Abstract
When a distribution system is to be designed, limits on terminal capability often must be taken into account. These capacity constraints in this and other facility location problems constitute severe obstacles in exact solving processes. Within this paper, we focused on study of approximate methods based on Lagrangean relaxation of the capacity constraints, which has several advantageous properties. The first of them is that the relaxed problem, known as the uncapacitated location problem, can be solved exactly even for real sized instances [6], [4]. The second useful property of the Lagrangean relaxation is that the objective function value of the optimal solution of the relaxed problem provides lower bound of the optimal solution of the original problem. We present two methods for obtaining suitable values of Lagrangean multipliers. The classical one is based on a sub-gradient method applied on capacity constraints after their special adjustment. The second method is designed as an adaptive method with random experiments for determination of candidates for move from the current solution to the next one. These two methods were tested, compared and the associated results are reported in the concluding part of this paper.
Highlights
Cost optimal design of the most of distribution and servicing systems consists in decisions on number and locations of facilities, from which customer’s demands are satisfied
To avoid this complication and to obtain a good solution of the capacitated facility location problem in sensible time, we employ approximate methods based on Lagrangean relaxation of the capacity constraints, which has several advantageous properties
Real sized instances of the uncapacitated problem were broadly tested [6], [4] and it was proved that it is possible to obtain their optimal solution in a sensible time
Summary
Cost optimal design of the most of distribution and servicing systems consists in decisions on number and locations of facilities, from which customer’s demands are satisfied. In contrast to an uncapacitated facility location problem, which can be solved exactly for real-sized instances containing hundreds of possible locations and thousands of customers, the capacitated location problem resists to all attempts to solve it exactly in reasonable time To avoid this complication and to obtain a good solution of the capacitated facility location problem in sensible time, we employ approximate methods based on Lagrangean relaxation of the capacity constraints, which has several advantageous properties. The third property is that any optimal solution of the Lagrangean relaxation preserves so called compactness of particular customer clusters, which arise from a customer assignment to the individual facility locations This property is not directly connected with the facility location, but it has great impact on applications following up with a distribution system design. Both methods were tested, compared and the associated results are reported in the section “Numerical experiments” of this paper and some explanation of their various behaviors is suggested
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
