This paper presents a generic modeling framework to simultaneously decide about production quantities and maintenance operations for a capacitated resource facing a dynamic demand for different types of products. As the resource needs to be setup for each specific type of product, a lot-sizing problem occurs. In addition it is assumed that production causes intensive wear and tear. For this rea...

Primal-dual algorithms have played an integral role in recent developments in approximation algorithms, and yet there has been little work on these algorithms in the context of LP relaxations that have been strengthened by the addition of more sophisticated valid inequalities. We introduce primal-dual schema based on the LP relaxations devised by Carr, Fleischer, Leung & Phillips for the minimu...

We consider a mixed integer set which generalizes two well-known sets: the single node fixedcharge network set and the single arc design set. Such set arises as a relaxation of feasible sets of general mixed integer problems such as lot-sizing and network design problems. We derive several families of valid inequalities that, in particular, generalize the arc residual capacity inequalities and ...

Production planning is an important task in manufacturing systems. We consider a real-world capacitated lot-sizing problem (CLSP) from the process industry. Because the problem requires discrete lot-sizes, domain-specific methods from the literature are not directly applicable. We therefore approach the problem with WSAT (OIP), a new domainindependent heuristic for integer optimization which ge...

This paper presents a capacitated lot-sizing problem in flow-shop system with energy consideration. The planning horizon is defined by a set of periods. Each period is characterized by demand, duration, electricity cost and maximum peak power. Both non-linear and linear mixed integer programming are proposed to solve the problem with the objective of minimizing the production costs. The costs a...

We address a multi-item capacitated lot-sizing problem with setup times, safety stock and demand shortages. Demand cannot be backlogged, but can be totally or partially lost. Safety stock is an objective to reach rather than an industrial constraint to respect. The problem is np-hard. We propose a Lagrangian relaxation of the resource capacity constraints. We develop a dynamic programming algor...

We address a multi-item capacitated lot-sizing problem with setup times that arises in real-world production planning contexts. Demand cannot be backlogged, but can be totally or partially lost. Safety stock is an objective to reach rather than an industrial constraint to respect. The problem is NP-hard. We propose mixed integer programming heuristics based on a planning horizon decomposition s...

We address a multi-item capacitated lot-sizing problem with setup times and shortage costs that arises in real-world production planning problems. Demand cannot be backlogged, but can be totally or partially lost. The problem is NP-hard. A mixed integer mathematical formulation is presented. Our approach in this paper is to propose some classes of valid inequalities based on a generalization of...

This paper presents a new algorithm for the dynamic Multi-Level Capacitated Lot Sizing Problem with Setup Carry-Overs (MLCLSP-L). The MLCLSP-L is a big-bucket model that allows the production of any number of products within a period, but it incorporates partial sequencing of the production orders in the sense that the first and the last product produced in a period are determined by the model....

In this paper we present some results of our systematic studies of ne-grained parallel versions of the island model of genetic algorithms and of variants of the neighborhood model (also called diiusion model) on the massively parallel computer MasPar MP1 with 16k processing elements. These parallel genetic algorithms have been applied to a range of diierent problems (e.g. traveling salesperson,...