Round-robin tournaments with homogeneous rounds

We study single and double round-robin tournaments for n teams, where in each round a fixed number (g) of teams is present and each team present plays a fixed number (m) of matches in this round. In a single, respectively double, round-robin tournament each pair of teams play one, respectively two, matches. In the latter case the two matches should be played in different rounds. We give necessary combinatorial conditions on the triples (n,g,m) for which such round-robin tournaments can exist, and discuss three general construction methods that concern the cases m=1, m=2 and m=g−1. For n≤20 these cases cover 149 of all 173 non-trivial cases that satisfy the necessary conditions. In 147 of these 149 cases a tournament can be constructed. For the remaining 24 cases the tournament does not exist in 2 cases, and is constructed in all other cases. Finally we consider the spreading of rounds for teams, and give some examples where well-spreading is either possible or impossible

Het toewijzen van voorkeursactiviteiten

De artikel beschrijft alternatieven op de gebruikelijke manier van het opgeven van voorkeuren met een eerste, tweede, derde (etc.) voorkeur

An assessment of a days off decomposition approach to personnel scheduling

This paper studies a two-phase decomposition approach to solve the personnel scheduling problem. The first phase creates a days off schedule, indicating working days and days off for each employee. The second phase assigns shifts to the working days in the days off schedule. This decomposition is motivated by the fact that personnel scheduling constraints are often divided in two categories: one specifies constraints on working days and days off, while the other specifies constraints on shift assignments. To assess the consequences of the decomposition approach, we apply it to public benchmark instances, and compare this to solving the personnel scheduling problem directly. In all steps we use mathematical programming. We also study the extension that includes night shifts in thefirst phase of the decomposition. We present a detailed results analysis, and analyze the effect of various instance parameters on the decompositions' results. In general, we observe that the decompositions significantly reduce the computation time, and that they produce good solutions for most instances