Bonus, effort, costs, market size and teams' performance

This paper examines the effects of a win bonus, effort, costs and team size, on the demand for talented players, the win percentage and the profits of small and big teams. Teams play a Cournot game, under the following objective functions: (i) teams maximize profits, (ii) teams maximize win percentage, (iii) the small team maximizes profit and the big win percentage, and (iv) vice versa. The effects are based on a priori selected parameter values and bounds, as well as from optimal solutions of non-linear programs, by maximizing anyone of the four win percentage formulae, derived from the respective Cournot reaction functions.Teams; talents; effort; win bonus; win percentage; competitive balance; profits

Optimal football strategies: AC Milan versus FC Barcelona

In a recent UEFA Champions League game between AC Milan and FC Barcelona, played in Italy (final score 2-3), the collected match statistics, classified into four offensive and two defensive strategies, were in favour of FC Barcelona (by 13 versus 8 points). The aim of this paper is to examine to what extent the optimal game strategies derived from some deterministic, possibilistic, stochastic and fuzzy LP models would improve the payoff of AC Milan at the cost of FC Barcelona.football game; offensive & defensive strategies; Deterministic LP; fuzzy LP; stochastic LP; Nash equilibria;

A Pure Binary LP Model to the Facility Layout Problem

In facility layout problems, a major concern is the optimal design or remodeling of the facilities of an organization. The decision maker’s objective is to arrange the facility in an optimal way, so that the interaction among functions (i.e. machines, inventories, persons) and places (i.e. offices, work locations, depots) is efficient. A simple pure-binary LP model is developed and solved for a small hospital, where five functions are to be redesigned to five different locations. The model is rather flexible and can be used, with small modifications, for larger facility layouts.Facility layout; Binary; Linear Programming; Optimization; Efficiency

A note on the effectiveness of some de-fuzzification measures in a fuzzy pure factors portfolio

There are several methods to convert fuzzy or stochastic LP to conventional LP models. In this simple paper we evaluate the effectiveness of three proposed methods, using a numerical example from a pure factors portfolio.: fuzzy; stochastic; linear programming; pure factors portfolio

The optimal layout of football players: A case study for AC Milan

This paper attempts to find the optimal formation of three midfielders and three forward football players on ground, using the classic Quadratic Assignment Problem or Facility Layout problem. Players are treated as “machines”, their positions as locations, and the flow of materials between machines as “flow of passes” and “flow of markings”. Based on detailed statistics from four matches of AC Milan, and formulated the problem as minimum (quick strategy), maximum (slow strategy), and mixed or balanced strategies, a number of various layouts emerged. Compared to the initial formation of players, the efficiency time gains in the unconditioned layouts are between 3 and 6.8%. Also, when the manager claims that his three forwards shouldn’t shift positions with the midfielders, the efficiency gains in these restricted layouts is about 14´´ to 74´´, which is about 1 to 3% of the approximately 40´ effective time spent into passes and markings from both teams.sports; layout; assignment; football players; passes; markings; time;

The relative efficiency of UEFA Champions League scorers

The mass media, the football supporters and other experts in many countries are often engaged in the ranking of football players. Given the heterogeneity of various leagues or series in which players play, such a comparison is almost impossible. On the other hand, the performance of players in international tournaments, like the FIFA world cup at the national team level, or the UEFA Champions League at the European Club level, can be measured, if we rely on “objective” measures and statistics. Obviously, since various positions of players are evaluated by different criteria, the heterogeneity is still apparent. In this paper we attempt to evaluate a small subset of a team’s players, namely its scorers, using UEFA:s official match-play statistics from the Champions League tournament 2006/07.efficiency; scorers; forwards; midfielders; Champions League; DEA

Option Strategies with linear programming

In practice, all option strategies are decided in advance, given the investor’s belief of the stock price. In this paper, instead of deciding in advance the most appropriate hedging option strategy, an LP problem is formulated, by considering all significant Greek parameters of the Black-Scholes formula, such as delta, gamma, theta, rho and kappa. The optimal strategy to select will be simply decided by the solution of that model. The LP model is applied to Ericsson’s call and puts options.Finance, option portfolios, Linear programming

Wage Differences, Bonus and Team Performances: A parametric non-linear integer programming model

We formulate a non-linear integer programming model and use plausible parameters to examine: (i) the effects of wage differences between Super- and Normal- players in the performance of four teams which participate in the UEFA CL group matches; (ii) whether the expected qualification bonus received by UEFA and paid to the players of the non-qualified teams, enhances effort and the teams manage to qualify. When performance is measured by points’ maximization, higher wage equality seems to improve the performance of three teams, irrespectively if the elasticity of substitution between Super- and Normal- players is high or low, while the most efficient team of the tournament is not affected by the wage structure. The U-formed performance for that team is not excluded. When performance is measured by profits’ maximization, the performance depends on both the “production” technology and on wage differences. When all teams operate under increasing returns and all pay the same, but varying relative wages, or when they operate under decreasing returns and pay the marginal value product of their players, the most “balanced” team performs better. The most “unbalanced” team performs best under increasing returns to scale and egalitarian wages. In the last case, the non-qualified teams did not manage to improve their performance and qualify, even if their players should receive the expected qualification bonus that UEFA pays.Players, Teams, Wages, Bonus, Performance, Tournament

A NLIP Model on Wage Dispersion and Team Performance

Using a Non-Linear Integer Programming (NLIP) model, I examine if wage differences between Super talents and Normal players improve the performance of four teams which participate in a tournament, such as in the UEFA Champions League (UCL) group matches. With ad-hoc wage differences, the optimal solutions of the model show that higher wage equality seems to improve the performance of all teams, irrespectively if the elasticity of substitution between Super- and Normal- players is high or low. In addition to that, a U-type performance exists in two teams with the highest and the second high elasticity of substitution. With team data from the 2011-12 UCL group matches and from the Italian Serie A over 2010-12 seasons, the wage dispersion has no effect on team performances

Team Performance in UEFA Champions League 2005-06

This study uses a multi-output multi-input Data Efficiency Analysis (DEA) to estimate the performance of all thirty-two participated football teams in the UEFA Champions League (CL) tournament 2005-06. The estimates are based on official match statistics from all 125 matches