 
Summary: Digital Object Identifier (DOI) 10.1007/s1010700304658
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 © SpringerVerlag 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],
