Worst-case analysis of the WSPT and MWSPT rules for single machine scheduling with one planned setup period

Job learning and deterioration coexist in many realistic machine-job scheduling situations. However, in literature, the constructed forms of the machine scheduling models with job learning and/or deteriorating effects were specific types of functions, which constrained their applicability in practice. This paper introduces a new single-machine scheduling model, where the actual processing time of a job is a general function of its starting time as well as scheduled position, which shows a broad generalization in contrast to that of certain existing models. For three objectives corresponding to the single-machine scheduling problem–total weighted completion time, discounted total weighted completion time, and maximum lateness — this paper presents their respective approximation result on the basis of the worst-case bound analysis from the optimal algorithm. The results demonstrate that under our proposed model, minimization of scheduling operations such as the makespan, sum of the kth power of completion times, and total lateness are polynomially solvable. Moreover, under some feasible conditions for the scheduling parameters, the minimum optimization problems of the total weighted completion time, discounted total weighted completion time, maximum lateness, and total tardiness are all recognized as polynomial forms and their solutions are provided.

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WORST-CASE ANALYSIS OF INDEXING RULES FOR SINGLE MACHINE SEQUENCING

Journal of the Operations Research Society of Japan ◽

10.15807/jorsj.36.234 ◽

1993 ◽

Vol 36 (4) ◽

pp. 234-242

Author(s):

Tsung-Chyan Lai

Keyword(s):

Single Machine ◽

Case Analysis ◽

Worst Case Analysis ◽

Worst Case

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SINGLE MACHINE SCHEDULING WITH JOB DELIVERY TO MINIMIZE MAKESPAN

Asia Pacific Journal of Operational Research ◽

10.1142/s0217595908001596 ◽

2008 ◽

Vol 25 (01) ◽

pp. 1-10 ◽

Cited By ~ 11

Author(s):

LINGFA LU ◽

JINJIANG YUAN

Keyword(s):

Single Machine ◽

Machine Scheduling ◽

Single Machine Scheduling ◽

Performance Ratio ◽

Extended Version ◽

Worst Case ◽

Transportation Time ◽

Transportation Times ◽

Worst Case Performance Ratio ◽

Job Delivery

In the single machine scheduling problem with job delivery to minimize makespan, jobs are processed on a single machine and delivered by a capacitated vehicle to their respective customers. We first consider the special case with a single customer, that is, all jobs have the same transportation time. Chang and Lee (2004) proved that this case is strongly NP-hard. They also provided a heuristic with the worst-case performance ratio [Formula: see text], and pointed out that no heuristic can have a worst-case performance ratio less than [Formula: see text] unless P = NP. In this paper, we provide a new heuristic which has the best possible worst-case performance ratio [Formula: see text]. We also consider an extended version in which the jobs have non-identical transportation times and the transportation time of a delivery batch is defined as the maximum transportation time of the jobs contained in it. We provide a heuristic with the worst-case performance ratio 2 for the extended version, and show that this bound is tight.

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Best Possible Approximation Algorithms for Single Machine Scheduling with Increasing Linear Maintenance Durations

The Scientific World JOURNAL ◽

10.1155/2014/547573 ◽

2014 ◽

Vol 2014 ◽

pp. 1-8 ◽

Cited By ~ 1

Author(s):

Xuefei Shi ◽

Dehua Xu

Keyword(s):

Approximation Algorithm ◽

Single Machine ◽

Machine Scheduling ◽

Single Machine Scheduling ◽

Point Of View ◽

Scheduling Problem ◽

Worst Case ◽

Time Approximation ◽

Polynomial Time Approximation Algorithm ◽

Maintenance Activities

We consider a single machine scheduling problem with multiple maintenance activities, where the maintenance duration function is of the linear formft=a+btwitha≥0andb>1. We propose an approximation algorithm named FFD-LS2I with a worst-case bound of 2 for problem. We also show that there is no polynomial time approximation algorithm with a worst-case bound less than 2 for the problem withb≥0unlessP=NP, which implies that the FFD-LS2I algorithm is the best possible algorithm for the caseb>1and that the FFD-LS algorithm, which is proposed in the literature, is the best possible algorithm for the caseb≤1both from the worst-case bound point of view.

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