A Polyhedral Study of Multiechelon Lot Sizing with Intermediate Demands

Authors:
Minjiao Zhang;Simge Küçükyavuz;Hande Yaman
Affiliations:
Department of Integrated Systems Engineering, The Ohio State University, Columbus, Ohio 43210;Department of Integrated Systems Engineering, The Ohio State University, Columbus, Ohio 43210;Department of Industrial Engineering, Bilkent University, Ankara, Turkey
Venue:
Operations Research
Year:
2012

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Abstract

In this paper, we study a multiechelon uncapacitated lot-sizing problem in series (m-ULS), where the output of the intermediate echelons has its own external demand and is also an input to the next echelon. We propose a polynomial-time dynamic programming algorithm, which gives a tight, compact extended formulation for the two-echelon case (2-ULS). Next, we present a family of valid inequalities for m-ULS, show its strength, and give a polynomial-time separation algorithm. We establish a hierarchy between the alternative formulations for 2-ULS. In particular, we show that our valid inequalities can be obtained from the projection of the multicommodity formulation. Our computational results show that this extended formulation is very effective in solving our uncapacitated multi-item two-echelon test problems. In addition, for capacitated multi-item, multiechelon problems, we demonstrate the effectiveness of a branch-and-cut algorithm using the proposed inequalities.