Dynamic Lot Sizing for Multi-Echelon Distribution Systems with Purchasing and Transportation Price Discounts

Moustapha Diaby and Alain Martel
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Moustapha Diaby: Arizona State University, Tempe, Arizona
Alain Martel: Laval University, Quebec, Canada

Operations Research, 1993, vol. 41, issue 1, 48-59

Abstract: We consider the problem of determining optimal purchasing and shipping quantities over a finite planning horizon for arborescent, multi-echelon physical distribution systems with deterministic, time-varying demands. We assume that the inventory holding cost at a given warehouse of the distribution network is a linear function of the inventory level, and that the total procurement cost (i.e., ordering, plus purchasing, plus transportation and reception costs) is a general piecewise-linear function of the quantities shipped to and from the warehouse. We formulate a mixed integer linear programming model of the problem and develop a Lagrangian relaxation-based procedure to solve it. We show computational results for problems with 12 periods, up to 15 warehouses, and 3 transportation price ranges.

Keywords: inventory/production: multi-echelon lot sizing; programming: integer; branch and bound; relaxation/subgradient (search for similar items in EconPapers)
Date: 1993
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