Breaks, cuts, and patterns

Wegeneralize the concept of a break by considering pairs of arbitrary rounds.Weshow that a set of homeaway patterns minimizing the number of generalized breaks cannot be found in polynomial time, unless P = NP. When all teams have the same break set, the decision version becomes easy; optimizing remains NP-hard.status: publishe

The transportation problem with exclusionary side constraints.

We consider the so-called Transportation Problem with Exclusionary Side Con- straints (TPESC), which is a generalization of the ordinary transportation problem. We determine the complexity status for each of two special cases of this problem, by proving NP-completeness, and by exhibiting a pseudo-polynomial time algorithm. For the general problem, we show that it cannot be approximated with a constant perfor- mance ratio in polynomial time (unless P=NP). These results settle the complexity status of the TPESC.

Soccer schedules in Europe: an overview

In this paper, we give an overview of the competition formats and the schedules used in 25 European soccer competitions for the season 2008-2009. We discuss how competitions decide the league champion, qualification for European tournaments, and relegation. Following Griggs and Rosa (Bull. ICA 18:65-68, 1996), we examine the popularity of the so-called canonical schedule. We investigate the presence of a number of properties related to successive home or successive away matches (breaks) and of symmetry between the various parts of the competition. We introduce the concept of ranking-balancedness, which is particularly useful to decide whether a fair ranking can be made. We also determine how the schedules manage the carry-over effect. We conclude by observing that there is quite some diversity in European soccer schedules, and that current schedules leave room for further optimizing

Exact algorithms for the matrix bid auction.

In a combinatorial auction, multiple items are for sale simultaneously to a set of buyers. These buyers are allowed to place bids on subsets of the available items. A special kind of combinatorial auction is the so-called matrix bid auction, which was developed by Day (2004). The matrix bid auction imposes restrictions on what a bidder can bid for a subsets of the items. This paper focusses on the winner determination problem, i.e. deciding which bidders should get what items. The winner determination problem of a general combinatorial auction is NP-hard and inapproximable. We discuss the computational complexity of the winner determination problem for a special case of the matrix bid auction. We present two mathematical programming formulations for the general matrix bid auction winner determination problem. Based on one of these formulations, we develop two branch-and-price algorithms to solve the winner determination problem. Finally, we present computational results for these algorithms and compare them with results from a branch-and-cut approach based on Day & Raghavan (2006).Algorithms; Bids; Branch-and-price; Combinatorial auction; Complexity; Computational complexity; Exact algorithm; Mathematical programming; Matrix; Matrix bids; Research; Winner determination;

The impact of the soccer schedule on TV viewership and stadium attendance : evidence from the Belgian Pro League

In the past decade, television broadcasters have been investing a huge amount of money for the Belgian Pro League broadcasting rights. These companies pursue an audience rating maximization, which depends heavily on the schedule of the league matches. At the same time, clubs try to maximize their home attendance and find themselves affected by the schedule as well. Our paper aims to capture the Belgian soccer fans’ preferences with respect to scheduling options, both for watching matches on TV and in the stadium. We carried out a discrete choice experiment using an online survey questionnaire distributed on a national scale. The choice sets are based on three match characteristics: month, kickoff time, and quality of the opponent. The first part of this survey concerns television broadcasting aspects. The second part includes questions about stadium attendance. The choice data is first analyzed with a conditional logit model which assumes homogenous preferences. Then a mixed logit model is fit to model the heterogeneity among the fans. The estimates are used to calculate the expected utility of watching a Belgian Pro League match for every possible setting, either on TV or in the stadium. These predictions are validated in terms of the real audience rating and home attendance data. Our results can be used to improve the scheduling process of the Belgian Pro League in order to persuade more fans to watch the matches on TV or in a stadium

Optimization modelling for analyzing fantasy sport games

In a fantasy sport game, participants act like a team manager building a team of real individual players of a professional sport. The real performances of these players (or their teams) are translated into points for their team managers. The managers’ aim is to collect as many points as possible thereby defeating the fantasy teams of opponents. First, we discuss a number of common game rule characteristics of fantasy sport games. Based on these characteristics, we present a mixed integer programming model to produce and analyze ex-post results for a large variety of fantasy sport games. We discuss how these results create value for both the game organizer and the participants. Finally, we apply our system in practice to a fantasy cycling game