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General Paper

Scheduling and lot sizing models for the single-vendor multi-buyer problem under consignment stock partnership

, , &
Pages 995-1009 | Received 01 May 2011, Accepted 01 Jul 2012, Published online: 21 Dec 2017
 

Abstract

We consider a centralized supply chain composed of a single vendor serving multiple buyers and operating under consignment stock arrangement. Solving the general problem is hard as it requires finding optimal delivery schedule to the buyers and optimal production lot sizes. We first provide a nonlinear mixed integer programming formulation for the general scheduling and lot sizing problem. We show that the problem is NP-hard in general. We reformulate the problem under the assumption of ‘zero-switch rule’. We also provide a simple sequence independent lower bound to the solution of the general model. We then propose a heuristic procedure to generate a near-optimal delivery schedule. We assess the cost performance of that heuristic by conducting sensitivity analysis on the key model parameters. The results show that the proposed heuristic promises substantial supply-chain cost savings that increase as the number of buyers increases.

Acknowledgements

The authors would like to thank the two anonymous reviewers for their insightful comments and helpful suggestions which have significantly improved the content and quality of the paper.

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