A backward approach in list scheduling algorithms for multi-machine tardiness problems

doi:10.1016/0305-0548(94)E0019-4

Computers & Operations Research

Volume 22, Issue 3, March 1995, Pages 307-319

https://doi.org/10.1016/0305-0548(94)E0019-4 Get rights and content

Abstract

List scheduling algorithms are commonly used for multi-machine scheduling problems, especially for those with precedence relationships among operations. In most list scheduling algorithms, operations are scheduled forward. In this paper, we suggest a backward approach in which the operations are scheduled backward. We discuss some details that must be considered when applying the backward approach to problems with due dates and suggest several methods of defining parameters needed in the backward approach. Performance of this approach is tested on job shop problems and identical machine problems with several types of precedence constaints.

References (23)

R. Ramasesh
Dynamic job shop scheduling: a survey of simulation studies
Omega
(1990)
K. Baker et al.
Job shop scheduling with modified due dates
J. Ops Mngmt
(1983)
E.M. Dar-El et al.
Job shop scheduling—a systematic approach
J. Manufact. Systems
(1982)
D.A. Elvers et al.
Time completion for various dispatching rules in job shops
Omega
(1983)
D. Sculli
Priority dispatching rules in an assembly shop
Omega
(1987)
S. French
Sequencing and Scheduling: an Introduction to the Mathematics of the Job-shop
(1982)
S.S. Panwalkar et al.
A survey of scheduling rules
Ops Res.
(1977)
J.H. Blackstone et al.
A state-of-the-art survey of dispatching rules for manufacturing job shop operations
Int. J. Prod. Res.
(1982)
W.L. Berry et al.
Critical ratio scheduling: an experimental analysis
Mngmt Sci.
(1975)
Y-D. Kim
A comparison of dispatching rules for job shops with multiple identical jobs and alternative routeings

P.J. O'Grady et al.

A general search sequencing rule for job shop sequencing

Int. J. Prod. Res.

(1985)

Cited by (32)

List scheduling and beam search methods for the flexible job shop scheduling problem with sequencing flexibility
2015, European Journal of Operational Research
Citation Excerpt :
Due to the limited amount of works that approach the extended version of the FJS problem and its practical applicability, the purpose of this paper is to contribute to the development of heuristic techniques able to produce reasonable results in acceptable time. First, a list scheduling algorithm is proposed, motivated by its simplicity and applicability to job scheduling in production environments (see, for example, Kim, 1995; Lee, Kim, & Choi, 2004; Mainieri & Ronconi, 2013). The natural extension of the list scheduling algorithm to a filtered beam search method is also investigated.
An extended version of the flexible job shop problem is tackled in this work. The considered extension to the classical flexible job shop problem allows the precedences between the operations to be given by an arbitrary directed acyclic graph instead of a linear order. Therefore, the problem consists of allocating the operations to the machines and sequencing them in compliance with the given precedences. The goal in the present work is the minimization of the makespan. A list scheduling algorithm is introduced and its natural extension to a beam search method is proposed. Numerical experiments assess the efficiency of the proposed approaches.
Scheduling algorithms for a semiconductor probing facility
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This paper focuses on a scheduling problem in a semiconductor wafer probing facility. In the probing facility, wafer lots with distinct ready times are processed on a series of workstations, each with identical parallel machines. We develop a heuristic algorithm for the problem with the objective of minimizing total tardiness of orders. The algorithm employs a bottleneck-focused scheduling method, in which a schedule at the bottleneck workstation is constructed first and then schedules for other workstations are constructed based on the schedule at the bottleneck. For scheduling wafer lots at the bottleneck workstation, we consider prospective tardiness of the lots as well as sequence-dependent setup times required between different types of wafer lots. We also present a rolling horizon method for implementation of the scheduling method on a dynamic situation. The suggested methods are evaluated through a series of computational experiments and results show that the methods work better than existing heuristic methods.
Scheduling algorithms to minimize the number of tardy jobs in two-stage hybrid flow shops
2009, Computers and Industrial Engineering
This paper considers a two-stage hybrid flow shop scheduling problem for the objective of minimizing the number of tardy jobs. Each job is processed through the two production stages in series, each of which has multiple identical parallel machines. The problem is to determine the allocation of jobs to the parallel machines as well as the sequence of the jobs assigned to each machine. To solve the problem, a branch and bound algorithm, which incorporates the methods to obtain the lower and upper bounds as well as the dominance properties to reduce the search space, is suggested that gives the optimal solutions. In addition, two-phase heuristic algorithms are suggested to obtain good solutions for large-size problems within a reasonable amount of computation time. To show the performances of the optimal and heuristic algorithms suggested in this paper, computational experiments are done on a number of randomly generated test problems, and the test results are reported.
A branch and bound algorithm for an identical parallel machine scheduling problem with a job splitting property
2008, Computers and Operations Research
Citation Excerpt :
In most heuristics, jobs are prioritized according to methods developed for the single machine tardiness problem and then scheduled on the machines according to the priorities [10–13]. On the other hand, Kolumas [14] presents a decomposition heuristic by extending a decomposition principle for the single machine tardiness problem to a parallel-machine setting, and Kim [15] suggests a backward approach for the list scheduling algorithms for multi-machine tardiness problems. Also, Lee and Pinedo [16] propose a simulated annealing algorithm for a parallel machine tardiness problem with sequence-dependent setup times, and Park [17] suggests a genetic algorithm for a parallel-machine problem with the objective of minimizing total weighted tardiness.
We focus on the problem of scheduling n independent jobs on m identical parallel machines with the objective of minimizing total tardiness of the jobs considering a job splitting property. In this problem, it is assumed that a job can be split into sub-jobs and these sub-jobs can be processed independently on parallel machines. We develop several dominance properties and lower bounds for the problem, and suggest a branch and bound algorithm using them. Computational experiments are performed on randomly generated test problems and results show that the suggested algorithm solves problems of moderate sizes in a reasonable amount of computation time.
Scope and purpose
In this paper, we consider an operations scheduling problem in a real manufacturing system that produces printed circuit boards (PCBs). In the PCB manufacturing system, production orders are specified by the product types, production quantities and due dates. In a bottleneck workstation of the manufacturing system, in which there are multiple parallel machines, a job required for a production order can be split into basic processing units, each of which can be processed on a machine. We present an algorithm that can give an optimal schedule for a scheduling problem in the workstation for the objective of minimizing total tardiness of production orders. Since meeting due dates of customers’ orders become more and more important for the survival of a manufacturing company in highly competitive market environments of these days, the algorithm may provide the company with a competitive edge in the industry.
Scheduling on parallel identical machines to minimize total tardiness
2007, European Journal of Operational Research
This paper focuses on the problem of scheduling n independent jobs on m identical parallel machines for the objective of minimizing total tardiness of the jobs. We develop dominance properties and lower bounds, and develop a branch and bound algorithm using these properties and lower bounds as well as upper bounds obtained from a heuristic algorithm. Computational experiments are performed on randomly generated test problems and results show that the algorithm solves problems with moderate sizes in a reasonable amount of computation time.
Hierarchical minimization of completion time variance and makespan in jobshops
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Citation Excerpt :
Only a few publications are available in the literature reporting the performance of backward scheduling in production environments. Kim [23] investigated the backward scheduling approach for multi-machine scheduling problems with due-date constraints. He described a variety of methods for setting ready times and due-dates of jobs, and tested different combinations using nine different dispatching rules.
This paper addresses the problem of minimizing makespan for a given set of n jobs to be processed on each of m machines in a static jobshop, subject to the minimum completion time variance (CTV). A lower bound on CTV is developed for the static jobshop problem. A backward scheduling approach is proposed using the observations on the development of lower bound for hierarchical minimization of CTV and makespan. A lower bound on makespan subject to minimum CTV is also presented for this problem. Finally, we present two simulated annealing heuristic approaches using the concepts of forward and backward scheduling. Their performances are compared against each other through the use of the lower bounds established in this work. The simulated annealing heuristic based on backward scheduling is shown to perform well by evaluating the developed heuristics on 82 jobshop problems taken from literature.

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^†: Yeong-Dae Kim is an Associate Professor at the Department of Industrial Engineering, Korea Advanced Institute of Science and Technology (KAIST). He received a B.S. degree from Seoul National University, Seoul, Korea, and M.S. degree from KAIST both in Industrial Engineering, and a Ph.D. degree in Industrial and Operations Engineering from the University of Michigan. He published his works in International Journal of Production Research, European Journal of Operational Research, International Journal of Flexible Manufacturing Systems, Journal of the Operational Research Society, IIE Transactions, Computers and Operations Research, and Journal of Manufacturing Systems.

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A backward approach in list scheduling algorithms for multi-machine tardiness problems

Abstract

Omega

J. Ops Mngmt

J. Manufact. Systems

Omega

Omega

Sequencing and Scheduling: an Introduction to the Mathematics of the Job-shop

A survey of scheduling rules

Ops Res.

A state-of-the-art survey of dispatching rules for manufacturing job shop operations

Int. J. Prod. Res.

Critical ratio scheduling: an experimental analysis

Mngmt Sci.

A comparison of dispatching rules for job shops with multiple identical jobs and alternative routeings

A general search sequencing rule for job shop sequencing

Int. J. Prod. Res.