Bicriteria scheduling problem for unrelated parallel machines
TL;DR: The results show that the proposed algorithm gives better results both in terms of the quality of solution and execution time than the heuristic proposed earlier.
Abstract: In this paper scheduling of n jobs, all requiring a single stage of processing, on m unrelated parallel machines is considered. No preemption of jobs is allowed. There are two scheduling objectives, namely to minimize the makespan and to minimize the maximum tardiness. An algorithm based on tabu search is proposed for the above problem. Computational results are reported with data generated using various combinations of process time and due dates. Comparison is also made with a heuristic proposed earlier. The results show that the proposed algorithm gives better results both in terms of the quality of solution and execution time.
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TL;DR: Simulated annealing (SA), a meta-heuristic, is employed in this study to determine a scheduling policy so as to minimize total tardiness, and shows that the proposed SA method significantly outperforms a neighborhood search method in terms of total tardyness.
Abstract: This paper presents a scheduling problem for unrelated parallel machines with sequence-dependent setup times, using simulated annealing (SA). The problem accounts for allotting work parts of L jobs into M parallel unrelated machines, where a job refers to a lot composed of N items. Some jobs may have different items while every item within each job has an identical processing time with a common due date. Each machine has its own processing times according to the characteristics of the machine as well as job types. Setup times are machine independent but job sequence dependent. SA, a meta-heuristic, is employed in this study to determine a scheduling policy so as to minimize total tardiness. The suggested SA method utilizes six job or item rearranging techniques to generate neighborhood solutions. The experimental analysis shows that the proposed SA method significantly outperforms a neighborhood search method in terms of total tardiness.
215 citations
Cites methods from "Bicriteria scheduling problem for u..."
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TL;DR: This article addresses a multi-stage flow shop scheduling problem with unrelated parallel machines with a simulated annealing (SA)-based heuristic to solve the addressed problem in a reasonable running time.
Abstract: This article addresses a multi-stage flow shop scheduling problem with unrelated parallel machines. Some practical processing restrictions such as independent setup and dependent removal times are taken into account as well. The objective is to minimize total flow time in the system. A simulated annealing (SA)-based heuristic is proposed to solve the addressed problem in a reasonable running time. The heuristic begins on a well-designed initial solution generator; then a simulated annealing procedure is applied for further improvement of the solution. To assure the quality and efficiency of the solution for the proposed SA-based heuristic, certain mechanisms are developed and introduced into the heuristic. The computational experimental results show that the proposed SA-based heuristic performs well with respect to accuracy and efficiency of solution.
129 citations
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TL;DR: Four search heuristics are proposed to address the problem, namely the earliest weighted due date, the shortest weighted processing time, the two-level batch scheduling heuristic, and the simulated annealing method.
Abstract: This paper presents several search heuristics and their performance in batch scheduling of parallel, unrelated machines. Identical or similar jobs are typically processed in batches in order to decrease setup times and/or processing times. The problem accounts for allotting batched work parts into unrelated parallel machines, where each batch consists of a fixed number of jobs. Some batches may contain different jobs but all jobs within each batch should have an identical processing time and a common due date. Processing time of each job of a batch is determined according to the machine group as well as the batch group to which the job belongs. Major or minor setup times are required between two subsequent batches depending on batch sequence but are independent of machines. The objective of our study is to minimize the total weighted tardiness for the unrelated parallel machine scheduling. Four search heuristics are proposed to address the problem, namely (1) the earliest weighted due date, (2) the shortest weighted processing time, (3) the two-level batch scheduling heuristic, and (4) the simulated annealing method. These proposed local search heuristics are tested through computational experiments with data from dicing operations of a compound semiconductor manufacturing facility.
117 citations
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TL;DR: In this article, the authors provide an extensive review of the literature on the scheduling problems with multiple objectives in the past 13 years and present some problems receiving less attention than the others.
Abstract: The real life scheduling problems often have several conflicting objectives. The solutions of these problems can provide deeper insights to the decision maker than those of single-objective problems. However, the literature of multi-objective scheduling is notably sparser than that of single-objective scheduling. Since the survey paper on multi-objective and bi-objective scheduling was conducted by Nagar et al. in 1995, there has been an increasing interest in multi-objective production scheduling, especially in multi-objective deterministic problem. The goal of this paper was to provide an extensive review of the literature on the scheduling problems with multiple objectives in the past 13 years. This paper also presents some problems receiving less attention than the others.
117 citations
Cites methods from "Bicriteria scheduling problem for u..."
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TL;DR: This survey reveals that while makespan minimization has been fairly widely studied, problems that include processing characteristics such as release times, sequence dependent setups, and preemptions remain largely unstudied.
Abstract: This paper surveys the literature related to solving traditional unrelated parallel-machine scheduling problems. It compiles algorithms for the makespan, total weighted sum of completion times, maximum tardiness, total tardiness, total earliness and tardiness, and multiple criteria performance measures. The review of the existing algorithms is restricted to the deterministic problems without setups, preemptions, or side conditions on the problem. Even for such traditional problems, this survey reveals that while makespan minimization has been fairly widely studied, problems that include processing characteristics such as release times, sequence dependent setups, and preemptions remain largely unstudied. Research in solving unrelated parallel-machine scheduling problems involving the minimization of the number of tardy jobs, weighted number of tardy jobs, total tardiness, and total weighted tardiness is quite limited.
78 citations
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References
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TL;DR: This paper presents tabu search, a heuristic procedure designed to guide other methods to escape the trap of local optimality, which has obtained optimal and near optimal solutions to a wide variety of classical and practical problems.
Abstract: Tabu search is a “higher level” heuristic procedure for solving optimization problems, designed to guide other methods (or their component processes) to escape the trap of local optimality. Tabu search has obtained optimal and near optimal solutions to a wide variety of classical and practical problems in applications ranging from scheduling to telecommunications and from character recognition to neural networks. It uses flexible structures memory (to permit search information to be exploited more thoroughly than by rigid memory systems or memoryless systems), conditions for strategically constraining and freeing the search process (embodied in tabu restrictions and aspiration criteria), and memory functions of varying time spans for intensifying and diversifying the search (reinforcing attributes historically found good and driving the search into new regions). Tabu search can be integrated with branch-and-bound and cutting plane procedures, and it has the ability to start with a simple implementation th...
979 citations
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TL;DR: In this paper, the best heuristic methods known up to now are compared to solve the flow shop sequencing problem and they improve the complexity of the best one, and a parallel taboo search algorithm is presented and experimental results show that this heuristic allows very good speed-up.
Abstract: In this paper the best heuristic methods known up to now are compared to solve the flow shop sequencing problem and we improve the complexity of the best one. Next, this problem is applied to taboo search, a new technique to solve combinatorial optimization problems, and computational experiments are reported. Finally a parallel taboo search algorithm is presented and experimental results show that this heuristic allows very good speed-up.
770 citations
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TL;DR: In this paper, a new heuristic method is presented for solving the m -machine, n -job flow shop scheduling problem, which is composed of two phases: the first finds an initial sequence using an analogy with the travelling salesman problem and the second tries to improve this solution using taboo search techniques.
Abstract: A new heuristic method is presented for solving the m -machine, n -job flow shop scheduling problem. This method, named spirit , is composed of two phases: the first finds an initial sequence using an analogy with the travelling salesman problem and the second tries to improve this solution using taboo search techniques. The results of the heuristic are compared with those from other well-known methods.
346 citations
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TL;DR: It is shown that no more than O(m 2) preemptions are necessary, in order to schedule n jobs on m unrelated processors so as to minimize makespan.
Abstract: It IS shown that certain problems of optimal preemptive scheduling of unrelated parallel processors can be formulated and solved as hnear programming problems As a by-product of the linear programming formulaUons of these problems, upper bounds are obtained on the number of preempuons required for optimal schedules In particular it is shown that no more than O(m 2) preemptions are necessary, m order to schedule n jobs on m unrelated processors so as to minimize makespan
274 citations
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TL;DR: The heuristic solutions are compared with optimal solutions obtained by branch and bound in numerous randomly generated problems and are found to be optimal in most cases.
Abstract: This paper treats the problem of minimizing the total weighted flow cost plus job-processing cost in a single machine sequencing problem for jobs having processing costs which are linear functions of processing times. The optimal job sequence and processing times are obtainable from the solution of an associated problem of optimal row and column selection in a symmetric matrix. Some sufficient conditions for expediting certain jobs are proved. In order to handle cases in which these conditions fail to complete the solution to the problem a heuristic algorithm with a provable performance bound is developed. The heuristic solutions are compared with optimal solutions obtained by branch and bound in numerous randomly generated problems and are found to be optimal in most cases.
192 citations