Minimizing mean absolute deviation of completion times about a common due date

Bagchi, Uttarayan; Sullivan, Robert S.; Chang, Yih–Long

doi:10.1002/nav.3800330206

Cited by 150 publications

(42 citation statements)

References 7 publications

(2 reference statements)

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“…Azizoglu and Webster [1997] introduced a branch-and-bound algorithm to solve the problem with setup times. Other researchers who worked on the same problems with a restricted (small) due date, included Bagchi et al [1986], Szwarc [1989Szwarc [ , 1996, , Alidee and Dragan [1997] and Mondal and Sen [2001].None of the previous papers consider sequence-dependent setup times. The majority of the literature on earliness and tardiness scheduling deals with problems that consider single machine only.…”

Section: Parallel Machines With Earliness/tardiness Problemmentioning

confidence: 99%

Scheduling with Setup Considerations: An MIP Approach

Omar¹,

Teo²,

Suppiah³

2007

Multiprocessor Scheduling, Theory and Applications

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Section: Parallel Machines With Earliness/tardiness Problemmentioning

confidence: 99%

Scheduling with Setup Considerations: An MIP Approach

Omar¹,

Teo²,

Suppiah³

2007

Multiprocessor Scheduling, Theory and Applications

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“…This objective function arises, for example, in the work of Kanet (1981), Sundararaghavan and Admed (1984), Bagchi et al (1986), Hall (1986), Emmons (1987), Szwarc (1989), and . The case cw, cdd, ns (and cpt or ncpt) gives rise to the objective function FiS) = a 2 £,• + j3 S Ti,…”

Section: Mahadev Pekec and Roberts / S121mentioning

confidence: 99%

On the Meaningfulness of Optimal Solutions to Scheduling Problems: Can an Optimal Solution be Nonoptimal?

Mahadev

Pekec

Roberts

1998

Operations Research

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We consider the problem of finding an optimal schedule for jobs on a single machine when there are penalties for both tardy and early arrivals. We point out that if attention is paid to how these penalties are measured, then a change of scale of measurement might lead to the anomalous situation where a schedule is optimal if these parameters are measured in one way, but not if they are measured in a different way that seems equally acceptable. In particular, we note that if the penalties measure utilities or disutilities, or loss of goodwill or customer satisfaction, then these kinds of anomalies can occur, for instance if we change both unit and zero point in scales measuring these penalties. We investigate situations where problems of these sorts arise for four specific penalty functions under a variety of different assumptions. The results of the paper have implications far beyond the specific scheduling problems we consider, and suggest that considerations of scale of measurement should enter into analysis of conclusions of optimality both in scheduling problems and throughout combinatorial optimization.M any practical problems involve the search for an optimal schedule. We consider the problem of scheduling n jobs on a single machine in which each job has a specified due date or completion time and a penalty is applied for a completion time different from the desired one. In many practical problems, a penalty is applied only for tardy completions; while more generally, a penalty is applied to both early and tardy completions, perhaps in a different way. The interest in scheduling problems where penalties are applied to early arrivals as well as late arrivals is closely tied to the concept of "just-in-time" production, the goal being to have "the right amount of materials of the right quality at the right time in the right place to produce the right quantity of items demanded by the next step of the production" (Cheng 1990). Because penalties can be applied to early arrivals, we allow the machine to lie idle and we schedule without preemption, i.e., we do not allow a job to be interrupted once it is started. The penalties we study involve weighting factors that weight the deviations from desired completion times.Often these weights are not uniquely determined. For instance, two weight assignments may be equally acceptable if they both give rise to the same ordering of the items or if one is related to the other by a change of scale. Typically weights are measured using some scale of measurement, and we examine the effect on the solution to a scheduling problem if we make admissible changes of scale. We show that in some cases such changes can transform an optimal solution into a nonoptimal one, and we systematically describe those situations when this anomaly occurs. More precisely, we show that the conclusion of optimality can be meaningless in a technical sense that we shall make precise. The main point of this paper is to show that considerations of scale change need to play a role in analysis of scheduli...

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“…Since the pioneer work of Kanet 3 which deals exclusively with the special case when the earliness and tardiness penalties are equal to one, many approximate algorithms have been proposed for various versions of the basic problem. Hall 4 and Bagchi et al 5,6 proposed algorithms for the absolute deviation SMETSP, which involve minimizing the sum of absolute deviations of the job completion times from a CDD. Hall and Posner 7 examined the unrestricted weighted earliness and tardiness problem.…”

Section: Introductionmentioning

confidence: 99%

A Particle Swarm Optimization Algorithm for Scheduling Against Restrictive Common Due Dates

Nearchou¹,

Omirou²

2013

IJCIS

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Abstract:Focusing on the just-in-time (JIT) operations management, earliness as well as, tardiness of jobs' production and delivery should be discouraged. In accordance to this philosophy, scheduling problems involving earliness and tardiness penalties are very critical for the operations manager. In this paper, a new population heuristic based on the particle swarm optimization (PSO) technique is presented to solve the single machine early/tardy scheduling problem against a restrictive common due date. This type of scheduling sets costs depending on whether a job finished before (earliness), or after (tardiness) the specified due date. The objective is to minimize a summation of earliness and tardiness penalty costs, thus pushing the completion time of each job as close as possible to the due date. The problem is known to be NP-hard, and therefore large size instances cannot be addressed by traditional mathematical programming techniques. The performance of the proposed PSO heuristic is measured over benchmarks problems with up to 1000 jobs taken from the open literature, and found quite high and promising in respect to the quality of the solutions obtained. Particularly, PSO was found able to improve the 82% of the existing best known solutions of the examined benchmarks test problems.

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Minimizing mean absolute deviation of completion times about a common due date

Cited by 150 publications

References 7 publications

Scheduling with Setup Considerations: An MIP Approach

Scheduling with Setup Considerations: An MIP Approach

On the Meaningfulness of Optimal Solutions to Scheduling Problems: Can an Optimal Solution be Nonoptimal?

A Particle Swarm Optimization Algorithm for Scheduling Against Restrictive Common Due Dates

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