For the airplane refueling problem local precedence implies global precedence

Vásquez, Óscar C.

doi:10.1007/s11590-014-0758-2

Cited by 7 publications

(8 citation statements)

References 20 publications

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“…For example Höhn and Jacobs (2012a) showed that if β = 2 and p i ≤ p j then i ≺ g j if and only if i ≺ j. The same characterization has been shown for a related objective function, where one wants to maximize w j C −1 j (Vásquez 2014). This situation motivates us to state the following conjecture.…”

Section: Our Contributionmentioning

confidence: 72%

The local–global conjecture for scheduling with non-linear cost

Bansal¹,

Dürr²,

Thắng³

et al. 2016

J Sched

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We consider the classical scheduling problem on a single machine, on which we need to schedule sequentially n given jobs. Every job j has a processing time p j and a priority weight w j , and for a given schedule a completion time C j . In this paper we consider the problem of minimizing the objective value j w j C β j for some fixed constant β > 0. This non-linearity is motivated for example by the learning effect of a machine improving its efficiency over time, or by the speed scaling model. For β = 1, the well-known Smith's rule that orders job in the non-increasing order of w j /p j give the optimum schedule. However, for β = 1, the complexity status of this problem is open. Among other things, a key issue here is that the ordering between a pair of jobs is not well-defined, and might depend on where the jobs lie in the schedule and also on the jobs between them. We investigate this question systematically and substantially generalize the previously known results in this direction. These results lead to interesting new dominance properties among schedules which lead to huge speed up in exact algorithms for the problem. An experimental study evaluates the impact of these properties on the exact algorithm

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Section: Our Contributionmentioning

confidence: 72%

The local–global conjecture for scheduling with non-linear cost

Bansal¹,

Dürr²,

Thắng³

et al. 2016

J Sched

View full text Add to dashboard Cite

show abstract

“…Latter, Bansal et al [4] confirmed this conjecture, and they also gave a counter example of the generalized conjecture that i ≺ l[a,b] j implies i ≺ g[a,b] j. For airplane refueling problem, Vsquez [17]…”

Section: Related Workmentioning

confidence: 93%

“…⊓ ⊔ Dominance rule Vsquez [17] proved the following dominance properties of airplane refueling problem.…”

Section: Preliminariesmentioning

confidence: 99%

“…As pointed out by Vsquez [17], we can rephrase the problem as a single machine scheduling problem, which is equivalent to finding a permutation π(the reverse of σ) that minimizes:…”

Section: Introductionmentioning

confidence: 99%

“…, |J|} → J, where σ(i) = j if airplane j is the i th airplane to leave the fleet. As a result, the objective value of the drop out order σ is: As pointed out by Vsquez [17], we can rephrase the problem as a single machine scheduling problem, which is equivalent to finding a permutation π(the reverse of σ) that minimizes:…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Fast Exact Algorithm for Airplane Refueling Problem

Luo

et al. 2019

Combinatorial Optimization and Applications

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We consider the airplane refueling problem, where we have a fleet of airplanes that can refuel each other. Each airplane is characterized by specific fuel tank volume and fuel consumption rate, and the goal is to find a drop out order of airplanes that last airplane in the air can reach as far as possible. This problem is equivalent to the scheduling problem 1|| wj (− 1 C j ). Based on the dominance properties among jobs, we reveal some structural properties of the problem and propose a recursive algorithm to solve the problem exactly. The running time of our algorithm is directly related to the number of schedules that do not violate the dominance properties. An experimental study shows our algorithm outperforms state of the art exact algorithms and is efficient on larger instances.

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On the local dominance properties in single machine scheduling problems

Jorquera-Bravo,

Vásquez

2024

Ann Oper Res

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For the airplane refueling problem local precedence implies global precedence

Cited by 7 publications

References 20 publications

The local–global conjecture for scheduling with non-linear cost

The local–global conjecture for scheduling with non-linear cost

A Fast Exact Algorithm for Airplane Refueling Problem

On the local dominance properties in single machine scheduling problems

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