RTCDMP Sample Clauses

RTCDMP. ‌ The time-relaxed timetable constrained distance minimisation problem is defined similar to how Xxxxxxxxx and Trick (2008) defined the TCDMP for time-constrained problems. The RTCDMP still consists out of finding an optimal home-away assignment, in terms of distance minimisation, for any given opponent schedule. However, this opponent schedule will now include one or more byes per team. While this seems like a minor adjustment, the impact on the complexity of the problem formulation is considerable. In fact, this problem is an adaptation of the problem studied in Section 4.2.1, where the opponent schedule is already fixed. Again, a more intuitive modelling approach is preferred for the scope of this master’s dissertation. ∈ ∈

RTCDMP. ‌ The time-relaxed timetable constrained distance minimisation problem is defined similar to how Xxxxxxxxx and Trick (2008) defined the TCDMP for time-constrained problems. The RTCDMP still consists out of finding an optimal home-away assignment, in terms of distance minimisation, for any given opponent schedule. However, this opponent schedule will now include one or more byes per team. While this seems like a minor adjustment, the impact on the complexity of the problem formulation is considerable. In fact, this problem is an adaptation of the problem studied in Section 4.2.1, where the opponent schedule is already fixed. Again, a more intuitive modelling approach is preferred for the scope of this master’s dissertation. ∈ ∈ | | ∪{ } ∈ ∈ ∪ {| | } In the following CP-model, T again denotes the set teams, while R denotes the set of rounds and R0 = R 0 . The number of byes is indicated by B and Ub sets the upper bound for the number of consecutive home or consecutive away games. The distance matrix is represented by D, and Dij equals the distance between the venues of team i and team j. The opponent schedule or time table is represented by TT , the opponent of team i in round r is indicated by TTir (TTi,r = 0 if team i has a bye in round r). In order to formulate this CP-model, two integer decision variable types are defined. To indicate whether a team plays at home, plays away or has a bye, decision variable hir is introduced for each i T and for each r R. hir equals 0 if team i plays away in round r, 1 if team i plays at home in round r and, similar to Bao (2009), 2 if team i has a bye in round r. Integer variable vir for each i T and each r R0 R + 1 indicates the venue where team i is located in round r. Dummy slots 0 and R + 1 are used to make sure every team starts and finishes the competition at their own venue. Dvirvi(r+1) indicates the distance team i travels between round r and round r + 1. This all results in the following CP-formulation for the RTCDMP. Σ Σ min: Dvirvi(r+1) (19) i∈T r∈R0 Σ