Location and capacity design of congested intermediate facilities in networks

Dandan  Hu; Zhi-Wei  Liu

doi:10.3934/jimo.2016.12.449

Article Contents

2016, Volume 12, Issue 2: 449-470. Doi: 10.3934/jimo.2016.12.449

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Location and capacity design of congested intermediate facilities in networks

Dandan Hu^1, and
Zhi-Wei Liu^2,

1.
School of Management, South-Central University for Nationalities, Wuhan, 430074
2.
Department of Automation, School of Power and Mechanical Engineering, Wuhan University, Wuhan, 430072

Received: July 31, 2014

Revised: January 31, 2015

Published: March 2016

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Abstract

This article deals with the problem of making simultaneous decisions on the location, capacity and demand flow assignment for intermediate facilities in a network. Two nonlinear mixed-integer program (NMIP) models for continuous and discrete capacity decisions are proposed, respectively. The objective is to minimize the total costs, including fixed location cost, transportation cost, congestion cost and capacity cost. Congestion at intermediate facilities is modeled as the ratio of total flow to surplus capacity by viewing each facility as an M/M/1 queuing system. To solve NMIP with continuous capacity decision, we apply the Lagrangean algorithm that has been proposed to solve the classic inventory-location model. For the NMIP with discrete capacity decision, we propose another Lagrangean algorithm where the problem is decomposed into $|K|$ subproblems that can be solved to optimality. The measures of allocation heuristic, capacity increase and capacity adjustment are taken to construct feasible solutions. Computational results indicate that the heuristics for the two models are both efficient and effective.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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