A polyhedral study of lot-sizing with supplier selection

Abstract The traditional lot-sizing problem is to find the least cost production lot-sizes in several time periods. We consider the lot-sizing model together with simultaneous selection of suppliers, which have variable and fixed costs. We study the underlying polytope. We provide valid inequalities for the uncapacitated case and we give sufficient and necessary conditions for facet-defining inequalities. We also give a full description of the underlying polyhedron. For the general capacitated case, we show how to derive several families of valid inequalities from standard lot-sizing valid inequalities.

[1]  Laurence A. Wolsey,et al.  The uncapacitated lot-sizing problem with sales and safety stocks , 2001, Math. Program..

[2]  Laurence A. Wolsey,et al.  Modelling Practical Lot-Sizing Problems as Mixed-Integer Programs , 2001, Manag. Sci..

[3]  Alper Atamtürk,et al.  Flow pack facets of the single node fixed-charge flow polytope , 2001, Oper. Res. Lett..

[4]  Laurence A. Wolsey,et al.  Uncapacitated lot-sizing: The convex hull of solutions , 1984 .

[5]  Miguel Constantino,et al.  Lower Bounds in Lot-Sizing Models: A Polyhedral Study , 1998, Math. Oper. Res..

[6]  Alper Atamtürk,et al.  A study of the lot-sizing polytope , 2004, Math. Program..

[7]  Miguel Fragoso Constantino,et al.  Lotsizing with backlogging and start-ups: the case of Wagner-Whitin costs , 1999, Oper. Res. Lett..

[8]  Miguel Constantino,et al.  A cutting plane approach to capacitated lot-sizing with start-up costs , 1996, Math. Program..

[9]  Martin W. P. Savelsbergh,et al.  On the capacitated lot-sizing and continuous 0-1 knapsack polyhedra , 2000, Eur. J. Oper. Res..

[10]  Laurence A. Wolsey,et al.  Production Planning by Mixed Integer Programming , 2010 .

[11]  U. S. Palekar,et al.  A variable redefinition approach for the lot sizing problem with strong set-up interactions , 2001 .

[12]  Thomas L. Magnanti,et al.  Facets and algorithms for capacitated lot sizing , 1989, Math. Program..

[13]  László Lovász,et al.  Graph Theory and Integer Programming , 1979 .

[14]  Laurence A. Wolsey,et al.  Dynamic knapsack sets and capacitated lot-sizing , 2003, Math. Program..

[15]  Martin W. P. Savelsbergh,et al.  Lifted flow cover inequalities for mixed 0-1 integer programs , 1999, Math. Program..

[16]  Yves Pochet.  Valid inequalities and separation for capacitated economic lot sizing , 1988 .

[17]  Laurence A. Wolsey,et al.  Modelling piecewise linear concave costs in a tree partitioning problem , 1994, Discret. Appl. Math..

[18]  Laurence A. Wolsey,et al.  Lot-Sizing with Constant Batches: Formulation and Valid Inequalities , 1993, Math. Oper. Res..

[19]  Laurence A. Wolsey,et al.  Lot-size models with backlogging: Strong reformulations and cutting planes , 1988, Math. Program..

[20]  Laurence A. Wolsey,et al.  Valid inequalities for mixed 0-1 programs , 1986, Discret. Appl. Math..