Minimizing absolute and squared deviations of completion times with different earliness and tardiness penalties and a common due date

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

doi:10.1002/1520-6750(198710)34:5<739::aid-nav3220340513>3.0.co;2-3

Cited by 94 publications

(41 citation statements)

References 9 publications

(13 reference statements)

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The jobs after j * are tardy and are sequenced in non-decreasing order of the ratio C j /γ j . Such a schedule is called a V-shaped sequence [3] [11]. The optimality of V-shaped schedules for common due date problems have also been observed in [83].…”

Section: Equal Order Arrival Timesmentioning

confidence: 99%

“…Under the assumption of equal job arrival times, a number of authors studied the common due date problem (CON), where all the jobs are assigned a common due date d and the goal is to jointly determine the common due date and a sequence [3] [79]. The objective functions considered in these papers can be characterized by the following general function of earliness, tardiness and the due date:…”

Section: Equal Order Arrival Timesmentioning

confidence: 99%

“…In [75], β j = β, γ j = γ and α j = α; in [3], β j = β, γ j = γ and α j = 0; in [21], β j = γ j = w j and α j = 0; in [24], β j = γ j = w j and α j = α. In this problem, it is easy to show that the optimal due date d is equal to the completion time of some job j * , i.e., d = C j * .…”

Section: Equal Order Arrival Timesmentioning

confidence: 99%

“…Optimality conditions for the case a = b = s along with an iterative procedure for determining d (for a given sequence) are given in [24]. Enumeration algorithms for jointly determining the due date and the optimal sequence are presented in [3] and [21].…”

Section: Equal Order Arrival Timesmentioning

confidence: 99%

See 3 more Smart Citations

Due Date Management Policies

Keskinocak

Tayur

2004

International Series in Operations Research &Amp; Management Science

View full text Add to dashboard Cite

Section: Equal Order Arrival Timesmentioning

confidence: 99%

Section: Equal Order Arrival Timesmentioning

confidence: 99%

Section: Equal Order Arrival Timesmentioning

confidence: 99%

Section: Equal Order Arrival Timesmentioning

confidence: 99%

See 2 more Smart Citations

Due Date Management Policies

Keskinocak

Tayur

2004

International Series in Operations Research &Amp; Management Science

View full text Add to dashboard Cite

“…and this objective function has been studied by, for example, Panwalkar et al (1982), Emmons (1987), and Bagchi et al (1987). The objective function arising in the case new, cdd, ns (and cpt or ncpt) has been studied, for example, by Ahmed and Sundararaghavan (1990), Cheng (1987), Emmons (1987), Ouaddus (1987), Bector et al (1988), Baker and Scudder (1989), Hall and Posner (1991), and Hoogeveen and van de Velde (1991).…”

Section: =1 1=1mentioning

confidence: 99%

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

Mahadev

Pekec

Roberts

1998

Operations Research

View full text Add to dashboard Cite

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...

show abstract

Scheduling stochastic jobs with asymmetric earliness and tardiness penalties

Cai¹,

Zhou²

1997

Naval Research Logistics

View full text Add to dashboard Cite

We consider a stochastic counterpart of the well‐known earliness‐tardiness scheduling problem with a common due date, in which n stochastic jobs are to be processed on a single machine. The processing times of the jobs are independent and normally distributed random variables with known means and known variances that are proportional to the means. The due dates of the jobs are random variables following a common probability distribution. The objective is to minimize the expectation of a weighted combination of the earliness penalty, the tardiness penalty, and the flow‐time penalty. One of our main results is that an optimal sequence for the problem must be V‐shaped with respect to the mean processing times. Other characterizations of the optimal solution are also established. Two algorithms are proposed, which can generate optimal or near‐optimal solutions in pseudopolynomial time. The proposed algorithms are also extended to problems where processing times do not satisfy the assumption in the model above, and are evaluated when processing times follow different probability distributions, including general normal (without the proportional relation between variances and means), uniform, Laplace, and exponential. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44, 531–557, 1997.

show abstract

Minimizing absolute and squared deviations of completion times with different earliness and tardiness penalties and a common due date

Cited by 94 publications

References 9 publications

Due Date Management Policies

Due Date Management Policies

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

Scheduling stochastic jobs with asymmetric earliness and tardiness penalties

Contact Info

Product

Resources

About