A simultaneous inventory control and facility location model with stochastic capacity constraints

Pablo A. Miranda, Rodrigo A. Garrido

Research output: Contribution to journalArticlepeer-review

61 Citations (Scopus)

Abstract

Traditionally, logistics analysts divide decisions levels into strategic, tactical and operational. Often these levels are considered separately for modeling purposes. The latter may conduce to make non-optimal decisions, since in reality there is interaction between the different levels. In this research, a cross-level model is derived to analyze decisions about inventory control and facility location, specially suited to urban settings, where the storage space is scarce and the vehicles' capacity is usually restricted. Both conditions, on the one hand make the problem difficult to solve optimally but on the other hand make it more realistic and useful in practice. This paper presents a simultaneous nonlinear-mixed-integer model of inventory control and facility location decisions, which considers two novel capacity constraints. The first constraint states a maximum lot size for the incoming orders to each warehouse, and the second constraint is a stochastic bound to inventory capacity. This model is NP-Hard and presents nonlinear terms in the objective function and a nonlinear constraint. A heuristic solution approach is introduced, based on Lagrangian relaxation and the subgradient method. Numerical experiments were designed and applied. The solution procedure presented good performance in terms of the objective function. One of the key conclusions of the proposed modeling approach is the fact that a reduction of the inventory capacity does not necessarily imply an increase in the number of installed warehouses. In fact, reducing the order size allows the optimal allocation of customers (those with higher variances) into different warehouses, reducing the total system's cost.

Original languageEnglish
Pages (from-to)39-53
Number of pages15
JournalNetworks and Spatial Economics
Volume6
Issue number1
DOIs
Publication statusPublished - 1 Mar 2006

Keywords

  • Chance constrained programming
  • Facilities location
  • Inventory
  • Lagrangian relaxation

ASJC Scopus subject areas

  • Software
  • Computer Networks and Communications
  • Artificial Intelligence

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