Analysis of Greedy Solutions for a Replacement Part Sequencing Problem

Friesen, Donald K.; Deuermeyer, Bryan L.

doi:10.1287/moor.6.1.74

Cited by 38 publications

(16 citation statements)

References 6 publications

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“…It has applications in the sequencing of maintenance actions for modular gas turbine aircraft engines, see [6]. In some sense it is dual -but in general not equivalent -to the well-known problem of minimizing the makespan which belongs to the class of packing problems.…”

Section: Related Objective Functionsmentioning

confidence: 99%

Comparing the minimum completion times of two longest-first scheduling-heuristics

Walter

2011

Cent Eur J Oper Res

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For the problem of non-preemptively scheduling n independent jobs on m identical parallel machines so that the minimum (or earliest) machine completion time is maximized, we compare two well-known longest-first heuristics -the LPT-(longest processing time) and the RLPT-heuristic (restricted LPT).We prove that the minimum completion time of the LPT-schedule is at least as long as the minimum completion time of the RLPT-schedule. Furthermore, we show that the minimum completion time of the RLPT-heuristic always remains within a factor of 1/m of the optimal minimum completion time. The paper finishes with a conjecture on the probabilistic behavior of the RLPT-heuristic compared to the LPT-heuristic in case of two machines.

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Section: Related Objective Functionsmentioning

confidence: 99%

Comparing the minimum completion times of two longest-first scheduling-heuristics

Walter

2011

Cent Eur J Oper Res

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“…The same objective was studied before for example in [5], where some additional motivation can be found.…”

Section: Introductionmentioning

confidence: 99%

A Note on Semi-online Machine Covering

Ebenlendr

Noga

Sgall

et al. 2006

Approximation and Online Algorithms

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Abstract. In the machine cover problem we are given m machines and n jobs to be assigned (scheduled) so that the smallest load of a machine is as large as possible. A semi-online algorithm is given in advance the optimal value of the smallest load for the given instance, and then the jobs are scheduled one by one as they arrive, without any knowledge of the following jobs. We present a deterministic algorithm with competitive ratio 11/6 ≤ 1.834 for machine covering with any number of machines and a lower bound showing that no deterministic algorithm can have a competitive ratio below 43/24 ≥ 1.791.

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“…The problem of finding a schedule which maximizes the minimum load, also known as the cover, is the famous Santa Claus problem on uniformly related machines (see e.g. [23,35,2,8,21,11,22]). Both these problems are concerned with the optimization of the extremum values of the set of machine loads.…”

Section: Introductionmentioning

confidence: 99%

A Unified Approach to Truthful Scheduling on Related Machines

Epstein¹,

Levin²,

Stee³

2013

Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms

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We present a unified framework for designing deterministic monotone polynomial time approximation schemes (PTAS's) for a wide class of scheduling problems on uniformly related machines. This class includes (among others) minimizing the makespan, maximizing the minimum load, and minimizing the p norm of the machine loads vector. Previously, this kind of result was only known for the makespan objective. Monotone algorithms have the property that an increase in the speed of a machine cannot decrease the amount of work assigned to it. The key idea of our novel method is to show that for goal functions that are sufficiently well-behaved functions of the machine loads, it is possible to compute in polynomial time a highly structured nearly optimal schedule. An interesting aspect of our approach is that, in contrast to all known approximation schemes, we avoid rounding any job sizes or speeds throughout. We can therefore find the exact best structured schedule using dynamic programming. The state space encodes a sufficient amount of information such that no postprocessing is needed, allowing an elegant and relatively simple analysis without any special cases. The monotonicity is a consequence of the fact that we find the best schedule in a specific collection of schedules. Monotone approximation schemes have an important role in the emerging area of algorithmic mechanism design. In the game-theoretical setting of these scheduling problems there is a social goal, which is one of the objective functions that we study. Each machine is controlled by a selfish singleparameter agent, where its private information is its cost of processing a unit sized job, which is also the inverse of the speed of its machine. Each agent wishes to maximize its own profit, defined as the payment it receives from the mechanism minus its cost for processing all jobs assigned to it, and places a bid which corresponds to its private information. For each one of the problems, we show that we can calculate payments that guarantee truthfulness in an efficient manner. Thus, there exists a dominant strategy where agents report their true speeds, and we show the existence of a truthful * Department of Mathematics, University of Haifa, 31905 Haifa, Israel. lea@math.haifa.ac.il.† Faculty of Industrial Engineering and Management, The Technion, 32000 Haifa, Israel. levinas@ie.technion.ac.il.‡ Max Planck Institute for Informatics, Saarbrücken, Germany. vanstee@mpi-inf.mpg.de mechanism which can be implemented in polynomial time, where the social goal is approximated within a factor of 1+ ε for every ε > 0.

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Analysis of Greedy Solutions for a Replacement Part Sequencing Problem

Cited by 38 publications

References 6 publications

Comparing the minimum completion times of two longest-first scheduling-heuristics

Comparing the minimum completion times of two longest-first scheduling-heuristics

A Note on Semi-online Machine Covering

A Unified Approach to Truthful Scheduling on Related Machines

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