Single machine resource allocation scheduling problems with deterioration effect and general positional effect

This paper addresses the single-machine scheduling problems with simultaneous considerations of job rejection, deterioration effects, and deteriorating multimaintenance activities. A job is either rejected, in which case a rejection penalty has to be paid, or accepted and processed on the single machine. Three deterioration effect models are investigated, and it is assumed that each machine may be subject to several maintenance activities over the scheduling horizon, and the duration of the maintenance depends on its running time. Moreover, due to the restriction of the budget of maintenance, the upper bound of the total maintenance frequencies on the machine is assumed to be known in advance. The objective is to find jointly the optimal accepted job set, the optimal maintenance frequencies, the optimal maintenance positions, and the optimal accepted job sequence such that the cost function based on the total completion time and rejection penalty is minimized. It is shown that all the versions of the problem under study are polynomial time solutions.

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Note on a unified approach to the single-machine scheduling problem with a deterioration effect and convex resource allocation

Journal of Manufacturing Systems ◽

10.1016/j.jmsy.2015.12.002 ◽

2016 ◽

Vol 38 ◽

pp. 134-140 ◽

Cited By ~ 8

Author(s):

Chuanli Zhao ◽

Chou-Jung Hsu ◽

Wen-Hsiang Wu ◽

Shuenn-Ren Cheng ◽

Chin-Chia Wu

Keyword(s):

Resource Allocation ◽

Single Machine ◽

Machine Scheduling ◽

Single Machine Scheduling ◽

Scheduling Problem ◽

Unified Approach ◽

Deterioration Effect ◽

Convex Resource Allocation

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Refined conditions for V-shaped optimal sequencing on a single machine to minimize total completion time under combined effects

Journal of Scheduling ◽

10.1007/s10951-019-00628-4 ◽

2019 ◽

Vol 23 (6) ◽

pp. 665-680

Author(s):

Alan J. Soper ◽

Vitaly A. Strusevich

Keyword(s):

Single Machine ◽

Processing Time ◽

Cumulative Effect ◽

Single Machine Scheduling ◽

Scheduling Problems ◽

Priority Rules ◽

Optimal Sequence ◽

Positional Effect ◽

Wide Range ◽

Completion Times

AbstractWe address single-machine scheduling problems for which the actual processing times of jobs are subject to various effects, including a positional effect, a cumulative effect and their combination. We review the known results on the problems to minimize the makespan, the sum of the completion times and their combinations and identify the problems for which an optimal sequence cannot be found by simple priority rules such as Shortest Processing Time (SPT) and/or Longest Processing Time (LPT). Typically, these are problems to minimize the sum of the completion times under a deterioration effect, and we verify under which conditions for these problems an optimal permutation is V-shaped (an LPT subsequence followed by an SPT subsequence). We demonstrate that previously used techniques for proving that an optimal sequence is V-shaped are not properly justified. We use the corrected method to describe a wide range of problems with a pure positional effect and a combination of a cumulative effect with a positional effect for which an optimal sequence is V-shaped. On the other hand, we show that even the refined approach has its limitations.

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Single-machine resource allocation scheduling with due-date assignment, deterioration effect and position-dependent weights

Engineering Optimization ◽

10.1080/0305215x.2019.1608980 ◽

2019 ◽

Vol 52 (4) ◽

pp. 701-714

Author(s):

Weiwei Liu ◽

Yao Yao ◽

Chong Jiang

Keyword(s):

Resource Allocation ◽

Single Machine ◽

Due Date ◽

Due Date Assignment ◽

Deterioration Effect

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Single Machine Scheduling with Resource-Dependent Ready Times and Positional Deterioration Effect

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.481.207 ◽

2013 ◽

Vol 481 ◽

pp. 207-211

Author(s):

Dan Wang ◽

Na Yin

Keyword(s):

Continuous Function ◽

Single Machine ◽

Polynomial Solution ◽

Machine Scheduling ◽

Single Machine Scheduling ◽

Release Time ◽

Scheduling Problems ◽

Deterioration Effect ◽

Machine Scheduling Problems ◽

Total Resource

The paper deals with the single machine scheduling problems with positional deterioration effect. It is assumed that the release time of a job is a positive strictly decreasing continuous function of the amount of consumed resource. We present a polynomial solution for the total resource consumption minimization problem under the constraint that the makespan does not exceed a given limit.

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