Luisa Carpente

Values for Strategic Games in Which Players Cooperate

In this paper we propose a method to associate a coalitional interval game with each strategic game. The method is based on the lower and upper values of finite two-person zero-sum games. We axiomatically characterize this new method. As an intermediate step, we provide some axiomatic characterizations of the upper value of finite two-person zero-sum games.

The Constrained Equal Awards Rule for Bankruptcy Problems with a Priori Unions

In this paper, we provide two extensions of the constrained equal awards rule for bankruptcy situations to the class of bankruptcy situations with a priori unions. We present some characterisations and relations with corresponding games. The two new extensions are illustrated by a specific application.

The Shapley valuation function for strategic games in which players cooperate

In this note we use the Shapley value to define a valuation function. A valuation function associates with every non-empty coalition of players in a strategic game a vector of payoffs for the members of the coalition that provides these players’ valuations of cooperating in the coalition. The Shapley valuation function is defined using the lower-value based method to associate coalitional games with strategic games that was introduced in Carpente et al. (2005). We discuss axiomatic characterizations of the Shapley valuation function.

The truncated core for games with upper bounds

We define and study games with upper bounds. In one of these games there are upper bounds on the possible payoffs for some coalitions. These restrictions require adjustments in the definitions of solution concepts. In the current paper we study the effect of the restrictions on the core and define and study the so-called truncated core.

How to divide a cake when people have different metabolism

This paper deals with bankruptcy problems in which the players have different utility functions defined in terms of the quantity of allocated resources. We tackle this kind of situation by means of a game without transferable utility and provide two characterizations of the CEA-rule in this context.

New Approaches for the School Timetabling Problem

School timetabling is a hard task that educational centers have to perform regularly and which implies a large waste of time and human efforts. For such reason designing techniques for the automatic generation of timetables is still of interest. Even though many contributions exist, the characteristics of the problem vary depending on the school policies, the country (laws), and other particular variables.The complexity of this problem makes it difficult to find anoptimal solution, so approximated techniques are traditionally used in practice. In this paper, we focus in the Spanish school timetabling problem and present several approaches to deal with it. The first technique proposed is based on the random non ascendent method (RNA). Then we provide several genetic algorithms which differ on the policies used for selecting how the next generation is created (including elitism) as well as on the levels of mutation considered. Finally, we study how to combine the two previous approaches. We run experiments both on synthetic and real scenarios in order to compare all the proposals. Even though the RNA and some of the pure genetic algorithms obtain good results in practice, we show that by joining RNA with genetic algorithms we gain stability in the results.

Spatial decision support system for the route management for milk collection from dairy farms

In this research, a new spatial decision support system (SDSS) was developed, which solves the milk collection problem in two stages. First it applies an algorithm, employing heuristic techniques, generating solutions in a short period of time. In a second step, a graphic interface has been developed, which allows interaction and changes to be carried out in a rapid and intuitive way on the routes generated by the routing algorithm. The route manager can also carry out a broad range of “What if” simulations to find the solution that minimizes cost. With the use of this tool, significant savings have been obtained in terms of the collection time and kilometers covered by freight, while still keeping the current fleet of vehicles. Sensitivity analysis shows that the total cost of the process is more sensitive to increasing truck capacity than duplicating vehicle working shifts. The existence of farms with difficult access increases the collection costs substantially.

A Vehicle Routing Problem with Periodic Replanning

In this work we focus on the problem of truck fleet management of the company GESUGA. This company is responsible of the collection and proper treatment of animals not intended for human consumption. On a daily basis, with the uncollected requests, the company designs the routes for the next day. However, these routes have to be replanned during their execution as new requests appear from customers that the company would be interested in attending. The problem treated belongs to the family MDCVRPTW with the particularity of the route redesign. For its resolution we have adapted linear programming models, simulation techniques and metaheuristic algorithms.

Allocation Rules for Games with Optimistic Aspirations

In this paper we introduce games with optimistic aspirations and identify attractive allocation rules for such games through axiomatizations. A game with optimistic aspirations specifies two values for each coalition of players: the first value is the worth that the players in the coalition can guarantee for themselves in the event that they coordinate their actions (where the word guarantee implies a very conservative attitude), and the second value is the amount that the players in the coalition aspire to get under reasonable but very optimistic assumptions about the demands of the players who are not included in the coalition. We explain games with optimistic aspirations as well as our motivation for introducing such games by means of an example.