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: Computer results indicate that the solution time goes up only linearly with the size of the problem, and the algorithm determines the precedence relationships among pairs of jobs and eliminates the first and the last few jobs in an optimal sequence.
Abstract: : In a recent paper, Hamilton Emmons has established theorems relating to the order in which pairs of jobs are to be processed in an optimal schedule to minimize the total tardiness of performing jobs on one machine. Using these theorems, the algorithm of this paper determines the precedence relationships among pairs of jobs (whenever possible) and eliminates the first and the last few jobs in an optimal sequence. The remaining jobs are then ordered by incorporating the precedence relationships in a dynamic programming framework. Propositions are proved which considerably reduce the total computation involved in the dynamic programming phase. Computational results indicate that the solution time goes up only linearly with the size (n) of the problem. The median solution time for solving 50 job problems was 0.36 seconds on UNIVAC 1108 computer. (Author)
123 citations
TL;DR: This work considers scheduling a set of jobs on parallel processors, when all jobs have a common due date and earliness and lateness are penalized at different cost rates.
Abstract: We consider scheduling a set of jobs on parallel processors, when all jobs have a common due date and earliness and lateness are penalized at different cost rates. For identical processors, the secondary criteria of minimizing makespan and machine occupancy are addressed. The extension to different, uniform processors is also solved.
123 citations
TL;DR: The chapter focuses on the applications of this model in computer systems, and points out some other interpretations, because tasks and machines may also represent ships and dockyards, classes and teachers, patients and hospital equipment, or dinners and cooks.
Abstract: Publisher Summary This chapter discusses the deterministic problems of scheduling tasks on machines (processors), which is one of the most rapidly expanding areas of combinatorial optimization. These problems are stated as follows: A given set of tasks is to be processed on a set of available processors, so that all processing conditions are satisfied and a certain objective function is minimized (or maximized). It is assumed, in contrast to stochastic scheduling problems, that all task parameters are known a priori in a deterministic way. This assumption is well justified in many practical situations. On the other hand, it permits the solving of scheduling problems having a different practical interpretation from that of the stochastic approach. This interpretation is a valuable complement to the stochastic analysis and is often imposed by certain applications as—for example, in computer control systems working in a hard-real-time environment and in many industrial applications. The chapter focuses on the applications of this model in computer systems. It also points out some other interpretations, because tasks and machines may also represent ships and dockyards, classes and teachers, patients and hospital equipment, or dinners and cooks.
100 citations
TL;DR: In this paper, the scheduling of n jobs around a common due date, so as to minimize the average total earliness plus total lateness of the jobs, is studied. And the model is extended to allow for the availability of multiple parallel processors and an efficient algorithm is developed for that problem.
Abstract: This article concerns the scheduling of n jobs around a common due date, so as to minimize the average total earliness plus total lateness of the jobs. Optimality conditions for the problem are developed, based on its equivalence to an easy scheduling problem. It seems that this problem inherently has a huge number of optimal solutions and an algorithm is developed to find many of them. The model is extended to allow for the availability of multiple parallel processors and an efficient algorithm is developed for that problem. In this more general case also, the algorithm permits great flexibility in finding an optimal schedule.
98 citations
TL;DR: An O(n log n) algorithm is given for solving the linear programming problem obtained by relaxing the integrality constraints in a zero-one programming formulation of the problem, and this linear programming lower bound is used in a reduction algorithm that eliminates jobs from the problem.
Abstract: This paper considers the problem of scheduling n jobs, each having a processing time, a due date and a weight, on a single machine to minimize the weighted number of late jobs. An O(n log n) algorithm is given for solving the linear programming problem obtained by relaxing the integrality constraints in a zero-one programming formulation of the problem. This linear programming lower bound is used in a reduction algorithm that eliminates jobs from the problem. Also, a branch and bound algorithm that uses the linear programming lower bound is proposed. Computational results with branch and bound algorithms that use this and other lower bounds and with a dynamic programming algorithm for problems with up to 1000 jobs are given.
87 citations