Minimizing maximum tardiness for unrelated parallel machines
TL;DR: In this article, the scheduling of n jobs, all requiring a single stage of processing, on m unrelated parallel machines is considered, and the scheduling objective is to minimize the maximum tradiness.
About: This article is published in International Journal of Production Economics.The article was published on 1994-03-01. It has received 35 citations till now. The article focuses on the topics: Fair-share scheduling & Flow shop scheduling.
Citations
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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.
233 citations
Cites background or methods from "Minimizing maximum tardiness for un..."
...Suresh and Chaudhuri [10] and Adamopoulos and Pappis [11] suggested new heuristics for various due date and processing time combinations....
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...Given the number of job lots to be processed, for each job pair (i; j), the sequence-dependent setup times sijk on a machine k were randomly chosen from Uniform [10, 90]....
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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.
124 citations
TL;DR: A methodology for minimizing the weighted tardiness of jobs in unrelated parallel machining scheduling with sequence-dependent setups is presented and the use of a specific search algorithm led to identifying solutions of better quality or that required lower computation time, but not both.
118 citations
Cites background from "Minimizing maximum tardiness for un..."
...Keywords: Unrelated parallel machine scheduling; Sequence-dependent setups; Tabu search...
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...Consider, for instance, the swap between J4 scheduled on M31 and J7 scheduled on M1, in the initial solution....
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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.
88 citations
Cites background or methods from "Minimizing maximum tardiness for un..."
...Suresh, V. and D. Chaudhuri, “Minimizing maximum tardiness for unrelated parallel-machines,” International Journal of Production Economics, 34, 223–229 (1994)....
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...Suresh and Chaudhuri [41], who studied the max||R T problem realized a similar relationship between maxT and maxC ....
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...Therefore, to solve this problem, Suresh and Chaudhuri [40] developed and tested three heuristics for this problem class....
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...Like Suresh and Chaudhuri, they modified their PTAS algorithm to solve the bicriteria problem of cost and maxC ....
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...This type of situation commonly occurs in the drilling operations of PWB Manufacturing [44] machine shops [40], and many other operating centers....
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TL;DR: An effective heuristic based on threshold-accepting methods, tabu lists, and improvement procedures is proposed to minimize total tardiness and significantly outperforms an ATCS procedure and a simulated annealing method for problems in larger sizes.
Abstract: This research deals with scheduling jobs on unrelated parallel machines with auxiliary equipment constraints Each job has a due date and requires a single operation A setup for dies is incurred if there is a switch from processing one type of job to another type For a die type, the number of dies is limited Due to the attributes of the machines and the fitness of dies to each, the processing time for a job depends on the machine on which the job is processed, each job being restricted to processing on certain machines In this paper, an effective heuristic based on threshold-accepting methods, tabu lists, and improvement procedures is proposed to minimize total tardiness An extensive experiment is conducted to evaluate the computational characteristics of the proposed heuristic Computational experiences demonstrate that the proposed heuristic is capable of obtaining optimal solutions for small-sized problems, and significantly outperforms an ATCS procedure and a simulated annealing method for problems in larger sizes
85 citations
References
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TL;DR: It is shown that the optimal job sequence for the single-machine problem can be easily determined, and it is proved that the same optimal due-date result can be generalized to the parallel- machine problem.
Abstract: In this paper we consider the problem of scheduling a set of simultaneously available jobs on several parallel and identical machines. The problem is to find the optimal due-date, assuming this to be the same for all jobs. We also seek to sequence the jobs such that some are early and some are late so as to minimize a penalty function. For the single-machine problem, we present a simple proof of the well-known optimality result that the optimal due-date coincides with one of the job completion times. We show that the optimal job sequence for the single-machine problem can be easily determined. We prove that the same optimal due-date result can be generalized to the parallel-machine problem. However, determination of the optimal job sequence for such a problem is much more complex, and we present a simple heuristic to find an approximate solution. On the basis of a limited experiment, we observe that the heuristic is very effective in obtaining near-optimal solutions.
55 citations
TL;DR: An algorithm to preemptively schedule n tasks on m uniform processors that schedules all tasks to complete by their due times whenever possible and generates O(mn) preemptions in the worst case.
Abstract: An algori thm to preemptively schedule n tasks on m uniform processors is presented. It is assumed that each task is available at t ime 0. Associated with each task is a due time by which it is to be completed. The algorithm schedules all tasks to complete by their due times whenever possible. The asymptotic time complexity of the algorithm is O(n log n + ran). It generates O(mn) preemptions in the worst case. An example of n tasks requiring O(mn) preemptions is also presented. The algorithm can also be used when all tasks have the same due times but different release times.
51 citations
TL;DR: Jobs with random processing times, random due dates, and weights are to be scheduled on parallel machines so as to minimize the expected total weight of tardy jobs.
46 citations
TL;DR: It is illustrated that scheduling procedures can be simplified considerably when they are preceded by a planning stage, and the authors learned this fact through interaction with managers of the firm, and this changed the preconceived direction of the work in this application.
Abstract: This paper describes a scheduling system developed and implemented at a semiconductor company that manufactures specialty epitaxial wafers. We discuss implementation issues and describe the algorithms that form the basis of the scheduling system. We present computational results with representative data, and illustrate that scheduling procedures can be simplified considerably when they are preceded by a planning stage. The authors learned this fact through interaction with managers of the firm, and this changed the preconceived direction of the work in this application. The result is a formalization of the planning and scheduling problems.
23 citations
TL;DR: In this article, a unified approach based on linear programming is proposed to determine the optimal sequence and the corresponding optimal due date(s) in a single machine system for jobs in a production system.
21 citations