Fast Approximation Algorithms for the One-Warehouse Multi-Retailer Problem Under General Cost Structures and Capacity Constraints

Jean-Philippe Lucien Gayon (1) , Guillaume Massonnet (2) , Christophe Rapine (3) , Gautier Stauffer (1)

1 G-SCOP_OC - Optimisation Combinatoire
2 LS2N - Laboratoire des Sciences du Numérique de Nantes
3 LGIPM - Laboratoire de Génie Industriel, de Production et de Maintenance

We consider a well-studied multi-echelon (deterministic) inventory control problem, known in the literature as the one-warehouse multi-retailer (OWMR) problem. We propose a simple and fast 2-approximation algorithm for this NP-hard problem, by recombining the solutions of single-echelon relaxations at the warehouse and at the retailers. We then show that our approach remains valid under quite general assumptions on the cost structures and under capacity constraints at some retailers. In particular, we present the first approximation algorithms for the OWMR problem with nonlinear holding costs, truckload discount on procurement costs, or with capacity constraints at some retailers. In all cases, the procedure is purely combinatorial and can be implemented to run in low polynomial time.

Mots clés: approximation algorithms; combinatorial algorithm; multi-echelon inventory problem; lot sizing

Domaines: Recherche opérationnelle [math.OC]

Jean-Philippe Lucien Gayon, Guillaume Massonnet, Christophe Rapine, Gautier Stauffer. Fast Approximation Algorithms for the One-Warehouse Multi-Retailer Problem Under General Cost Structures and Capacity Constraints. Mathematics of Operations Research, 2017, 42 (3), pp.854-875. ⟨10.1287/moor.2016.0830⟩. ⟨hal-01978078⟩