Reformulation by discretization: Application to economic lot sizing

In this paper we apply a discretization reformulation technique to the classical economic lot sizing problem. This reformulation yields the same LP bounds as the original model. We show, however, that by reducing adequately the coefficients of some variables, one obtains an enhanced reformulation whose LP relaxation solution is integer.

[1]  Stephen C. Graves,et al.  Technical Note - An n-Constraint Formulation of the (Time-Dependent) Traveling Salesman Problem , 1980, Oper. Res..

[2]  J. Schneider The time-dependent traveling salesman problem , 2002 .

[3]  A. Federgruen,et al.  A Simple Forward Algorithm to Solve General Dynamic Lot Sizing Models with n Periods in 0n log n or 0n Time , 1991 .

[4]  R. Kipp Martin,et al.  Large scale linear and integer optimization - a unified approach , 1998 .

[5]  Harvey M. Wagner,et al.  Dynamic Version of the Economic Lot Size Model , 2004, Manag. Sci..

[6]  G. D. Eppen,et al.  Solving Multi-Item Capacitated Lot-Sizing Problems Using Variable Redefinition , 1987, Oper. Res..

[7]  Stephen C. Graves,et al.  The Travelling Salesman Problem and Related Problems , 1978 .

[8]  Albert P. M. Wagelmans,et al.  Economic Lot Sizing: An O(n log n) Algorithm That Runs in Linear Time in the Wagner-Whitin Case , 1992, Oper. Res..

[9]  Luís Gouveia,et al.  A 2n Constraint Formulation for the Capacitated Minimal Spanning Tree Problem , 1995, Oper. Res..

[10]  S. Voß,et al.  A classification of formulations for the (time-dependent) traveling salesman problem , 1995 .

[11]  Luís Gouveia,et al.  On the capacitated concentrator location problem: a reformulation by discretization , 2006, Comput. Oper. Res..

[12]  R. Kipp Martin,et al.  Generating Alternative Mixed-Integer Programming Models Using Variable Redefinition , 1987, Oper. Res..

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

[14]  Alok Aggarwal,et al.  Improved Algorithms for Economic Lot Size Problems , 1993, Oper. Res..