Francisco R. Fernández

A multiperiod two-echelon multicommodity capacitated plant location problem

Abstract In this paper we deal with a facility location problem where one desires to establish facilities at two different distribution levels by selecting the time periods. Our model intends to minimize the total cost for meeting demands for all the products specified over the planning horizon at various customer locations while satisfying the capacity requirements of the production plants and intermediate warehouses. We address this problem by means of a formulation as a mixed integer programming problem. A Lagrangean relaxation is proposed to solve the problem, together with a heuristic procedure that constructs feasible solutions of the original problem from the solutions at the lower bounds obtained by the relaxed problems. Computational tests are provided showing the good performance of this approach for a wide range of problems.

Multi-criteria analysis with partial information about the weighting coefficients

Abstract In this paper we address the problem of ranking a set of alternatives with partial information about the weighting coefficients. We introduce a family of quasiorders that are easily interpretable and manageable, which includes among others, the natural quasiorder in R n and other well known preference structures in the literature. The enrichment of the preference structure with respect to the natural quasiorder is measured by means of an absolute measure we introduce.

A flexible approach to location problems

Abstract. When dealing with location problems we are usually given a set of existing facilities and we are looking for the location of one or several new facilities. In the classical approaches weights are assigned to existing facilities expressing the importance of the new facilities for the existing ones.¶In this paper, we consider a pointwise defined objective function where the weights are assigned to the existing facilities depending on the location of the new facility. This approach is shown to be a generalization of the median, center and centdian objective functions. In addition, this approach allows the formulation of completely new location models. Efficient algorithms as well as structural results for this algebraic approach to location problems are presented. A complexity analysis and extensions to the multifacility and restricted case are also considered.

Vector linear programming in zero-sum multicriteria matrix games

In this paper, a multiple-objective linear problem is derived from a zero-sum multicriteria matrix game. It is shown that the set of efficient solutions of this problem coincides with the set of Paretooptimal security strategies (POSS) for one of the players in the original game. This approach emphasizes the existing similarities between the scalar and multicriteria matrix games, because in both cases linear programming can be used to solve the problems. It also leads to different scalarizations which are alternative ways to obtain the set of all POSS. The concept of ideal strategy for a player is introduced, and it is established that a pair of Pareto saddle-point strategies exists if both players have ideal strategies. Several examples are included to illustrate the results in the paper.

Sequential incorporation of imprecise information in multiple criteria decision processes

Abstract In this paper we deal with multicriteria decision processes and develop tools that permit to ease the task of analysing such models. We provide a methodology to sequentially incorporate imprecise preference information which is given by means of general linear relations in the weighting coefficients. The results presented allow us to evaluate the quality of the information supplied and can be used to reduce the number of irrelevant alternatives to be presented to the decision maker (DM). Several examples based on multiple criteria linear programming illustrate the results of the paper.

The use of partial information on weights in multicriteria decision problems

An improved apparatus for winding yarn or thread onto a bobbin to form a yarn package is described which comprises a support assembly for maintaining uniform pressure between the drive roll and yarn package during winding so that a yarn package having greater uniformity is produced. The described apparatus further includes an improved take-up roll having a braking means cooperating with a yarn package or bobbin release means, whereby the yarn package cannot be released from the take-up roll until the take-up roll has ceased rotation. Also described is a doffing mechanism associated with the winder for doffing yarn packages from the take-up roll after they are released by the package release means.

Core solutions in vector-valued games

In this paper, we analyze core solution concepts for vector-valued cooperative games. In these games, the worth of a coalition is given by a vector rather than by a scalar. Thus, the classical concepts in cooperative game theory have to be revisited and redefined; the important principles of individual and collective rationality must be accommodated; moreover, the sense given to the domination relationship gives rise to two different theories. Although different, we show the areas which they share. This analysis permits us to propose a common solution concept that is analogous to the core for scalar cooperative games.

Multicriteria goal games

In this paper, we deal with multicriteria matrix games. Different solution concepts have been proposed to cope with these games. Recently, the concept of Pareto-optimal security strategy which assures the property of security in the individual criteria against an opponents deviation in strategy has been introduced. However, the idea of security behind this concept is based on expected values, so that this security might be violated by mixed strategies when replications are not allowed. To avoid this inconvenience, we propose in this paper a new concept of solution for these games: the G-goal security strategy, which includes as part of the solution the probability of obtaining prespecified values in the payoff functions. Thus, attitude toward risk together with payoff values are considered jointly in the solution analysis.

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.

Multi-criteria minimum cost spanning tree games

Abstract The minimum cost spanning tree game (mcst-game) is a well-known model within operations research games that has been widely studied in the literature. In this paper we introduce the multi-criteria version of the mcst-game as a set-valued TU-game. We prove that the extension of Birds cost allocation rule provides dominance core elements in this game. We also give a family of core solutions that are different from the previous one; these solutions are based on proportional allocations obtained using scalar solutions of the multi-criteria spanning tree problem. Besides, we prove necessary and sufficient conditions ensuring that the preference core of this game is not empty.