A special approach based on Lagrangean relaxation will be discussed here for its ability to cope with limited capacities of located facilities. Using the Lagrangean relaxation, the model of the original problem is rearranged to a model, which can be solved by exact algorithms for considerably large size. The capacities of the located facilities bring serious difficulties concerning solving technique, in the cases, where real-sized facility location problems are solved. In contrast to an uncapacitated facility location problem, which can be solved exactly in reasonable time for real-sized case containing hundreds of possible locations and thousands of customers.In this paper, we shall discuss a transformation of the capacitated location problem into the uncapacitated location problem by means of Lagrangean relaxation of capacity constraints. To demonstrate the efficiency of the studied approach, numerical experiments were performed and their results are reported in the concluding part of this paper.
Highlights
A distribution system can be considered as a sort of a transportation system, which enables delivering goods from one or several sources to customers
One of possible approaches to a capacitated location problem can be based on its rearrangement to the uncapacitated location problem, solution of which can be found relatively fast, for real-life size
The associated location problem can be formulated as follows: given a set of possible facility locations and a set of customers, which are served from a finite number of located facilities, find which facilities should be used and which customers should be served from which facilities so that to minimise the total cost of serving all the customers and the fixed investment costs of building and maintaining the facilities
Summary
A distribution system can be considered as a sort of a transportation system, which enables delivering goods from one or several sources to customers. This delivering can be either direct or with transhipment at several places (these are generally called terminals or facilities) – see Fig. 1. We shall investigate the capacitated location problem, with limited annual capacities of individual facilities. The capacitated location problem can be formulated as 0 – 1 linear programming problem, but the searching of its exact solution is very time-consuming or nearly impossible for large cases. One of possible approaches to a capacitated location problem can be based on its rearrangement to the uncapacitated location problem, solution of which can be found relatively fast, for real-life size
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