M. G. Fiestras-Janeiro

Cooperative game theory and inventory management

Supply chain management is related to the coordination of materials, products and information flows among suppliers, manufacturers, distributors, retailers and customers involved in producing and delivering a final product or service. In this setting the centralization of inventory management and coordination of actions, to further reduce costs and improve customer service level, is a relevant issue. In this paper, we provide a review of the applications of cooperative game theory in the management of centralized inventory systems. Besides, we introduce and study a new model of centralized inventory: a multi-client distribution network.

Cooperation in Markovian queueing models

In this paper we study some cooperative models in Markovian queues. We stress the case of several agents agreeing to maintain a common server for their populations in which a priority scheme with preemption has been established. In this situation we propose and characterize an allocation rule for the holding costs that provides core allocations.

Characterizations of the Deegan-Packel and Johnston power indices

Abstract In this paper, we provide a new characterization of the Deegan–Packel power index, which uses a new monotonicity property, and two characterizations of the Johnston power index by employing some usual properties of the literature and two new transfer properties. Finally, a real-world numerical example taken from the political field illustrates the main differences between these two indices.

Multivariate statistical analysis of precipitation chemistry in northwestern Spain

Abstract149 samples of rainwater were collected in the proximity of a power station in northwestern Spain at three rainwater monitoring stations. We analyze the resulting data using multivariate statistical techniques. Firstly, the Principal Component Analysis shows that there are three main sources of pollution in the area (a marine source, a rural source and an acid source). The impact from pollution from these sources on the immediate environment of the stations is studied using Factorial Discriminant Analysis.

A note on coalitional manipulation and centralized inventory management

Abstract In this note we deal with inventory games as defined in Meca et al. (Math. Methods Oper. Res. 57:483–491, 2003). In that context we introduce the property of immunity to coalitional manipulation, and demonstrate that the SOC-rule (Share the Ordering Cost) is the unique allocation rule for inventory games which satisfies this property.

Cooperation on capacitated inventory situations with fixed holding costs

In this paper we analyze a situation in which several firms deal with inventory problems concerning the same type of product. We consider that each firm uses its limited capacity warehouse for storing purposes and that it faces an economic order quantity model where storage costs are irrelevant (and assumed to be zero) and shortages are allowed. In this setting, we show that firms can save costs by placing joint orders and obtain an optimal order policy for the firms. Besides, we identify an associated class of costs games which we show to be concave. Finally, we introduce and study a rule to share the costs among the firms which provides core allocations and can be easily computed.

A Review of Some Recent Results on Power Indices

In this chapter, we provide a review of some recent results on power indices related to work done by the research group SaGaTh. We review axiomatic characterizations of several of the most important indices in the literature. Furthermore, we include a power index based on a desirability relation and two new power indices based on quasi-minimal winning coalitions. Finally, we summarize some results in other areas related with power indices.

A Bankruptcy Approach to the Core Cover

In this paper we establish a relationship between the core cover of a compromise admissible game and the core of a particular bankruptcy game: the core cover of a compromise admissible game is, indeed, a translation of the set of coalitionally stable allocations captured by an associated bankruptcy game. Moreover, we analyze the combinatorial complexity of the core cover and, consequently, of the core of a compromise stable game.

A New Power Index for Spatial Games

In this paper we present a new power index for spatial games. We study some of its properties and indicate its advantages in comparison with the other existing indexes. Finally we illustrate our results with an example taken from a Spanish regional Parliament.

The concept of proper solution in linear programming

In this paper, we study the optimal solutions of a dual pair of linear programming problems that correspond to the proper equilibria of their associated matrix game. We give conditions ensuring the existence of such solutions, show that they are especially robust under perturbation of right-hand-side terms, and describe a procedure to obtain them.