Fully Polynomial Approximation Schemes for Single-Item Capacitated Economic Lot-Sizing Problems

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

Scheduling linear deteriorating jobs with an availability constraint on a single machine

2006-2007 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

Combinatorial Optimization

This report summarizes the meeting on Combinatorial Optimization where new and promising developments in the field were discussed. Th

Order Acceptance and Scheduling: A Taxonomy and Review

Over the past 20 years, the topic of order acceptance has attracted considerable attention from those who study scheduling and those who practice it. In a firm that strives to align its functions so that profit is maximized, the coordination of capacity with demand may require that business sometimes be turned away. In particular, there is a trade-off between the revenue brought in by a particular order, and all of its associated costs of processing. The present study focuses on the body of research that approaches this trade-off by considering two decisions: which orders to accept for processing, and how to schedule them. This paper presents a taxonomy and a review of this literature, catalogs its contributions and suggests opportunities for future research in this area

Mathematics in the Supply Chain

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Meta-Heuristics for Dynamic Lot Sizing: a review and comparison of solution approaches

Proofs from complexity theory as well as computational experiments indicate that most lot sizing problems are hard to solve. Because these problems are so difficult, various solution techniques have been proposed to solve them. In the past decade, meta-heuristics such as tabu search, genetic algorithms and simulated annealing, have become popular and efficient tools for solving hard combinational optimization problems. We review the various meta-heuristics that have been specifically developed to solve lot sizing problems, discussing their main components such as representation, evaluation neighborhood definition and genetic operators. Further, we briefly review other solution approaches, such as dynamic programming, cutting planes, Dantzig-Wolfe decomposition, Lagrange relaxation and dedicated heuristics. This allows us to compare these techniques. Understanding their respective advantages and disadvantages gives insight into how we can integrate elements from several solution approaches into more powerful hybrid algorithms. Finally, we discuss general guidelines for computational experiments and illustrate these with several examples

Algorithms for discrete, non-linear and robust optimization problems with applications in scheduling and service operations

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2011.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student submitted PDF version of thesis.Includes bibliographical references (p. 101-107).This thesis presents efficient algorithms that give optimal or near-optimal solutions for problems with non-linear objective functions that arise in discrete, continuous and robust optimization. First, we present a general framework for designing approximation schemes for combinatorial optimization problems in which the objective function is a combination of more than one function. Examples of such problems include those in which the objective function is a product or ratio of two or more linear functions, parallel machine scheduling problems with the makespan objective, robust versions of weighted multi-objective optimization problems, and assortment optimization problems with logit choice models. For many of these problems, we give the first fully polynomial time approximation scheme using our framework. Next, we present approximation schemes for optimizing a rather general class of non-linear functions of low rank over a polytope. In contrast to existing results in the literature, our approximation scheme does not require the assumption of quasi-concavity of the objective function. For the special case of minimizing a quasi-concave function of low-rank, we give an alternative algorithm which always returns a solution which is an extreme point of the polytope. This algorithm can also be used for combinatorial optimization problems where the objective is to minimize a quasi-concave function of low rank. We also give complexity-theoretic results with regards to the inapproximability of minimizing a concave function over a polytope. Finally, we consider the problem of appointment scheduling in a robust optimization framework. The appointment scheduling problem arises in many service operations, for example health care. For each job, we are given its minimum and maximum possible execution times. The objective is to find an appointment schedule for which the cost in the worst case scenario of the realization of the processing times of the jobs is minimized. We present a global balancing heuristic, which gives an easy to compute closed form optimal schedule when the underage costs of the jobs are non-decreasing. In addition, for the case where we have the flexibility of changing the order of execution of the jobs, we give simple heuristics to find a near-optimal sequence of the jobs.by Shashi Mittal.Ph.D

An overview of decision table literature 1982-1995.

This report gives an overview of the literature on decision tables over the past 15 years. As much as possible, for each reference, an author supplied abstract, a number of keywords and a classification are provided. In some cases own comments are added. The purpose of these comments is to show where, how and why decision tables are used. The literature is classified according to application area, theoretical versus practical character, year of publication, country or origin (not necessarily country of publication) and the language of the document. After a description of the scope of the interview, classification results and the classification by topic are presented. The main body of the paper is the ordered list of publications with abstract, classification and comments.