The Continuous Assignment Problem and Its Application to Preemptive and Non-Preemptive Scheduling with Irregular Cost Functions

Sourd, Francis

doi:10.1287/ijoc.1030.0034

Cited by 19 publications

(27 citation statements)

References 20 publications

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“…In fact, one of our major contributions in this paper is the development of a strong lower bound for the problem 1/r j / j E j + π j T j . Also, note that two lower bounds that are closely related to ours were proposed by Sourd and Kedad-Sidhoum (2003) and Sourd (2004) and were successfully implemented in B&B algorithms to solve the problem 1// j E j + π j T j . These authors obtain optimal solutions for problem instances with 20 jobs within a few seconds, and 30-job instances can be solved to optimality within at most a few minutes.…”

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confidence: 67%

“…These authors obtain optimal solutions for problem instances with 20 jobs within a few seconds, and 30-job instances can be solved to optimality within at most a few minutes. We discuss the similarities and differences between our research and the approaches presented by Sourd and Kedad-Sidhoum (2003) and Sourd (2004) in more detail at the end of this section.…”

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confidence: 73%

“…The approaches presented by Sourd and Kedad-Sidhoum (2003) and Sourd (2004), developed independently from our approaches (also see Bülbül 2002), deserve special attention here because the lower bounds proposed in these papers are closely related to ours. In both of these papers, B&B algorithms are developed to solve the problem 1// j E j + π j T j , and the focus is on obtaining good lower bounds.…”

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confidence: 82%

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Preemption in single machine earliness/tardiness scheduling

Bülbül

Kaminsky

Yano

2007

J Sched

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We consider a single machine earliness/tardiness scheduling problem with general weights, ready times and due dates. Our solution approach is based on a time-indexed preemptive relaxation of the problem. For the objective function of this relaxation, we characterize cost coefficients that are the best among those with a piecewise linear structure with two segments. From the solution to the relaxation with these best objective function coefficients, we generate feasible solutions for the original non-preemptive problem. We report extensive computational results demonstrating the speed and effectiveness of this approach.

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confidence: 67%

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confidence: 73%

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confidence: 82%

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Preemption in single machine earliness/tardiness scheduling

Bülbül

Kaminsky

Yano

2007

J Sched

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“…Unfortunately, our computational experience has shown that solving the LP of this problem is time-consuming and results in weak bounds for most of the instances. To overcome this difficulty, Sourd and KedadSidhoum [23] and Sourd [21] proposed to calculate the lower bound for discrete and continuous problems, respectively. Both of these two approaches considered a preemptive lower bound of the original problem.…”

Section: B Lower Bound and Upper Bound Proceduresmentioning

confidence: 99%

New Solution Approaches to the General Single- Machine Earliness-Tardiness Problem

Yau

Pan²,

Shi

2008

IEEE Trans. Automat. Sci. Eng.

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Abstract-This paper addresses the general single-machine earliness-tardiness problem with distinct release dates, due dates, and unit costs. The aim of this research is to obtain an exact nonpreemptive solution in which machine idle time is allowed. In a hybrid approach, we formulate and then solve the problem using dynamic programming (DP) while incorporating techniques from branch-and-bound (BB). This approach (DP-BB) has been proven to be effective in solving certain types of scheduling problems. We further propose a new adaptation of the approach to a general problem with a nonregular objective function. To address some shortcomings of DP-BB, we also apply a branchand-bound approach in which partial dynamic programming dominance (BB-PDP) is exploited. Computational experiments were conducted with randomly generated test instances in order to evaluate the effectiveness of the two approaches. The results clearly showed that our new approaches can solve all the instances with up to 40 jobs and most of the instances with 50 jobs, which outperforms those frequently used approaches in scheduling research.Note to Practitioners-The single-machine scheduling problems with nonregular objective functions are usually harder to solve in comparison to the problems having regular objectives. Most effective algorithms for regular objective problems take advantage of the objective's special feature, which makes it difficult to be applied universally. Sometimes, however, this difficulty can be resolved by changing conventional concepts in the algorithm. This paper addresses a typical nonregular scheduling problem and adopts a technique which has been successfully applied to the regular ones. We extend the traditional concept of "dominance" from one point to piecewise linear so that the technique can be applied to problems with a piecewise linear objective function. Future research can further extend the "linear dominance" to "quadratic dominance" so that this technique can be applied to the single-machine earliness-tardiness problem with a quadratic objective function as well.

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“…Nuass [4] described a special purpose branch-and-bound algorithm for solving assignment problems. Sourd [7] studied the continuous assignment problem with the aim of solving This research discusses how to optimize personnel assignment problem then solved by using Hungarian method. This optimization process is applied to case study of the central post office Bandung in assigning employees to deliver the packet to the destination location based on several criteria owned by each employee and also conducted a sensitivity analysis of data changes that may occur so as not to change the optimal assignment from the initial problem.…”

Section: Introductionmentioning

confidence: 99%

Optimization of Personnel Assignment Problem Based on Traveling Time by Using Hungarian Methods: Case Study on the Central Post Office Bandung

Supian

Wahyuni

Nahar

et al. 2018

IOP Conf. Ser.: Mater. Sci. Eng.

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Abstract. In this paper, traveling time workers from the central post office Bandung in delivering the package to the destination location was optimized by using Hungarian method. Sensitivity analysis against data changes that may occur was also conducted. The sampled data in this study are 10 workers who will be assigned to deliver mail package to 10 post office delivery centers in Bandung that is Cikutra, Padalarang, Ujung Berung, Dayeuh Kolot, AsiaAfrica, Soreang, Situ Saeur, Cimahi, Cipedes and Cikeruh. The result of this research is optimal traveling time from 10 workers to 10 destination locations. The optimal traveling time required by the workers is 387 minutes to reach the destination. Based on this result, manager of the central post office Bandung can make optimal decisions to assign tasks to their workers.

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The Continuous Assignment Problem and Its Application to Preemptive and Non-Preemptive Scheduling with Irregular Cost Functions

Cited by 19 publications

References 20 publications

Preemption in single machine earliness/tardiness scheduling

Preemption in single machine earliness/tardiness scheduling

New Solution Approaches to the General Single- Machine Earliness-Tardiness Problem

Optimization of Personnel Assignment Problem Based on Traveling Time by Using Hungarian Methods: Case Study on the Central Post Office Bandung

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