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Digital Object Identifier (DOI) 10.1007/s10107-003-0465-8 Math. Program., Ser. A 99: 443465 (2004)

Summary: Digital Object Identifier (DOI) 10.1007/s10107-003-0465-8
Math. Program., Ser. A 99: 443­465 (2004)
Alper Atamt¨urk · Juan Carlos Mu~noz
A study of the lot­sizing polytope
Received: October 8, 2002 / Accepted: June 25, 2003
Published online: August 18, 2003 ­ © Springer-Verlag 2003
Abstract. The lot­sizing polytope is a fundamental structure contained in many practical production plan-
ning problems. Here we study this polytope and identify facet­defining inequalities that cut off all fractional
extreme points of its linear programming relaxation, as well as liftings from those facets. We give a polyno-
mial­time combinatorial separation algorithm for the inequalities when capacities are constant. We also report
computational experiments on solving the lot­sizing problem with varying cost and capacity characteristics.
1. Introduction
Given the demand, production cost, and inventory holding cost for a product and produc-
tion capacities and production setup cost for each time period over a finite discrete­time
horizon, the lot­sizing problem is to determine how much to produce and hold as inven-
tory in each time period so that the sum of production, inventory holding, and setup costs
over the horizon is minimized. The lot­sizing problem (LSP) is NP­hard (Florian et al.
[9]). Several special cases, including the uncapacitated and constant­capacity cases, of
the problem are solved in polynomial time; see Bitran and Yanasse [5], Federgruen and
Tzur [7], Florian and Klein [8], van Hoesel and Wagelmans [20], Wagelmans et al. [21],


Source: Atamtürk, Alper - Department of Industrial Engineering and Operations Research, University of California at Berkeley


Collections: Engineering