http://repub.eur.nl/res/aut/1253/ List of Publications en http://repub.eur.nl/static-eur/img/logo.png http://repub.eur.nl http://repub.eur.nl/res/pub/14435/ 2001-05-01T00:00:00Z 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 that produces solutions with a relative deviation from optimality that is bounded by a constant. In this paper we show that such methods do exist by presenting an even stronger result: the existence of fully polynomial approximation schemes. The approximation scheme is first developed for a quite general model, which has concave back logging and production cost functions and arbitrary (monotone) holding cost functions. Subsequently we discuss important special cases of the model and extensions of the approximation scheme to even more general models. http://repub.eur.nl/res/pub/2319/ 2000-06-05T00:00:00Z In this paper we consider the important special case of the economic lot-sizing problem in which there are no speculative motives to hold inventory. We analyze the effects of varying all setup costs by the same amount. This is equivalent to studying the set of optimal production periods when the number of such periods changes. We show that this optimal set changes in a very structured way. This fact is interesting in itself and can be used to develop faster algorithms for such problems as the computation of the stability region and the determination of all efficient solutions of a lot-sizing problem. Furthermore, we generalize two related convexity results which have appeared in the literature. http://repub.eur.nl/res/pub/1406/ 1997-01-01T00:00:00Z 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 deviation from optimality that is bounded by a constant. In this paper we show that such methods do exist, by presenting an even stronger result: the existence of fully polynomial approximation schemes. The approximation scheme is first developed for a quite general model, which has concave backlogging and production cost functions and arbitrary (monotone) holding cost functions. Subsequently we discuss important special cases of the model and extensions of the approximation scheme to even more general models. http://repub.eur.nl/res/pub/2304/ 1996-09-01T00:00:00Z Presents an algorithm which determines the optimal permutations for all machine speeds in O(n log n) time where the algorithm n is the number of jobs. Description of the two-machine flow shop problem; Use of the algorithm as an elementary dominance relation; Description of the algorithm; Correctness of the algorithm. http://repub.eur.nl/res/pub/2305/ 1996-01-01T00:00:00Z Presents an algorithm that solves the constant capacities economic lot-sizing problem, with concave production costs and linear holdings cost in O(T3) time. Notations used; Results of a greedy algorithm; Global algorithm for solving lot-sizing problems. http://repub.eur.nl/res/pub/2306/ 1994-11-15T00:00:00Z When jobs have to be processed on a set of identical parallel machines so as to minimize the makespan of the schedule, list scheduling rules form a popular class of heuristics. The order in which jobs appear on the list is assumed here to be determined by the relative size of their processing times; well-known special cases are the LPT rule and the SPT rule, in which the jobs are ordered according to non-increasing and non-decreasing processing time respectively. When all processing times are exactly known, a given list scheduling rule will generate a unique assignment of jobs to machines. However, when there exists a priori uncertainty with respect to one of the processing times, then there will be, in general, several possibilities for the assignment that will be generated once the processing time is known. This number of possible assignments may be viewed as a measure of the sensitivity of the list scheduling rule that is applied. We derive bounds on the maximum number of possible assignments for several list scheduling heuristics, and we also study the makespan associated with these assignments. In this way we obtain analytical support for the intuitively plausible notion that the sensitivity of a list scheduling rule increases with the quality of the schedule produced. http://repub.eur.nl/res/pub/2308/ 1994-02-01T00:00:00Z A class of strong valid inequalities is described for the single-item uncapacitated economic lot-sizing problem with start-up costs. It is shown that these inequalities yield a complete polyhedral characterization of the problem. The corresponding separation problem is formulated as a shortest path problem. Finally, a reformulation as a plant location problem is shown to imply the class of strong valid inequalities, which shows that this reformulation is tight, also.