In this paper, we study deterministic dynamic lot-sizing problems with service level constraints on the total number of periods in which backorders can occur over the finite planning horizon. We give a natural mixed integer programming formulation for the single item problem (LS-SL-I) and study the structure of its solution. We show that an optimal solution to this problem can be found in O(n2κ...

We study two different lot-sizing problems with time windows that have been proposed recently. For the case of production time windows, in which each client specific order must be produced within a given time interval, we derive tight extended formulations for both the constant capacity and uncapacitated problems with Wagner-Whitin (non-speculative) costs. For the variant with nonspecific order...

We consider the dynamic lot-sizing problem with finite capacity and possible lost sales for a process that could be kept warm at a unit variable cost for the next period t + 1 only if more than a threshold value Qt has been produced and would be cold, otherwise. Production with a cold process incurs a fixed positive setup cost, Kt and setup time, St, which may be positive. Setup costs and times...

We consider the single item lot-sizing problem with capacities that are non-decreasing over time. When the cost function is i) non-speculative or Wagner-Whitin (for instance, constant unit production costs and non-negative unit holding costs), and ii) the production set-up costs are non-increasing over time, it is known that the minimum cost lotsizing problem is polynomially solvable using dyna...

In this paper we propose exact solution methods for a bilevel uncapacitated lot-sizing problem with backlogs. This is an extension of the classical uncapacitated lot-sizing problem with backlogs, in which two autonomous and self-interested decision makers constitute a twoechelon supply chain. The leader buys items from the follower in order to meet external demand at lowest cost. The follower a...

The wellknown CLSP problem is generalized including sequence dependent setup times and overtimes and modeling it as a quadratic mixed 0-1 integer programming problem called Capacitated Lot Sizing Problem with Sequence Dependent Setups and Overtimes. We develop a heuristics based on Lagrangean relaxation and tabu search for solving the problem. At the end, some computational results are presented.

In this paper we describe the model of an actual problem from the chemical industry, for which we developed a planning and lot-sizing tool. The production process is characterized by a two-stage product structure as well as sequence-dependent setup cost and setup times. The develop a model which is a modified version of the General Lot-sizing and Scheduling Problem (GLSP) framework and combines...

This paper proposes a mixed integer programming model for single-item capacitated lot-sizing problem with setup times, safety stock, demand shortages, outsourcing and inventory capacity. Due to the complexity of problem, three meta-heuristics algorithms named simulated annealing (SA), vibration damping optimization (VDO) and harmony search (HS) have been used to solve this model. Additionally, ...

A game merging the lot-sizing problem with a Cournot competition model is for the first time theoretically studied. Each player is a producer with her own production facility, modeled as an uncapacitated lot-sizing problem (i.e., production incurs set-up and variable costs and inventories are allowed). A Cournot competition is played in each time period (market) with each player deciding the qu...