Scheduling tasks with sequence-dependent processing times

Bianco, Lucio; Ricciardelli, Salvatore; Rinaldi, Giovanni; Sassano, Antonio

doi:10.1002/1520-6750(198804)35:2<177::aid-nav3220350203>3.0.co;2-v

Cited by 93 publications

(37 citation statements)

References 4 publications

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“…and [4]) introduced a branch and bound method for solving the same problem, using a Lagrange dual for estimating the lower bound of the optimal value. In particular, jobs are assumed to subject to arbitrary release times in [3] and [4].…”

Section: Introductionmentioning

confidence: 99%

Low-complexity algorithms for sequencing jobs with a fixed number of job-classes

Veen

Zhang

1996

Computers & Operations Research

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In this paper we consider the problem of scheduling n jobs such that makespan is minimized. It is assumed that the jobs can be divided into K job-classes and that the change-over time between two consecutive jobs depends on the job-classes to which the two jobs belong. In this setting, we discuss the one machine scheduling problem with arbitrary processing times and the parallel machines scheduling problem with identical processing times. In both cases it is assumed that the number of job-classes K is fixed. By using an appropriate * Corresponding author. 1integer programming formulation with a fixed number of variables and constraints, it is shown that these two problems are solvable in polynomial time. For the one machine scheduling case it is shown that the complexity of our algorithm is linear in the number of jobs n. Moreover, if the problem is encoded according to the high multiplicity model of Hochbaum and Shamir, the time complexity of the algorithm is shown to be a polynomial in log n. In the parallel machine scheduling case, it is shown that if the number of machines is fixed the same results hold. 2 Scope and PurposeOne of the key problems in manufacturing operations is to determine the assignment of jobs to machines and the sequence of the jobs on each machine. In this paper we consider an environment in which the machines are identical, change-over times in between the processing of two consecutive jobs are job-dependent and the objective is to maximize the utilization of the machines which is equivalent to minimizing the makespan. Unfortunately, such problems fall into the strongly N P-hard category. However, it is the purpose of this paper to show that the computational complexity drastically improves if the jobs are divided into a small number of groups where each group consists of "similar" jobs. Such situations can be found in applications where the jobs in a group are identical or the jobs in a group require a similar state of the machine, like e.g. color for a painting machine or toolloading in flexible manufacturing systems. We give fast algorithms for the one-machine problem and the problem with multiple machines and identical processing times.

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Section: Introductionmentioning

confidence: 99%

Low-complexity algorithms for sequencing jobs with a fixed number of job-classes

Veen

Zhang

1996

Computers & Operations Research

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“…In the container and bottle industry, the settings change depending on the sizes and shapes of the containers. Further, in the plastic industry, different types and colors of jobs require sequence-dependent setups (Das et al, 1995;Franca, 1996;Srikar and Ghosh, 1986;Bianco, 1988). Similar practical situations arise in the chemical, pharmaceutical, food processing, metal processing, and paper industries (Bitran and Gilbert, 1990).…”

Section: Literature Reviewmentioning

confidence: 99%

A New Mathematical Model for Flexible Flow Lines with Blocking Processor and Sequence-Dependent Setup Time

Tavakkoli–Moghaddam¹,

Safaei²

2007

Multiprocessor Scheduling, Theory and Applications

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“…A branch-and-bound algorithm was presented but no detailed computational results were given. BIANCO, RINALDI, and SASSANO (1987), BIANCO et al (1988) and BIANCO and BIELLI (1993) adopted the job shop scheduling view (with successive separation) for the single-runway problem. They presented a mixed-integer zero-one formulation of the problem together with a tree search algorithm based upon a Lagrangean lower bound, a lower bound derived from scheduling theory and a heuristic procedure.…”

Section: Previous Workmentioning

confidence: 99%

“…Computational results were presented for a number of test problems involving up to 15 planes, and for three larger test problems. Of these three larger problems, one involved 20 planes, Bianco et al (1987Bianco et al ( , 1988; the other two involved 30 and 44 planes, Bianco et al (1987), Bianco and Bielli (1993).…”

Section: Previous Workmentioning

confidence: 99%

Scheduling Aircraft Landings—The Static Case

Beasley

Krishnamoorthy

Sharaiha

et al. 2000

Transportation Science

361

309

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In this paper, we consider the problem of scheduling aircraft (plane) landings at an airport. This problem is one of deciding a landing time for each plane such that each plane lands within a predetermined time window and that separation criteria between the landing of a planeInthispaper,weconsidertheproblemofscheduling aircraft (plane) landings at an airport. This problem is one of deciding a landing time on a runway for each plane in a given set of planes such that each plane lands within a predetermined time window, and that separation criteria between the landing of a plane, and the landing of all successive planes, are respected.This paper is organized as follows. In Section 1, we set the problem in context. In Section 2, we present a mixed-integer zero-one formulation of the problem for the single runway case. We then discuss previous work on the problem in Section 3. In Section 4, we extend the formulation to the multiple runway case, and, in Section 5, we strengthen the linear programming (LP) relaxations of these formulations by introducing additional constraints. These formulations can be solved using LP-based tree search. An effective heuristic for the problem (for any number of runways) is presented in Section 6. Computational results for both the heuristic and the optimal algorithm for a number of test problems involving up to 50 planes and four runways are presented in Section 7.It is important to note here that, although throughout this paper we shall typically refer to planes landing, the models presented in this paper are applicable to problems involving just takeoffs only and to problems involving a mix of landings and takeoffs on the same runway. We should also stress here that we are dealing only with the static case. In other words, we are dealing with the off-line case where we have complete knowledge of the set of planes that are going to land. The dynamic, or on-line, case, where decisions about the landing times for planes must be made as time passes and the situation changes (planes land, new planes appear, etc.) is the subject of a separate paper (BEASLEY et al., 1995).

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Scheduling tasks with sequence-dependent processing times

Cited by 93 publications

References 4 publications

Low-complexity algorithms for sequencing jobs with a fixed number of job-classes

Low-complexity algorithms for sequencing jobs with a fixed number of job-classes

A New Mathematical Model for Flexible Flow Lines with Blocking Processor and Sequence-Dependent Setup Time

Scheduling Aircraft Landings—The Static Case

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