A note on the equivalence of two heuristics to minimize total tardiness

Article Abstract:

The PSK heuristic proposed by S.S. Panwalkar, M. Smith and C.P. Koulamas for solving single machine tardiness problem provides an alternative implementation of the Modified Due Date (MDD) rule developed by K.R. Baker and J.W. Bertrand and based on the shortest processing time and earlier due date models. This explains the good solutions generated by the PSK rule. However, the Wilkerson-Irwin rule is not equivalent to the MDD policy, despite T.C. Cheng's assertion regarding their equivalency.

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On minimizing resource consumption with constraints on the makespan and the total completion time

Article Abstract:

The single machine scheduling problem with the objective of minimizing the total resource consumption when the amount of consumed resources depends on the release date of a job is considered. Specifically, Chun-Lun Li's results are extended to the cases of a convex decreasing consumption function and multiple consumption functions to develop conditions for the feasibility of solutions when constraints on the total completion time and the makespan are taken into account.

Resource allocation

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A note on minimizing the weighted sum of tardy and early completion penalties in a single machine: a case of small common due date

Article Abstract:

The problem of minimizing the weighted absolute deviation of completion times from a common due date in the single-machine scheduling of several batches of multiples jobs is considered. Specifically, the optimality of the largest processing time order is shown to be applicable for cases with a small due date and where the weights of jobs are proportional to processing times. In addition, an algorithm for generating optimal solutions to the problem is described.

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