We consider the single item capacitated lot–sizing problem, a well-known production planning model that often arises in practical applications, and derive new classes of valid inequalities for it. We first derive new, easily computable valid inequalities for the continuous 0–1 knapsack problem, which has been introduced recently and has been shown to provide a useful relaxation of mixed 0-1 int...

We consider the single item capacitated lot sizing problem a well known produc tion planning model that often arises in practical applications and derive new classes of valid inequalities for it We also derive new easily computable valid inequalities for the continuous knapsack problem The continuous knapsack problem has been introduced recently and has been shown to provide a useful relaxation...

Lot sizing and scheduling in flow shop has been considered in this paper. Our study includes a multi-level and multi-period capacitated lot sizing and scheduling problem (CLSP) with sequence-dependent setups, setups carry over in flow shop. In manufacturing environments backlogging is unavoidable. If the production capacity is infinite, any demand can be satisfied

We present a fully polynomial time approximation scheme (FPTAS) for a capacitated economic lot-sizing problem with a monotone cost structure. An FPTAS delivers a solution with a given relative error ε in time polynomial in the problem size and in 1/ε. Such a scheme was developed by van Hoesel and Wagelmans [8] for a capacitated economic lot-sizing problem with monotone concave (convex) producti...

NP{hard cases of the single{item capacitated lot{sizing problem have been the topic of extensive research and continue to receive considerable attention. However, surprisingly few theoretical results have been published on approximation methods for these problems. To the best of our knowledge, until now no polynomial approximation method is known which produces solutions with a relative deviati...

This paper addresses the independent multi-plant, multi-period, and multi-item capacitated lot sizing problem where transfers between the plants are allowed. This is an NP-hard combinatorial optimization problem and few solution methods have been proposed to solve it. We develop a GRASP (Greedy Randomized Adaptive Search Procedure) heuristic as well as a pathrelinking intensification procedure ...

In this paper, we consider the well-known constant-batch lot-sizing problem, which we refer to as the single module capacitated lot-sizing (SMLS) problem, and multi-module capacitated lot-sizing (MMLS) problem. We provide sufficient conditions under which the (k, l, S, I) inequalities of Pochet and Wolsey (Math of OR 18: 767-785, 1993), the mixed (k, l, S, I) inequalities, derived using mixing ...