Two exact algorithms for the traveling umpire problem

Li, Xue; Luo, Zhixing; Lim, Andrew

doi:10.1016/j.ejor.2014.12.038

Cited by 14 publications

(7 citation statements)

References 21 publications

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“…Before this work, only three 14-team instances had their optimal proven. Xue et al (2015) required around 46 hours to prove optimality for two of these instances (the runtime to obtain the optimal solution for instance 14B-5,3, collected from Trick and Yildiz website, 2 is unknown). The proposed branch-and-bound with decomposition-based lower bounds is able to find (and prove) these optimal solutions in around 4 minutes, in total.…”

Section: Results Of the Branch-and-bound With Decomposition-based Lower Boundsmentioning

confidence: 99%

“…The best bounds are highlighted. The time limit for these hard instances was set to 48 hours, in order to enable comparison with the approaches proposed by Xue et al (2015). In this table, we omit the results obtained with the mathematical formulation as they were not competitive.…”

Section: Results Of the Branch-and-bound With Decomposition-based Lower Boundsmentioning

confidence: 99%

“…This section is organized as follows. First the results obtained by the presented approach are compared with the best known results from the literature (de Oliveira et al, 2014;Toffolo et al, 2014;Trick & Yildiz, 2007, 2011, 2013Wauters et al, 2014;Xue et al, 2015), as well as with the results obtained using formulation (1)-(8). Finally, the impact of the components of the presented branch-and-bound is discussed in Section 5.2.…”

Section: Computational Experimentsmentioning

confidence: 99%

“…Two branching strategies were investigated and many bounds were improved. Xue, Luo, and Lim (2015) presented two exact approaches to the TUP: a branchand-bound algorithm relying on a Lagrangian relaxation for obtaining 1 Trick and Yildiz (2007) lower bounds and a branch-and-price-and-cut algorithm. The latter approach enabled solving two 14-team instances within the runtime limit of 48 hours.…”

Section: Introductionmentioning

confidence: 99%

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Branch-and-bound with decomposition-based lower bounds for the Traveling Umpire Problem

Toffolo

Wauters

Malderen

et al. 2016

European Journal of Operational Research

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The Traveling Umpire Problem (TUP) is an optimization problem in which umpires have to be assigned to games in a double round robin tournament. The objective is to obtain a solution with minimum total travel distance over all umpires, while respecting hard constraints on assignments and sequences. Up till now, no general nor dedicated algorithm was able to solve all instances with 12 and 14 teams. We present a novel branch-and-bound approach to the TUP, in which a decomposition scheme coupled with an efficient propagation technique produces the lower bounds. The algorithm is able to generate optimal solutions for all the 12-and 14-team instances as well as for 11 of the 16-team instances. In addition to the new optimal solutions, some new best solutions are presented and other instances have been proven infeasible.

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Section: Results Of the Branch-and-bound With Decomposition-based Lower Boundsmentioning

confidence: 99%

Section: Results Of the Branch-and-bound With Decomposition-based Lower Boundsmentioning

confidence: 99%

Section: Computational Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Branch-and-bound with decomposition-based lower bounds for the Traveling Umpire Problem

Toffolo

Wauters

Malderen

et al. 2016

European Journal of Operational Research

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“…Toffolo et al (2014) presents a branch and price algorithm which improved the solutions of five instances of 16-teams and proved the infeasibility of some others for the first time. Xue et al (2015) introduced two other exact algorithms which were capable of solving two 14 teams-instances to optimality for the first time. Recently, Toffolo et al (2016b) presented a branch and bound algorithm coupled with a decomposition method that produces strong lower bounds.…”

Section: Problem Definitionmentioning

confidence: 99%

Analysis of a constructive matheuristic for the traveling umpire problem

Chandrasekharan

Toffolo

Wauters

2018

Journal of Quantitative Analysis in Sports

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The Traveling Umpire Problem (TUP) is a combinatorial optimization problem concerning the assignment of umpires to the games of a fixed double round-robin tournament. The TUP draws inspiration from the real world multi-objective Major League Baseball (MLB) umpire scheduling problem, but is, however, restricted to the single objective of minimizing total travel distance of the umpires. Several hard constraints are employed to enforce fairness when assigning umpires, making it a challenging optimization problem. The present work concerns a constructive matheuristic approach which focuses primarily on large benchmark instances. A decomposition-based approach is employed which sequentially solves Integer Programming (IP) formulations of the subproblems to arrive at a feasible solution for the entire problem. This constructive matheuristic efficiently generates feasible solutions and improves the best known solutions of large benchmark instances of 26, 28, 30 and 32 teams well within the benchmark time limit. In addition, the algorithm is capable of producing feasible solutions for various small and medium benchmark instances competitive with those produced by other heuristic algorithms. The paper also details experiments conducted to evaluate various algorithmic design parameters such as subproblem size, overlap and objective functions.

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