A Benders approach for the constrained minimum break problem

Abstract

Abstract. This paper presents a hybrid IP/CP algorithm for designing a double round robin schedule with a minimal number of breaks. Both mirrored and non-mirrored schedules with and without place constraints are considered. The algorithm uses Benders cuts to obtain feasible homeaway pattern sets in few iterations and this approach leads to significant reductions in computation time for hard instances. Furthermore, the algorithm is capable of solving a number of previously unsolved benchmark problems for the Traveling Tournament Problem with constant distances.

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

“…Rasmussen and Trick [14] presented a MILP model to check if the condition is satisfied for all subsets of cardinality Z. The model finds the subset of patterns with fewest possible mutual games.…”

“…To check feasibility of Part 2, we use both the pattern diversity condition and the multiple pattern separation condition known from [14]. However, both feasibility checks can be strengthened compared to the original presentation due to the additional constraints considered in this application.…”

“…The constraint (4.30) makes sure that Z teams are included in the subset and constraints (4.31) and (4.32) require that β s is equal to the number of home games if δ s = 1 and equal to the number of away games if δ s = 0. We can now use the pattern diversity condition [14] to perform the first feasibility check.…”

“…This difference results in a number of additional constraints which must be satisfied in order to get a fair tournament. Furthermore, this work is the first applying the techniques of the pattern generating Benders approach (PGBA) presented by Rasmussen and Trick [14] to a practical application.…”

Constructive Algorithms for the Constant Distance Traveling Tournament Problem

“…The CDTTP and its variations are discussed in [3,5]. The CDTTP can be considered as a special class of the original TTP [1] such that all distances between team sites are one.…”