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We consider a single machine scheduling problem in which the objective is to minimize the mean absolute deviation of job completion times about a common due date. We present an algorithm for determining multiple optimal schedules under restrictive assumptions about the due date. and an implicit enumeration procedure when the assumptions do not hold. Wc also establish the similarity of this problem to the two parallel machines mean flow time problem.

This paper addresses a nonpreemptive single machine scheduling problem where all jobs have a common due date and have zero ready time. The scheduling objective is to minimize mean squared deviation (MSD) of job completion times about the due date. This nonregular measure of performance is appropriate when earliness and tardiness are both penalized, and when large deviations of completion time from the due date are undesirable. A special case of the MSD problem, referred to as the unconstrained MSD problem, is shown to be equivalent to the completion time variance problem (CTV) studied by Merten and Muller (Merten, A. G., M. E. Muller. 1972. Variance minimization in single machine sequencing problems. Management Sci. 18(September) 518--528.) and Schrage (Schrage, L. 1975. Minimizing the time-in-system variance for a finite jobset. Management Sci. 21(May) 540--543.). Strong results for this latter problem are combined with several new propositions to develop a reasonably efficient procedure for solving the unconstrained MSD problem. This enables us to improve the existing procedures for the CTV problem. We also propose a branching procedure for the constrained MSD problem and present computational results.production/scheduling: job shop, deterministic, inventory/production: measures of effectiveness, programming: integer algorithms, branch and bound

We consider a single‐machine scheduling problem in which all jobs have the same due date and penalties are assessed for both early and late completion of jobs. However, earliness and tardiness are penalized at different rates. The scheduling objective is to minimize either the weighted sum of absolute deviations (WSAD) or the weighted sum of squared deviations (WSSD). For each objective we consider two versions of the problem. In the unconstrained version an increase in the due date does not yield any further decrease in the objective function. We present a constructive algorithm for the unconstrained WSAD problem and show that this problem is equivalent to the two‐parallel, nonidentical machine, mean flow‐time problem. For the unconstrained WSSD and the constrained WSAD and WSSD problems we propose implicit enumeration procedures based on several dominance conditions. We also report on our computational experience with the enumeration procedures.

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