Scheduling with job rejection and nonsimultaneous machine available time on unrelated parallel machines

Jiang, Dakui; Tan, Jiayin

doi:10.1016/j.tcs.2015.12.020

Cited by 16 publications

(7 citation statements)

References 13 publications

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“…The objective is to minimize the makespan and the total cost of rejecting orders. Due to its NP-hard property, the problem was first studied with a polynomial-time algorithm to obtain a lower bound on the optimal objective value of the problem and then examined a heuristic by using some relaxation techniques [23].…”

Section: Literature Reviewmentioning

confidence: 99%

Fuzzy Order Acceptance and Scheduling on Identical Parallel Machines

Barak

Koyuncu

2021

Symmetry

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In this study, we focus on the fuzzy order acceptance and scheduling problem in identical parallel machines (FOASIPM), which is a scheduling and optimization problem to decide whether the firm should accept or outsource the order. In general, symmetry is a fundamental property of optimization models used to represent binary relations such as the FOASIPM problem. Symmetry in optimization problems can be considered as an engineering tool to support decision-making. We develop a fuzzy mathematical model (FMM) and a Genetic Algorithm (GA) with two crossover operators. The FOASIPM is formulated as an FMM where the objective is to maximize the total net profit, which includes the revenue, the penalty of tardiness, and the outsourcing. The performance of the proposed methods is tested on the sets of data with orders that are defined by fuzzy durations. We use the signed distance method to handle the fuzzy parameters. While FMM reaches the optimal solution in a reasonable time for datasets with a small number of orders, it cannot find a solution for datasets with a large number of orders due to the NP-hard nature of the problem. Genetic algorithms provide fast solutions for datasets with a medium and large number of orders.

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Section: Literature Reviewmentioning

confidence: 99%

Fuzzy Order Acceptance and Scheduling on Identical Parallel Machines

Barak

Koyuncu

2021

Symmetry

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“…Computational experiments show that the problem can be solved in polynomial time when the quantity of machines is fixed. Jiang and Tan [4] study the unrelated parallel machine scheduling model with job acceptance option. Each job order is either accepted and processed without interruption, or is declined at a penalty cost.…”

Section: 1mentioning

confidence: 99%

A Column Generation Algorithm for the Resource-Constrained Order Acceptance and Scheduling on Unrelated Parallel Machines

Song

Xue

Hua

et al. 2021

Mathematical Problems in Engineering

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In this paper, we investigate the resource-constrained order acceptance and scheduling on unrelated parallel machines that arise in make-to-order systems. The objective of this problem is to simultaneously select a subset of orders to be processed and schedule the accepted orders on unrelated machines in such a way that the resources are not overutilized at any time. We first propose two formulations for the problem: mixed integer linear programming formulation and set partitioning. In view of the complexity of the problem, we then develop a column generation approach based on the set partitioning formulation. In the proposed column generation approach, a differential evolution algorithm is designed to solve subproblems efficiently. Extensive numerical experiments on different-sized instances are conducted, and the results demonstrate that the proposed column generation algorithm reports optimal or near-optimal solutions that are evidently better than the solutions obtained by solving the mixed integer linear programming formulation.

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“…Lin et al [9] presented a deterministic 3-approximation algorithm and a randomized 3-approximation algorithm for two unrelated parallel machine scheduling problem with rejection. Jiang and Tan [10] presented a heuristic with worst-case ratio of 2 for an unrelated parallel machine scheduling with rejection and nonsimultaneous machine available time to minimize the sum of the makespan and total rejection cost. Above studies, including literature on unrelated parallel machines in the two survey papers, mostly employed the a priori optimization approach to sum objectives as an aggregated function, which cannot provide Pareto-optimal solutions for trade-off.…”

Section: Literature Reviewmentioning

confidence: 99%

Multiobjective Order Acceptance and Scheduling on Unrelated Parallel Machines with Machine Eligibility Constraints

Wang

2018

Mathematical Problems in Engineering

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This paper studies the order acceptance and scheduling problem on unrelated parallel machines with machine eligibility constraints. Two objectives are considered to maximize total net profit and minimize the makespan, and the mathematical model of this problem is formulated as multiobjective mixed integer linear programming. Some properties with respect to the objectives are analysed, and then a classic list scheduling (LS) rule named the first available machine rule is extended, and three new LS rules are presented, which focus on the maximization of the net profit, the minimization of the makespan, and the trade-off between the two objectives, respectively. Furthermore, a list-scheduling-based multiobjective parthenogenetic algorithm (LS-MPGA) is presented with parthenogenetic operators and Pareto-ranking and selection method. Computational experiments on randomly generated instances are carried out to assess the effectiveness and efficiency of the four LS rules under the framework of LS-MPGA and discuss their application environments. Results demonstrate that the performance of the LS-MPGA developed for trade-off is superior to the other three algorithms.

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Scheduling with job rejection and nonsimultaneous machine available time on unrelated parallel machines

Cited by 16 publications

References 13 publications

Fuzzy Order Acceptance and Scheduling on Identical Parallel Machines

Fuzzy Order Acceptance and Scheduling on Identical Parallel Machines

A Column Generation Algorithm for the Resource-Constrained Order Acceptance and Scheduling on Unrelated Parallel Machines

Multiobjective Order Acceptance and Scheduling on Unrelated Parallel Machines with Machine Eligibility Constraints

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