Ten notes on equal-processing-time scheduling

Baptiste, Philippe; Brucker, Peter; Knust, Sigrid; Timkovsky, Vadim G.

doi:10.1007/s10288-003-0024-4

Cited by 43 publications

(36 citation statements)

References 22 publications

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“…In [2], a polynomial time algorithm with the complexity O(n 6m+1 ) was proposed for problem P m | r j , p j = p | w j U j . The algorithm is based on the following observations and definitions:…”

Section: 115mentioning

confidence: 99%

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Parallel machine problems with equal processing times: a survey

Kravchenko

Werner

2011

J Sched

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The basic scheduling problem we are dealing with is the following. There are n jobs, each requiring an identical execution time. All jobs have to be processed on a set of parallel machines. Preemptions can be either allowed or forbidden. The aim is to construct a feasible schedule such that a given criterion is minimized. For a couple of problems of this type, recently the complexity status has been solved and several interesting results have been presented. In this paper, we survey existing approaches for the problem class considered.

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Section: 115mentioning

confidence: 99%

Section: In [28]mentioning

confidence: 99%

Parallel machine problems with equal processing times: a survey

Kravchenko

Werner

2011

J Sched

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“…Baptiste (1999) gives a polynomial time algorithm for the 1|r j , p j = p| w j U j problem based on dynamic programming. In Baptiste et al (2004) ten equal-processing-time scheduling problems are shown to be solvable in polynomial time, among which is the P m|r j , p j = p| w j U j problem. An overview of more problems with equal processing times can be found in Leung (2004).…”

Section: Introductionmentioning

confidence: 99%

Minimizing total weighted tardiness on a single machine with release dates and equal-length jobs

Akker

Diepen²,

Hoogeveen

2010

J Sched

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In this paper we study the problem of scheduling n jobs with release dates, due dates, weights, and equal processing times on a single machine. The objective is to minimize total weighted tardiness. We formulate the problem as a time-indexed ILP after which we solve the LPrelaxation. We show that for certain special cases (namely when either all due dates, all weights, or all release dates are equal, or when all due dates and release dates are equally ordered), the solution for the LP-relaxation is either integral or can be adjusted in polynomial time into an integral one. For the general case we present a branching rule that performs well. Furthermore we show that the same approach holds for the m identical, parallel machines variant of the problem. Finally we show that with a minor modification the same approach also holds for the single-machine problems of minimizing the sum of weighted late jobs (1|r j , p j = p| w j U j ) and the sum of weighted late work (1|r j , p j = p| w j V j ) as well as their respective variants with m identical, parallel machines. We further show how we can solve these problems by applying column genera-

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“…This reduction is based on a construction presented by Baptiste at al. [3] who consider the problem P m |r i , p i = 1, chains| f i .…”

Section: Equal Consumption Of Convertersmentioning

confidence: 99%

Minimizing costs is easier than minimizing peaks when supplying the heat demand of a group of houses

Fink

Hurink

2015

European Journal of Operational Research

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This paper studies planning problems for a group of heating systems which supply the hot water demand for domestic use in houses. These systems (e.g. gas or electric boilers, heat pumps or microCHPs) use an external energy source to heat up water and store this hot water for supplying the domestic demands. The latter allows to some extent a decoupling of the heat production from the heat demand. We focus on the situation where each heating system has its own demand and buffer and the supply of the heating systems is coming from a common source. In practice, the common source may lead to a coupling of the planning for the group of heating systems. On the one hand, the external supply of the energy for heating up the water may have to be bought by an energy supplier on e.g. a day-ahead market. As the price of energy varies over time on such markets, this supplier is interested in a planning which minimizes the total cost to supply the heating systems with energy. On the other hand, the bottleneck to supply the energy also may be the capacity of the distribution system (e.g. the electricity networks or the gas network). As this has to be dimensioned for the maximal consumption, in this case it is important to minimize the maximal peak.The two mentioned coupling constraints for supplying the energy for producing the heat, lead to two different objectives for the planning of the group of heating systems: minimizing cost and minimizing the maximal peak. In this paper, we study the algorithmic complexity of the two resulting planning problems. For minimizing costs, a classical dynamic programming approach is given which solves the problem in polynomial time. On the other hand, we prove that minimizing the maximal peak is NP-hard and discuss why this problem is hard. Based on this, we show that this problem becomes polynomial if all heating systems have the same consumption of energy when turned on. Finally, we present a Fix Parameter Tractable (FPT) algorithm for minimizing the maximal peak which is linear in the number of time intervals.

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Ten notes on equal-processing-time scheduling

Abstract: Equal-processing-time scheduling problems whose complexity status has been unknown are shown to be solved in polynomial time by well-known and relatively new techniques. Single-machine, parallel-machine, parallel-batch, openshop, flow-shop and job-shop environments are touched upon.

Cited by 43 publications

References 22 publications

Parallel machine problems with equal processing times: a survey

Parallel machine problems with equal processing times: a survey

Minimizing total weighted tardiness on a single machine with release dates and equal-length jobs

Minimizing costs is easier than minimizing peaks when supplying the heat demand of a group of houses

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