Quality of move-optimal schedules for minimizing total weighted completion time

Brueggemann, Tobias; Hurink, Johann L.; Kern, Walter

doi:10.1016/j.orl.2005.08.003

Cited by 11 publications

(13 citation statements)

References 6 publications

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“…The problem under study, Q|| ∑ w j C j , is a generalization of the problem in an environment with identical parallel machines, represented by P|| ∑ w j C j . For this problem, Brueggemann et al [43] determined that the performance guarantee for solutions obtained using the Jump neighborhood lies within the interval [1.2, (3m − 1)/2m]. Regarding this result, it can be observed that the parametric upper bound for the performance guarantee for the Jump neighborhood proposed in Lemma 5 coincides with the value reported in [43] when s 1 = s m = 1.…”

Section: Discussionmentioning

confidence: 51%

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Developing New Bounds for the Performance Guarantee of the Jump Neighborhood for Scheduling Jobs on Uniformly Related Machines

Muñoz,

Latorre-Núñez,

Ramos-Maldonado

2023

Mathematics

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This study investigates the worst-case performance guarantee of locally optimal solutions to minimize the total weighted completion time on uniformly related parallel machines. The investigated neighborhood structure is Jump, also called insertion or move. This research focused on establishing the local optimality condition expressed as an inequality and mapping that maps a schedule into an inner product space so that the norm of the mapping is closely related to the total weighted completion time of the schedule. We determine two new upper bounds for the performance guarantee, which take the form of an expression based on parameters that describe the family of instances: the speed of the fastest machine, the speed of the slowest machine, and the number of machines. These new bounds outperform the parametric upper bound previously established in the existing literature and enable a better understanding of the performance of the solutions obtained for the Jump neighborhood in this scheduling problem, according to parameters that describe the family of instances.

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Section: Discussionmentioning

confidence: 51%

“…These open gaps highlight a research opportunity to establish a tight performance guarantee for the problem or narrow the gap between the upper and lower bounds. However, the challenge seems complicated since some gaps have remained open for over fifteen years, such as the gap of the P|| ∑ w j C j problem [43].…”

Section: Related Workmentioning

confidence: 99%

Developing New Bounds for the Performance Guarantee of the Jump Neighborhood for Scheduling Jobs on Uniformly Related Machines

Muñoz,

Latorre-Núñez,

Ramos-Maldonado

2023

Mathematics

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“…This penalty seems to be appropriate when each job should be provided with a different due date, the weighting expressing the relative importance of each order. Some recent references addressing weighted completion time minimisation are Tang et al (2006) for the hybrid flowshop, and Brueggemann et al (2006) for the identical machine case.…”

Section: Simultaneous Approachmentioning

confidence: 99%

Available-to-promise (ATP) systems: a classification and framework for analysis

Framiñán

Leisten

2009

International Journal of Production Research

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Available-To-Promise (ATP) systems deal with a number of managerial decisions related to Order Capture activities in a company, including order acceptance/rejection, due date setting, and resource scheduling. These different but interrelated decisions have been often studied in an isolated manner, and, to the best of our knowledge, no framework has been presented to integrate them into the broader perspective of Order Capture. This paper attempts to provide a general framework for ATP-related decisions. By doing so, we 1) identify the different decision problems to be addressed, 2) present the different literature-based models supporting related decisions into a coherent framework, and 3) review the main contributions in the literature for each one of these. We first describe different approaches for Order Capture available in the literature, depending on two parameters related to the application context of ATP systems, namely the inclusion of explicit information about due dates in the decision model, and the level of integration among decisions. According to these parameters, up to six approaches for ATP-related decisions are identified. Secondly, we show the subsequent decision problems derived from the different approaches, and describe the main issues and key references involving each one of these decision problems. Finally, a number of conclusions and future research lines are discussed.

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“…The number of moves needed to find a jump‐optimal solution by means of an iterative improvement procedure is \documentclass{article} \usepackage{mathrsfs} \usepackage{amsmath, amssymb} \pagestyle{empty} \begin{document} \begin{align*}\mathcal{O}(n^2)\end{align*} \end{document} (as shown by Brucker et al [3]) and there exist instances for which this bound is asymptotically tight (as shown by Hurkens and Vredeveld [12]). Other results on performance guarantees of local optima in the area of scheduling have been derived by Brueggemann et al [4] (for minimizing the total weighted completion time as objective function) and by Recalde et al [15] (for makespan minimization on a certain variant of related parallel machines).…”

Section: Introductionmentioning

confidence: 99%

Exponential size neighborhoods for makespan minimization scheduling

Brueggemann¹,

Hurink²,

Vredeveld³

et al. 2011

Naval Research Logistics

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Abstract:We investigate the quality of local search heuristics for the scheduling problem of minimizing the makespan on identical parallel machines. We study exponential size neighborhoods (whose size grows exponentially with the input length) that can be searched in polynomial time, and we derive worst-case approximation guarantees for the local optima of such neighborhoods. The so-called split neighborhood splits a feasible schedule into two layers, and then recombines the two layers by finding a perfect matching. We show that the makespan of every local optimum for split is at most a factor of 2 away from the globally optimal makespan. We then combine the split neighborhood with two neighborhoods from the literature. The combination of split with the jump neighborhood only marginally improves the approximation guarantee, whereas the combination with the lexicographicjump neighborhood decreases the approximation guarantee from 2 to 3/2.

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Quality of move-optimal schedules for minimizing total weighted completion time

Cited by 11 publications

References 6 publications

Developing New Bounds for the Performance Guarantee of the Jump Neighborhood for Scheduling Jobs on Uniformly Related Machines

Developing New Bounds for the Performance Guarantee of the Jump Neighborhood for Scheduling Jobs on Uniformly Related Machines

Available-to-promise (ATP) systems: a classification and framework for analysis

Exponential size neighborhoods for makespan minimization scheduling

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