An inverse economic lot-sizing approach to eliciting supplier cost parameters

Recent literature on supply chain coordination offers a wide range of game theoretic and optimization approaches that ensure efficient planning in the supply chain, but assume that the involved parties have complete information about each other. However, in reality, complete information is rarely available, and those models alone do not present any incentive for the parties to reveal their private information, e.g., the cost parameters that they use when solving their planning problems. This paper proposes an inverse lot-sizing model for eliciting the cost parameters of a supplier from historic demand vs. optimal delivery lot-size pairs, gathered during repeated earlier encounters. It is assumed that the supplier solves a single-item, multi-period, uncapacitated lot-sizing problem with backlogs to optimality to calculate its lot-sizes, and the buyer is aware of this fact. The inverse lot-sizing problem is reformulated to an inverse shortest path problem, which is, in turn, solved as a linear program. This model is used to compute the ratios of the supplier's cost parameters, i.e., the setup, the holding, and the backlog cost parameters consistent with all the historic samples. The elicited cost parameters can be used as input for various game theoretic or bilevel optimization models for supply chain coordination. Computational experiments on randomly generated problem instances indicate that the approach is very efficient in predicting future supplier actions from the historic records. (C) 2013 Elsevier B.V. All rights reserved.