New results for an open time-dependent scheduling problem

Stanisław Gawiejnowicz () and Wiesław Kurc
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Stanisław Gawiejnowicz: Adam Mickiewicz University Poznań
Wiesław Kurc: Adam Mickiewicz University Poznań

Journal of Scheduling, 2020, vol. 23, issue 6, No 9, 733-744

Abstract: Abstract We present several new results for a single machine time-dependent scheduling problem of minimizing the total completion time of a set of linearly deteriorating jobs with unit basic processing times. First, we show new properties of cyclic transformations of V-shaped sequences for this problem. Next, applying the results, we prove a new necessary condition of schedule optimality for the considered problem, which decreases the previous bound on the cardinality of the set containing all possible optimal schedules by a multiplicative factor which is at most proportional to the reciprocal of the square root of the number of jobs. Finally, we compare the strength of the new and the previous necessary conditions by estimation of the numbers of schedules satisfying the respective conditions.

Keywords: Scheduling; Single machine; Deteriorating jobs; Total completion time; V-shapeness; Necessary conditions of optimality (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10951-020-00662-7

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