Capacitated Multi-Item Lot-Sizing Problems with Time Windows

Abstract

This research concerns a new family of capacitated multi-item lot-sizing problems, namely, lot-sizing problems with time windows. Two classes of the problem are analyzed and solved using different Lagrangian heuristics. Capacity constraints and a subset of time window constraints are relaxed resulting in particular single-item time window problems that are solved in polynomial time. Other relaxations leading to the classical Wagner-Whitin problem are also tested. Several smoothing heuristics are implemented and tested, and their results are compared. The gaps between lower and upper bounds for most problems are very small (less than 1%). Moreover, the proposed algorithms are robust and do not seem to be too affected when different parameters of the problem are varied.

Capacitated lot‐sizing and scheduling with parallel machines, back‐orders, and setup carry‐over

“…Various formulations of the big bucket CLSP and solution approaches including extensions to multilevel product structures are well known (e.g., [5,6,29,37,39,41,50,57]). Reviews and taxonomies of such models and solution procedures are given by Bahl et al [2], Maes and Van Wassenhove [33], Kuik et al [30], Karimi et al [27], Jans and Degraeve [25], Quadt and Kuhn [46], and Buschkühl et al [7].…”

“…Conditions (6) state that a machine needs to have the correct setup state to carry it over to the next period. That is, if a machine m carries over a setup state for product p from period t to t + 1 (ζ ptm = 1), the machine must have made a setup for this product in period t (γ ptm = 1) or the setup state had been carried over from the previous period (ζ p,t−1,m = 1).…”

Dynamic lot‐sizing model with production time windows

“…As shown in Table 1, it takes a lot of time to obtain an optimal solution when the planning horizon T is larger than 40. For practical purposes, it would be desirable to apply a pseudo polynomial time algorithm or a heuristic algorithm as was done in [2,4]. Finally, we note that in the case of non-customer specific time windows with concave costs the O(T 3 ) algorithm in [8] can be applied to find an optimum solution.…”

“…If there is no such restriction, the general model is called customer specific [4]. Recently, Brahimi et al [2] extended the model into capacitated multi-item case with non-customer/customer specific production time windows and Wolsey [18] presented tight extended formulations for various production and delivery time window models.…”

Lot-sizing with production and delivery time windows

“…In Brahimi, Dauzère-Pérès and al. [3,2,6] the production time window is the interval during which the order must be produced. For this problem, two variants are considered: in the first each order is distinct (client-specific), whereas in the second orders are indistinguishable (non-specific).…”