The single machine problem with a quadratic cost function of completion times

Article Abstract:

Research has been conducted on a single machine sequencing problem with a quadratic cost function of completion times. A precedence relation has been developed that determines the ordering between adjacent jobs in which the precedence relation changes direction after a critical start time. A solution procedure incorporating these relations was applied to problems with job sizes between 15 and 100. The procedure solved 191 out of 200 test problems without using enumeration methods. The nine problems that were not solved directly were easily solved by inspection after they had been reduced to 10 smaller problems.

Operations research, Research, Management science, Stochastic processes, Quadratic programming

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A sequencing problem with release dates and clustered jobs

Article Abstract:

A one-machine scheduling problem is considered in which the objective is to minimize the sum of weighted completion times subject to release dates. For cases in which jobs are clustered, a polynomial time algorithm is developed. It is necessary to process the jobs in each cluster sequentially and to make sure the clusters are ordered. An efficient heuristic for the weighted completion time problem without clusters is used to present the insights developed. Also described is a class of release date problems for which the heuristic finds an optimal solution.

Models, Scheduling (Management), Production planning

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Asymptotic methods in the probabilistic analysis of sequencing and packing heuristics

Article Abstract:

There has been substantial interest recently in heuristics' average-case performance. Sequencing and packing problems in this area are explored. Methods are examined that have been utilized to get formal, probabilistic analyses of heuristics for one-dimensional bin packing and for 'makespan' scheduling. It is suggested that fresh methods are needed in the probabilistic analysis of packing and sequencing problems.

Methods, Integer programming, Probabilistic number theory

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