Comparing dual access approaches for exact solution of location problems

Jaroslav Janacek,Johanna Kovacikova

doi:10.26552/com.c.1999.2.4-8

Jaroslav Janacek, Johanna Kovacikova

Open Access

https://doi.org/10.26552/com.c.1999.2.4-8

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Abstract

The paper deals with exact solution of two uncapacitated location problems. The location problem consists in placing some facilities of unrestricted capacity in the formed network. The facility can have various natures. It could be aservice centre, whose location can be done at anode of the network, or it can be adirect train, which can be placed into a transport plan. In comparison with the former case, this facility has the nature of a graph edge.The key-stone of the computational success of the often used branch and bound method is the lower bound tightness. This paper, reports numerical experiments with the dual access approach used for the solution of the node location problem in a large network and compares several possible approaches to lower bound enumeration for the edge location problem.

Highlights

Ak sa zaoberáme navrhovaním alebo riadením sieťových systémov, ako sú napríklad distribučné systémy [2], [6], alebo systémy vlakotvorby [5], často sa stretávame s kapacitne neobmedzenou umiestňovacou úlohou
The location problem arises when some facilities of unrestricted capacity are placed in the formed network
The uncapacitated location problem forms an exclusion of the family of 0Ϫ1 programming problems

Summary

Introduction

Ak sa zaoberáme navrhovaním alebo riadením sieťových systémov, ako sú napríklad distribučné systémy [2], [6], alebo systémy vlakotvorby [5], často sa stretávame s kapacitne neobmedzenou umiestňovacou úlohou. The location problem arises when some facilities of unrestricted capacity are placed in the formed network. The uncapacitated location problem forms an exclusion of the family of 0Ϫ1 programming problems It has been proven [4] that the LP-relaxation lower bound is a good bound for the. Úlohy tohto typu v porovnaní s inými úlohami, kde tento typ výpočtu dolnej hranice zlyhal [7]. To viedlo k myšlienke použiť LP-relaxáciu pre riešenie úlohy návrhu siete, ktorá je špeciálnym prípadom umiestňovacej úlohy, kde umiestňované zariadenie má charakter úseku. It allows for the idea to use the LP-relaxation for the network design problem, which is a special sort of location problem where the placed facility has the nature of edge. In the chapter we try to compare the two problems from the point of view of solution procedures as well as computational effort

Location problem models

Computational intractability of the location problems

Lower bounds for location problems

Computational Study