On Upper Bound for the Bottleneck Product Rate Variation Problem

Khadka, Sundar; Becker, Till

doi:10.1007/978-3-319-45117-6_34

Cited by 2 publications

(4 citation statements)

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“…Likewise, a lower bound and an upper bound of a feasible solution of TPRVP nD(1 − r max ) m and nD 1 − 1 D m , m being a positive integer investigated in [11].…”

Section: Discussionmentioning

confidence: 99%

“…It is note-worthy that a lower bound on the absolute deviation objective function for the BPRVP has been established by Steiner and Yeomans [16]. Likewise the lower bound for TPRVP has been investigated to be LB m = nD (1 − r max ) m , see [11].…”

Section: Lower Boundmentioning

confidence: 99%

“…The problem with different objective functions yields solution in the same complexity O(DlogD), where D stands for the total demand of all the models, of the problem with an absolute deviation objective [4,8,16]. An improved upper bound to the BPRVP has been investigated in [10]. Moreover, the problem with the asymmetric objective function that means different penalty for the inventory and for the shortage has been established [9].…”

Section: Introductionmentioning

confidence: 99%

“…The complexity of the exact solution method is D 3 , where D is total demand of all copies. The lower and the upper bounds of the TPRVP have also been established, [11]. However, the upper bound can further be improved.…”

Section: Introductionmentioning

confidence: 99%

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Improved Upper Bound to Product Rate Variation Problem

Khadka

2020

Nepali Math. Sci. Rep.

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The sequencing problem which minimizes the deviation between the actual (integral) and the ideal (rational) cumulative production of a variety of models of a common base product is called the product rate variation problem. If the objective is to minimize the maximum deviation, the problem is bottleneck product rate variation problem and the problem with the objective of minimizing all the deviations is the total product rate variation problem. The problem has been widely studied with several pseudo-polynomial time exact algorithms and heurism-tics. The lower bound of a feasible solution to the problem has been investigated to be tight. However, the upper bound of a feasible solution had been established in the literature which could further be improved. In this paper, we propose the improved upper bound for BPRVP and TPRVP.

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“…Likewise, a lower bound and an upper bound of a feasible solution of TPRVP nD(1 − r max ) m and nD 1 − 1 D m , m being a positive integer investigated in [11].…”

Section: Discussionmentioning

confidence: 99%

Section: Lower Boundmentioning

confidence: 99%