Cooperation between Multiple Newsvendors with Warehouses

This study considers a supply chain that consists of n retailers, each of them facing a newsvendor problem, m warehouses and a supplier.The retailers are supplied with a single product via some warehouses.In these warehouses, the ordered amounts of goods of these retailers become available after some lead time.At the time that the goods arrive at the warehouses, demand realizations are known by the retailers.The retailers can increase their expected joint profits by coordinating their orders and making allocations after demand realization.For this setting, we consider an associated cooperative game between the retailers.We show that this associated cooperative game has a nonempty core. Finally, we study a variant of this game, where the retailers are allowed to leave unsold goods at the warehouses.supply chain management;newsvendor;warehouse;game theory;balancedness

Supply chain collaboration

In the past, research in operations management focused on single-firm analysis. Its goal was to provide managers in practice with suitable tools to improve the performance of their firm by calculating optimal inventory quantities, among others. Nowadays, business decisions are dominated by the globalization of markets and increased competition among firms. Further, more and more products reach the customer through supply chains that are composed of independent firms. Following these trends, research in operations management has shifted its focus from single-firm analysis to multi-firm analysis, in particular to improving the efficiency and performance of supply chains under decentralized control. The main characteristics of such chains are that the firms in the chain are independent actors who try to optimize their individual objectives, and that the decisions taken by a firm do also affect the performance of the other parties in the supply chain. These interactions among firms’ decisions ask for alignment and coordination of actions. Therefore, game theory, the study of situations of cooperation or conflict among heterogenous actors, is very well suited to deal with these interactions. This has been recognized by researchers in the field, since there are an ever increasing number of papers that applies tools, methods and models from game theory to supply chain problems

Large Newsvendor Games

We consider a game, called newsvendor game, where several retailers, who face a random demand, can pool their resources and build a centralized inventory that stocks a single item on their behalf. Profits have to be allocated in a way that is advantageous to all the retailers. A game in characteristic form is obtained by assigning to each coalition its optimal expected profit. A similar game (modeled in terms of costs) was considered by Muller et al. (2002), who proved that this game is balanced for every possible joint distribution of the random demands. In this paper we consider newsvendor games with possibly an infinite number of newsvendors. We prove in great generality results about balancedness of the game, and we show that in a game with a continuum of players, under a nonatomic condition on the demand, the core is a singleton. For a particular class of demands we show how the core shrinks to a singleton when the number of players increases.newsvendor games, nonatomic games, core, balanced games.

Cooperation between Multiple Newsvendors with Warehouses

This study considers a supply chain that consists of n retailers, each of them facing a newsvendor problem, m warehouses and a supplier.The retailers are supplied with a single product via some warehouses.In these warehouses, the ordered amounts of goods of these retailers become available after some lead time.At the time that the goods arrive at the warehouses, demand realizations are known by the retailers.The retailers can increase their expected joint profits by coordinating their orders and making allocations after demand realization.For this setting, we consider an associated cooperative game between the retailers.We show that this associated cooperative game has a nonempty core. Finally, we study a variant of this game, where the retailers are allowed to leave unsold goods at the warehouses.

Initial inventory levels for a book publishing firm = Kezdőkészletek egy könyvkiadó vállalatnál

Egy könyvkiadó vállalatot vizsgálunk. A kiadó kiadványait a szokásos értékesítési láncon (kis- és nagykereskedelem) keresztül értékesíti. A kérdés az, hogy egy új könyv példányait hogyan allokálja az értékesítési láncban. Feltételezzük, hogy a kereslet ismert, Poisson-eloszlású. A készletezés költségeit szintén ismertnek tételezzük fel. Cél a költségek minimalizálása. = The aim of the paper is to analyze a practical real world problem. A publishing house is given. The publishing firm has contacts to a number of wholesaler / retailer enterprises and direct contact to customers to satisfy the market demand. The book publishers work in a project industry. The publisher faces with the problem to allocate the stocks of a given, newly published book to the wholesaler and retailer, and to hold some copies to satisfy the customers direct from the publisher. The distribution of the demand is unknown, but it can be estimated. The costs consist of inventory holding and shortage, backorder costs. The decision maker wants to minimize these relevant costs. The problem can be modeled as a one-warehouse and N-retailer supply chain with not identical demand distribution. The problem structure is similar that of a newsvendor model. It is assumed that the demand distribution follows a Poisson distribution

On the core of m-attribute games

We study a special class of cooperative games with transferable utility (TU), called (Formula presented.) -attribute games. Every player in an (Formula presented.) -attribute game is endowed with a vector of (Formula presented.) attributes that can be combined in an additive fashion; that is, if players form a coalition, the attribute vector of this coalition is obtained by adding the attributes of its members. Another fundamental feature of (Formula presented.) -attribute games is that their characteristic function is defined by a continuous attribute function (Formula presented.) —the value of a coalition depends only on evaluation of (Formula presented.) on the attribute vector possessed by the coalition, and not on the identity of coalition members. This class of games encompasses many well-known examples, such as queueing games and economic lot-sizing games. We believe that by studying attribute function (Formula presented.) and its properties, instead of specific examples of games, we are able to develop a common platform for studying different situations and obtain more general results with wider applicability. In this paper, we first show the relationship between nonemptiness of the core and identification of attribute prices that can be used to calculate core allocations. We then derive necessary and sufficient conditions under which every (Formula presented.) -attribute game embedded in attribute function (Formula presented.) has a nonempty core, and a set of necessary and sufficient conditions that (Formula presented.) should satisfy for the embedded game to be convex. We also develop several sufficient conditions for nonemptiness of the core of (Formula presented.) -attribute games, which are easier to check, and show how to find a core allocation when these conditions hold. Finally, we establish natural connections between TU games and (Formula presented.) -attribute games.</p

Cooperation in Supply Chain Networks: Motives, Outcomes, and Barriers

This paper analyzes the phenomenon of cooperation in modern supply chains in the light of Game Theory. We first provide a discussion on the meaning of cooperation in supply chains, its motives, outcomes and barriers. We then highlighted the applicability of Cooperative Game Theory as methodology for analyzing cooperation in supply chains. Second, we review recent studies that analyze the cooperation in supply chains by means of cooperative game theory. A special emphasis will be given inventory centralizations games. Finally, gaps in the literature are identified to clarify and to suggest future research opportunities

Dynamic Realization Games in Newsvendor Inventory Centralization

Consider a set N of n (>1) stores with single-item and single-period nondeterministic demands like in a classic newsvendor setting with holding and penalty costs only. Assume a risk-pooling single-warehouse centralized inventory ordering option. Allocation of costs in the centralized inventory ordering corresponds to modelling it as a cooperative cost game whose players are the stores. It has been shown that when holding and penalty costs are identical for all subsets of stores, the game based on optimal expected costs has a non empty core (Hartman et. al., 2000, Muller \textit{et. al.}, 2002). In this paper we examine a related inventory centralization game based on demand realizations that has, in general, an empty core even with identical penalty and holding costs (Hartman and Dror, 2005). We propose a repeated cost allocation scheme for dynamic realization games based on allocation processes introduced by Lehrer (2002a). We prove that the cost subsequences of the dynamic realization game process, based on Lehrer's rules, converge almost surely to either a least square value or the core of the expected game. We extend the above results to more general dynamic cost games and relax the independence hypothesis of the sequence of players' demands at different stages