Single-Machine Scheduling with Learning Effect, Deteriorating Jobs and Convex Resource Dependent Processing Times

This paper considers single-machine scheduling with learning effect, deteriorating jobs and convex resource dependent processing times, i.e., the processing time of a job is a function of its starting time, its position in a sequence and its convex resource allocation. The objective is to find the optimal sequence of jobs and the optimal convex resource allocation separately to minimize a cost function containing makespan, total completion (waiting) time, total absolute differences in completion (waiting) times and total resource cost. It is proved that the problem can be solved in polynomial time.

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Single-Machine Scheduling with Resource-Dependent Learning Effect and Deteriorating Jobs

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.423-426.2224 ◽

2013 ◽

Vol 423-426 ◽

pp. 2224-2227

Author(s):

Yan Peng Fan ◽

Chuan Li Zhao

Keyword(s):

Resource Allocation ◽

Single Machine ◽

Learning Effect ◽

Operation Time ◽

Deteriorating Jobs ◽

Polynomial Time Algorithm ◽

Time Algorithm ◽

Single Machine Scheduling ◽

Optimal Sequence ◽

Dependent Learning

This paper considers single-machine due-window assignment and scheduling with learning effect and resource-dependent processing times. The processing time of a job is a function of its position in a sequence, its starting time, and its resource allocation. The objective is to determine the optimal sequence of jobs and optimal resource allocation so as to minimize the sum of earliness, tardiness, due-windows and resource and operation time cost, the considered problem is molded as an assignment problem and can be solved with a polynomial time algorithm.

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Some polynomial solvable single-machine scheduling problems with a truncation sum-of-processing-times-based learning effect

European J of Industrial Engineering ◽

10.1504/ejie.2012.047665 ◽

2012 ◽

Vol 6 (4) ◽

pp. 441 ◽

Cited By ~ 18

Author(s):

Chin Chia Wu ◽

Yunqiang Yin ◽

Wen Hsiang Wu ◽

Shuenn Ren Cheng

Keyword(s):

Single Machine ◽

Learning Effect ◽

Machine Scheduling ◽

Single Machine Scheduling ◽

Scheduling Problems ◽

Processing Times ◽

Machine Scheduling Problems

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A Bicriteria Approach for Single Machine Scheduling with Resource Allocation, Learning Effect and a Deteriorating Maintenance Activity

Asia Pacific Journal of Operational Research ◽

10.1142/s0217595917500117 ◽

2017 ◽

Vol 34 (04) ◽

pp. 1750011 ◽

Cited By ~ 1

Author(s):

Zhusong Liu ◽

Zhenyou Wang ◽

Yuan-Yuan Lu

Keyword(s):

Resource Allocation ◽

Single Machine ◽

Learning Effect ◽

Machine Scheduling ◽

Single Machine Scheduling ◽

Maintenance Activity ◽

Optimal Resource ◽

Deteriorating Maintenance ◽

Polynomially Solvable ◽

Completion Times

This paper considers the single machine scheduling with learning effect, resource allocation and deteriorating maintenance activity simultaneously. For the convex resource allocation consumption function, we provide a bicriteria analysis where the first (schedule) criterion is to minimize the total weighted sum of makespan, total completion time and total absolute differences in completion times, and the second (resource) criterion is to minimize the total weighted resource consumption. Our aim is to find the optimal resource allocations and job sequence that minimize the three different models of considering the two criterion. We show that these three models are polynomially solvable respectively.

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