Ana Meca

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 and competition in inventory games

Abstract. Inventory cost games are introduced in Meca et al. (1999). These games arise when considering the possibility of joint ordering in n-person EOQ inventory situations. Moreover, the SOC-rule is introduced and analysed as a cost allocation rule for this type of situations. In the current paper it is seen that n-person EPQ situations with shortages lead to exactly the same class of cost games. Furthermore, an alternative characterization of the SOC-rule is offered, primarily based on a transfer property which constitutes a special form of additivity. Necessary input variables for the SOC-rule are the (optimal) individual average number of orders per time unit in case there is no cooperation. Assuming that these average numbers are observable but not verifiable, we allow the players to select them strategically, while knowing that the SOC-rule will be (consecutively) applied as the cost allocation principle. Necessary and sufficient conditions are provided for the existence (and uniqueness) of a so-called constructive equilibrium in which all players make joint orders.

Benefit sharing in holding situations

A situation is studied where one agent has available an amount of storage facility and the other agents have some goods, part of which can be stored generating benefits. The problem of sharing the benefits produced by full cooperation between agents is tackled in this paper, by introducing a related cooperative game. This game turns out to be a big boss game with interesting theoretical properties. A solution concept, relying on optimal storage plans and associated holding prices, is also introduced, and its relationship with the core of the above holding game is explored in detail. The family of monotonic decreasing bijective mappings, defined on the set of non-negative real numbers, plays an important role in our approach.

Cooperation in assembly systems: The role of knowledge sharing networks

Process improvement plays a significant role in reducing production costs over the life cycle of a product. We consider the role of process improvement in a decentralized assembly system in which a buyer purchases components from several first-tier suppliers. These components are assembled into a finished product, which is sold to the downstream market. The assembler faces a deterministic demand/production rate and the suppliers incur variable inventory costs and fixed setup production costs. In the first stage of the game, which is modeled as a non-cooperative game among suppliers, suppliers make investments in process improvement activities to reduce the fixed production costs. Upon establishing a relationship with the suppliers, the assembler establishes a knowledge sharing network – this network is implemented as a series of meetings among suppliers and also mutual visits to their factories. These meetings facilitate the exchange of best practices among suppliers with the expectation that suppliers will achieve reductions in their production costs from the experiences learned through knowledge sharing. We model this knowledge exchange as a cooperative game among suppliers in which, as a result of cooperation, all suppliers achieve reductions in their fixed costs. In the non-cooperative game, the suppliers anticipate the cost allocation that results from the cooperative game in the second stage by incorporating the effect of knowledge sharing in their cost functions. Based on this model, we investigate the benefits and challenges associated with establishing a knowledge sharing network. We identify and compare various cost allocation mechanisms that are feasible in the cooperative game and show that the system optimal investment levels can be achieved only when the most efficient supplier receives the incremental benefits of the cost reduction achieved by other suppliers due to the knowledge transfer.

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.

An Integrated Transport System for Alacant's Students. UNIVERCITY

The dispersion between the different university campuses in Alacant raises the social necessity of designing a transport system capable of efficiently connecting the villages and cities of Alacant with the campuses. In this paper, we develop a centralized transport system for university students in the province of Alacant.

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.

ON COOPERATIVE GAMES RELATED TO MARKET SITUATIONS AND AUCTIONS

We consider a market situation with two corners. One corner consists of a single seller with one object, and the other corner consists of potential buyers who all want the object. We suppose that the valuations of the object for the different buyers are known by all of them. Then two types of cooperative games, which we call market games and ring games, corresponding to such market situations are considered.Market games are related to special total big boss games, while ring games are related to special convex games, the peer group games. It turns out that there exists a duality relation between the market game and the ring game arising from the same two-corner market situation. For both classes of games relevant solution concepts are studied.

Strategic bidding in continuous electricity auctions: an application to the Spanish electricity market

Abstract In this paper we introduce an asymmetric model of continuous electricity auctions with limited production capacity and bounded supply functions. The strategic bidding is studied with this model by means of an electricity market game. We prove that for every electricity market game with continuous cost functions a mixed-strategy Nash equilibrium always exists. In particular, we focus on the behavior of producers in the Spanish electricity market. We consider a very simple form for the Spanish electricity market: an oligopoly consisting just of independent hydro-electric power production units in a single wet period. We show that a pure-strategy Nash equilibrium for the Spanish electricity market game always exists.

Two Classes of Cooperative Games Related to One-Object Auction Situations

We consider a market situation with two corners. One corner consists of a single seller with one object, and the other corner consists of potential buyers who all want the object. We suppose that the valuations of the object for the different buyers is known by all of them. Then two cooperative games, which we call the auction game and the ring game, corresponding to such a market situation are considered. Auction games are related to special total big boss games, while ring games are related to special convex games, the peer group games. It turns out that there exists a duality relation between the auction game and the ring game arising from the same two-corner market situation. For both classes of games relevant solution concepts are studied.