Manuel A. Mosquera

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.

Sharing costs in highways: A game theoretic approach

This paper introduces a new class of games, highway games, which arise from situations where there is a common resource that agents will jointly use. That resource is an ordered set of several indivisible sections, where each section has an associated fixed cost and each agent requires some consecutive sections. We present an easy formula to calculate the Shapley value, and we present an efficient procedure to calculate the nucleolus for this class of games.

Proportionate flow shop games

In a proportionate flow shop problem several jobs have to be processed through a fixed sequence of machines and the processing time of each job is equal on all machines. By identifying jobs with agents whose costs linearly depend on the completion time of their jobs and assuming an initial processing order on the jobs, we face two problems: the first is how to obtain an optimal order that minimizes the total processing cost, the second is how to allocate the cost savings obtained by ordering the jobs optimally. In this paper we focus on the allocation problem. PFS games are defined as cooperative games associated to proportionate flow shop problems. It is seen that PFS games have a nonempty core. Moreover, it is shown that PFS games are convex if the jobs are initially ordered in decreasing urgency. For this case an explicit game independent expression for the Shapley value is provided.

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.

Centralized Inventory in a Farming Community

A centralized inventory problem is a situation in which several agents face individual inventory problems and make an agreement to coordinate their orders with the objective of reducing costs. In this paper we identify a centralized inventory problem arising in a farming community in northwestern Spain, model the problem using two alternative approaches, find the optimal inventory policies for both models, and propose allocation rules for sharing the optimal costs in this context.

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.

Equilibria in a competitive model arising from linear production situations with a common-pool resource

In this paper we deal with linear production situations in which there is a limited common-pool resource, managed by an external agent. The profit that a producer can attain depends on the amount of common-pool resource obtained through a certain procedure. We contemplate a competitive process among the producers and study the corresponding non-cooperative games, describing their (strict) Nash equilibria in pure strategies. It is shown that strict Nash equilibria form a subset of strong Nash equilibria, which in turn form a proper subset of Nash equilibria.

k-core covers and the core

This paper extends the notion of individual minimal rights for a transferable utility game (TU-game) to coalitional minimal rights using minimal balanced families of a specific type, thus defining a corresponding minimal rights game. It is shown that the core of a TU-game coincides with the core of the corresponding minimal rights game. Moreover, the paper introduces the notion of the