Bernard Dickman

Optimal common due-date with completion time tolerance

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.

Optimal common due-date with limited completion time

Abstract T.C.E. Cheng [Computers Ops Res. 15, 91–96 (1988)] recently presented an interesting variation of the common due-date scheduling problem. He considered the situation where jobs that only marginally miss the common due-date are not penalized. His major conclusion, as given in Lemma 1, is a sufficient but not necessary requirement for optimality. We prove that alternate optima exist.

Deterministic multiprocessor scheduling with multiple objectives

Abstract One common job scheduling objective is to minimize makespan. The problem can be modeled as integer linear programming (ILP) and will often have multiple alternative optimal solutions. However, secondary considerations, e.g. minimizing the second latest completion time, may very well dictate a preference between solutions with identical makespans. Because of the nature of the primary objective, standard approaches for optimizing a prioritized set of multiple objectives will not work. In this paper we prove that for unit time problems, an appropriate objective function can be formulated, which, when optimized, satisfies both the primary and secondary objectives. Moreover, the new formulation can be modeled as a classical assignment problem (AP). This has the added advantage of efficiency of solution and availability of software. Applications to computer processor scheduling and the military are presented.

Modeling Deterministic Opportunistic Replacement as an Integer Programming Problem

SYNOPTIC ABSTRACTThe field of opportunistic replacement deals with the benefits of performing maintenance on equipment prior to failure in order to avoid prohibitively high costs associated with failure. Problems of a deterministic nature, i.e., where the exact times of both mandatory replacement and maintenance opportunities are known at the outset, with infinite time horizons have been solved for the two component case using a specialized algorithm. This paper presents a more general integer programming formulation of the problem that will work for any specified time frame. The results are of theoretical as well as practical significance in solving problems such as maintenance scheduling in fusion power plants.