A note on the complexity of the problem of two-agent scheduling on a single machine

Ng, C. T.; Cheng, T.C.E.; Yuan, Junhui

doi:10.1007/s10878-006-9001-0

Cited by 135 publications

(62 citation statements)

References 5 publications

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“…The complexity of this problem is NP-hard as established by Leung et al [2010]. A pseudo-polynomial algorithm is presented by Ng et al [2006] for this problem under binary encoding. The dynamic programming approach presented by Ng et al [2006] could be used to generate all the non-dominated points for this problem.…”

Section: Problem Descriptionmentioning

confidence: 99%

“…A pseudo-polynomial algorithm is presented by Ng et al [2006] for this problem under binary encoding. The dynamic programming approach presented by Ng et al [2006] could be used to generate all the non-dominated points for this problem. However with a large number of jobs, the number of states in the dynamic program quickly explodes making it computationally challenging.…”

Section: Problem Descriptionmentioning

confidence: 99%

See 1 more Smart Citation

Single machine scheduling with interfering job sets

Khowala

Fowler

Keha

et al. 2014

Computers & Operations Research

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Section: Problem Descriptionmentioning

confidence: 99%

Section: Problem Descriptionmentioning

confidence: 99%

Single machine scheduling with interfering job sets

Khowala

Fowler

Keha

et al. 2014

Computers & Operations Research

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“…When the ε-constraint approach is used, a polynomial time algorithm is proposed to minimizing the number of tardy jobs of each agent. In (Ng et al 2006), the authors study Peha's problem introduced in (Peha 1995) by considering any processing times (not necessary identical). They present an N P -hardness proof and propose a dynamic programming algorithm to calculate a non-dominated solution.…”

Section: Introductionmentioning

confidence: 99%

Non-disjoint Multi-agent Scheduling Problem on Identical Parallel Processors

Sadi

Tuong

et al. 2016

Future Data and Security Engineering

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Abstract. Scheduling problems in which agents (users, customers, application masters, resource manager, etc.) have to share the same set(s) of resources are at the frontier of combinatorial optimization and cooperative game theory. This paper deals with scheduling problems arising when two agents, each with a set of nonpreemptive jobs, compete to perform their respective jobs on two common identical parallel machines. Each agent aims at minimizing a certain objective function that depends on the completion times of its jobs only. The objective functions we consider in our study are makespan and number of tardy jobs. The agents may share some jobs and this problem is called non-disjoint multi-agent scheduling problem . Finding the optimal solution for one agent with a constraint on the other agent's cost function is known to be N P-hard. To obtain best compromise solutions for each agent, we propose polynomial and pseudo-polynomial heuristics. Two mixed integer linear programming models are developed to calculate exact non-dominated solutions. Experimental results are conducted to measure the solutions quality given by heuristics.

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“…The objective functions are the maximum of regular functions, the number of late jobs, and the total weighted completion times. The problem in a similar two-agent single machine was further studied by Yuan (2006, 2008), Ng, Cheng and Yuan (2006), Agnetis, Pacciarelli and Pacifici (2007), Agnetis, Pascale andPacciarelli (2009), Leung, Pinedo and and Lee, Chung and Huang (2013). When release times are further considered, see (Lee, Chung & Hu, 2012;Yin, Wu, Cheng, Wu & Wu, 2014;Wu, Wu, Chen, Yin & Wu, 2013).…”

Section: Introductionmentioning

confidence: 99%

Two-agent scheduling in open shops subject to machine availability and eligibility constraints

Hsiao

2015

JIEM

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Abstract:Purpose: The aims of this article are to develop a new mathematical formulation and a new heuristic for the problem of preemptive two-agent scheduling in open shops subject to machine maintenance and eligibility constraints.Design/methodology: Using the ideas of minimum cost flow network and constraint programming, a heuristic and a network based linear programming are proposed to solve the problem. Findings:Computational experiments show that the heuristic generates a good quality schedule with a deviation of 0.25% on average from the optimum and the network based linear programming model can solve problems up to 110 jobs combined with 10 machines without considering the constraint that each operation can be processed on at most one machine at a time. In order to satisfy this constraint, a time consuming Constraint Programming is proposed.F o r n = 80 and m = 10, the average execution time for the combined models (linear programming model combined with Constraint programming) exceeds two hours. Therefore, the heuristic algorithm we developed is very efficient and is in need. Practical implications:Its practical implication occurs in TFT-LCD and E-paper manufacturing wherein units go through a series of diagnostic tests that do not have to be performed in any specified order.-1103-Journal of Industrial Engineering and Management -http://dx.doi.org/10.3926/jiem.1352 Originality/value: The main contribution of the article is to split the time horizon into many time intervals and use the dispatching rule for each time interval in the heuristic algorithm, and also to combine the minimum cost flow network with the Constraint Programming to solve the problem optimally.

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A note on the complexity of the problem of two-agent scheduling on a single machine

Cited by 135 publications

References 5 publications

Single machine scheduling with interfering job sets

Single machine scheduling with interfering job sets

Non-disjoint Multi-agent Scheduling Problem on Identical Parallel Processors

Two-agent scheduling in open shops subject to machine availability and eligibility constraints

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