Optimal common due-date with completion time tolerance

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Abstract

The common due-date problem involves minimizing the absolute deviation around a common due-date. An interesting variation modifies the problem so that no penalty costs are incurred for jobs completing within the tolerance interval of the common due-date. For tolerance intervals that are less than half the execution time of the shortest job, solution techniques have been developed. However, the techniques do not extend to tolerance intervals of any arbitrarily chosen size. In this paper, for a variety of penalty functions we develop a polynomial time solution algorithm for any size tolerance interval. We also demonstrate how optimizing techniques developed in this paper can be applied to a common due-date problem with a partial set of fixed jobs and a predetermined common due-date.

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    They present a polynomial solution procedure for Kanet's (1981) problem with small symmetric CDWs. Wilamowsky et al. (1996) extend these results to large symmetric and asymmetric CDWs and to different but non-individual earliness and tardiness penalties. Baker and Scudder (1990) present a solution procedure for Kanet's (1981) problem with small CDWs for each job and continuous penalty functions.

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Dr. Yonah Wilamowsky is Professor of Computing and Decision Sciences at Seton Hall University. He serves as a consultant to government agencies, corporations and law firms in statistics and operations research. His current research interests include job scheduling, multiple objective decision making as well as statistical applications in the law. He has published articles in such journals as Naval Research Logistics Quarterly, Journal of the Operational Research Society, American Journal of Mathematical and Management Sciences, and Property Tax Journal. Dr. Wilamowsky received his Ph.D. in Operations Research from New York University.

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Dr. Sheldon Epstein in Associate Dean and Professor of Computing and Decision Sciences at Seton Hall University. He also serves as a statistical consultant for municipalities and law firms on issues of real estate taxation and assessment uniformity. He previously was an Operations Research Analyst for Trans World Airlines. He received his Ph.D. in Operations Research from New York University. His research interests include statistics and the law, opportunistic replacement and decision theory. He has published articles in such journals as Naval Research Logistics Quarterly, Journal of the Operational Research Society, Computers and Operations Research, and Property Tax Journal.

Dr. Bernard Dickman is Associate Professor of Quantitative Methods at Hofstra University. He previously was a Management Science Consultant at the Celanese Corporation. He received his Ph.D. in Operations Research from New York University. His research interests include optimization theory, graph theory, and due-date scheduling. He has published articles in such journals as OMEGA, The Journal of Optimization Theory and Applications, Journal of the Operational Research Society, and American Journal of Mathematical and Management Sciences.

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