Low-complexity algorithms for sequencing jobs with a fixed number of job-classes

Veen, Jack A.A. van der; Zhang, Shuzhong

doi:10.1016/0305-0548(96)00016-0

Cited by 19 publications

(12 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For more on the job shop scheduling problem with sequence-dependent processing/setup times see LOCKETT and MUHLEMANN (1972), WHITE and WIL- SON (1977), SO (1990), GUINET (1991GUINET ( , 1993, SIMCHI-LEVI and BERMAN (1991), OVACIK and UZSOY (1993, JORDAN and DREXL (1995), LOW (1995), RUBIN and RAGATZ (1995), BRUCKER and THIELE (1996), FRANCA et al (1996), LIAO and YU (1996), VAN DER VEEN and ZHANG (1996), HWANG and SUN (1997), LEE, BHASKARAN, and PINEDO (1997), , TAN and NARASIMHAN (1997).…”

Section: Previous Workmentioning

confidence: 99%

Scheduling Aircraft Landings—The Static Case

Beasley

Krishnamoorthy

Sharaiha

et al. 2000

Transportation Science

361

309

View full text Add to dashboard Cite

In this paper, we consider the problem of scheduling aircraft (plane) landings at an airport. This problem is one of deciding a landing time for each plane such that each plane lands within a predetermined time window and that separation criteria between the landing of a planeInthispaper,weconsidertheproblemofscheduling aircraft (plane) landings at an airport. This problem is one of deciding a landing time on a runway for each plane in a given set of planes such that each plane lands within a predetermined time window, and that separation criteria between the landing of a plane, and the landing of all successive planes, are respected.This paper is organized as follows. In Section 1, we set the problem in context. In Section 2, we present a mixed-integer zero-one formulation of the problem for the single runway case. We then discuss previous work on the problem in Section 3. In Section 4, we extend the formulation to the multiple runway case, and, in Section 5, we strengthen the linear programming (LP) relaxations of these formulations by introducing additional constraints. These formulations can be solved using LP-based tree search. An effective heuristic for the problem (for any number of runways) is presented in Section 6. Computational results for both the heuristic and the optimal algorithm for a number of test problems involving up to 50 planes and four runways are presented in Section 7.It is important to note here that, although throughout this paper we shall typically refer to planes landing, the models presented in this paper are applicable to problems involving just takeoffs only and to problems involving a mix of landings and takeoffs on the same runway. We should also stress here that we are dealing only with the static case. In other words, we are dealing with the off-line case where we have complete knowledge of the set of planes that are going to land. The dynamic, or on-line, case, where decisions about the landing times for planes must be made as time passes and the situation changes (planes land, new planes appear, etc.) is the subject of a separate paper (BEASLEY et al., 1995).

show abstract

Section: Previous Workmentioning

confidence: 99%

Scheduling Aircraft Landings—The Static Case

Beasley

Krishnamoorthy

Sharaiha

et al. 2000

Transportation Science

361

309

View full text Add to dashboard Cite

show abstract

“…Due to the special combinatorial structure of the many-visits TSP, the connectivity problem can be solved efficiently. An alternative solution method based on integer programming yielding the same computational complexity has been given in Van der Veen and Zhang [128].…”

Section: The Circulant Tspmentioning

confidence: 99%

Well-Solvable Special Cases of the Traveling Salesman Problem: A Survey

Burkard

Deı̆neko

Dal³

et al. 1998

SIAM Rev.

158

104

View full text Add to dashboard Cite

Abstract. The traveling salesman problem (TSP) belongs to the most basic, most important, and most investigated problems in combinatorial optimization. Although it is an N P-hard problem, many of its special cases can be solved efficiently in polynomial time. We survey these special cases with emphasis on the results that have been obtained during the decade [1985][1986][1987][1988][1989][1990][1991][1992][1993][1994][1995]

show abstract

“…As a natural TSP-generalization, MV-TSP is a fundamental problem of independent interest. In addition, MV-TSP proved to be useful for modeling other problems, particularly in scheduling [7,22,37,40]. Suppose there are k jobs of n different types to be executed on a single, universal machine.…”

Section: Introductionmentioning

confidence: 99%

“…There have been further studies of the MV-TSP problem. Van der Veen and Zhang [40] discuss a problem equivalent to MV-TSP, called K-group TSP, and describe an algorithm with polylogarithmic dependence on the number k of visits (similarly to Cosmadakis and Papadimitriou). The value n however is assumed constant, and its effect on the run time is not explicitly computed (the dependence can be seen to be superexponential).…”

Section: Introductionmentioning

confidence: 99%

Time- and Space-optimal Algorithm for the Many-visits TSP

Berger

Kozma

Mnich

et al. 2020

ACM Trans. Algorithms

View full text Add to dashboard Cite

The many-visits traveling salesperson problem (MV-TSP) asks for an optimal tour of n cities that visits each city c a prescribed number k c of times. Travel costs may be asymmetric, and visiting a city twice in a row may incur a non-zero cost. The MV-TSP problem finds applications in scheduling, geometric approximation, and Hamiltonicity of certain graph families. The fastest known algorithm for MV-TSP is due to Cosmadakis and Papadimitriou (SICOMP, 1984). It runs in time n O(n) + O(n 3 log ∑ c k c ) and requires n ᶿ(n) space. An interesting feature of the Cosmadakis-Papadimitriou algorithm is its logarithmic dependence on the total length ∑ c k c of the tour, allowing the algorithm to handle instances with very long tours. The superexponential dependence on the number of cities in both the time and space complexity, however, renders the algorithm impractical for all but the narrowest range of this parameter. In this article, we improve upon the Cosmadakis-Papadimitriou algorithm, giving an MV-TSP algorithm that runs in time 2 O(n) , i.e., single-exponential in the number of cities, using polynomial space. The space requirement of our algorithm is (essentially) the size of the output, and assuming the Exponential-Time Hypothesis (ETH), the problem cannot be solved in time 2 o(n) . Our algorithm is deterministic, and arguably both simpler and easier to analyze than the original approach of Cosmadakis and Papadimitriou. It involves an optimization over directed spanning trees and a recursive, centroid-based decomposition of trees.

show abstract

Low-complexity algorithms for sequencing jobs with a fixed number of job-classes

Cited by 19 publications

References 10 publications

Scheduling Aircraft Landings—The Static Case

Scheduling Aircraft Landings—The Static Case

Well-Solvable Special Cases of the Traveling Salesman Problem: A Survey

Time- and Space-optimal Algorithm for the Many-visits TSP

Contact Info

Product

Resources

About