Integer optimization problems are concerned with the efficient allocation of limited resources to meet a desired objective when some of the resources in question can only be divided into discrete parts. In such cases, the divisibility constraints on these resources, which may be people, machines, or other discrete inputs, may restrict the possible alternatives to a finite set. Nevertheless, there are usually too many alternatives to make complete enumeration a viable option for instances of realistic size. For example, an airline may need to determine crew schedules that minimize the total operating cost; an automotive manufacturer may want to determine the optimal mix of models to produce in order to maximize profit; or a flexible manufacturing facility may want to schedule production for a plant without knowing precisely what parts will be needed in future periods. In today’s changing and competitive industrial environment, the difference between ad hoc planning methods and those that use sophisticated mathematical models to determine an optimal course of action can determine whether or not a company survives.

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Integer and Combinatorial Optimization

Round robin scheduling – a survey

http://www.cs.nott.ac.uk/~pszgxk/papers/corsportsbib.pdf

Invited Review: Scheduling in sports: An annotated bibliography

http://www.info.univ-angers.fr/pub/hao/papers/EJOR08.pdf

Adaptive Tabu Search for course timetabling

Volleyball Premier League Algorithm

https://mat.tepper.cmu.edu/trick/benders.pdf

A Benders approach for the constrained minimum break problem

Scheduling a triple round robin tournament for the best Danish soccer league

We define the timetable constrained distance minimization problem (TCDMP) which is a sports scheduling problem applicable for tournaments where the total travel distance must be minimized. The problem consists of finding an optimal home-away assignment when the opponents of each team in each time slot are given. We present an integer programming, a constraint programming formulation and describe two alternative solution methods: a hybrid integer programming/constraint programming approach and a branch and price algorithm. We test all four solution methods on benchmark problems and compare the performance. Furthermore, we present a new heuristic solution method called the circular traveling salesman approach (CTSA) for solving the traveling tournament problem. The solution method is able to obtain high quality solutions almost instantaneously, and by applying the TCDMP, we show how the solutions can be further improved.

/pdf/the-timetable-constrained-distance-minimization-problem-3aig77b0wz.pdf

The timetable constrained distance minimization problem

The Timetable Constrained Distance Minimization Problem is a sports scheduling problem applicable for tournaments where the total travel distance must be minimized. In this paper we define the problem and present an integer programming and a constraint programming formulation for the problem. Furthermore, we describe a hybrid integer programming/constraint programming approach and a branch and bound algorithm for solving the Timetable Constrained Distance Minimization Problem. Finally, the computational performances of the four solution methods are tested and compared.

/pdf/the-timetable-constrained-distance-minimization-problem-x22vmnkv48.pdf

Rasmus V. Rasmussen

Papers

Round robin scheduling – a survey

A Benders approach for the constrained minimum break problem

Scheduling a triple round robin tournament for the best Danish soccer league

The timetable constrained distance minimization problem

The timetable constrained distance minimization problem