Partial dominated schedules and minimizing the total completion time of deteriorating jobs

Ocetkiewicz, Krzysztof M.

doi:10.1080/02331934.2013.836647

Cited by 3 publications

(1 citation statement)

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“…For a special case of (P) in which all deterioration rates are not smaller than a certain constant u > 0, Ocetkiewicz (2010) proposed a fully polynomial-time approximation scheme (FPTAS) running in O(n 1+6 log 1+u 2 ( 1 ) 2 log 1+u 2 ) time, where > 0 is a given accuracy. For general case of problem (P), Ocetkiewicz (2013) proposed a branch-and-bound algorithm. Gawiejnowicz and Kurc (2015) shown that counterparts of Property 3 also hold for time-dependent scheduling problems with more general criterion functions than the total completion time, considering a generalization of problem (P) with the objective to minimize the l p norm…”

Section: Previous Research On Problem (P)mentioning

confidence: 99%

New results for an open time-dependent scheduling problem

Gawiejnowicz

Kurc

2020

J Sched

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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.

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Section: Previous Research On Problem (P)mentioning

confidence: 99%