This paper considers the capacitated multi-level lot-sizing problem with setup times, a class of difficult problems often faced in practical production planning settings. In the literature, relax-and-fix is a technique commonly applied to solve this problem due to the fact that setup decisions in later periods of the planning horizon are sensitive to setup decisions in the early periods but not...

We study the multi–item capacitated lot–sizing problem with setup times (MCL). This model appears often in practice, either in its pure form or with additional constraints, but it is very difficult to solve to optimality. In MCL demand for multiple items must be met over a time horizon, items compete for a shared capacity, and each setup uses up some of this capacity. By analyzing the polyhedra...

We introduce Horizon Decomposition in the context of Dantzig-Wolfe Decomposition, and apply it to the Capacitated Lot-Sizing Problem with Setup Times. We partition the problem horizon in contiguous overlapping intervals and create subproblems identical to the original problem, but of smaller size. The user has the flexibility to regulate the size of the master problem and the subproblem via two...

Lot-sizing problems are cornerstone optimization problems for production planning with time varying demand. We analyze the quality of bounds, both lower and upper, provided by a range of fast algorithms. Special attention is given to LP-based rounding algorithms.

The multi-item single level capacitated dynamic lot-sizing problem consists of scheduling N items over a horizon of T periods. The objective is to minimize the sum of setup and inventory holding costs over the horizon subject to a constraint on total capacity in each period. No backlogging is allowed. Only one machine is available with a fixed capacity in each period. In case of a single item p...

In production planning, sequence dependent setup times and costs are often incurred for switchovers from one product to another. When setup times and costs do not respect the triangular inequality, a situation may occur where the optimal solution includes more than one batch of the same product in a single period — in other words, at least one sub tour exists in the production sequence of that ...