Equal Surplus Sharing in Grey Inventory Games

Purpose – The purpose of this paper is to extend the results of Meca et al. (2004) depending on the grey information revealed by the individual firms. Design/methodology/approach – The authors introduce cooperative grey games and focus on sharing ordering cost rule (SOC-rule) to distribute the joint cost. Findings – In this study, the authors introduce a model, where inventory costs are assumed as grey numbers instead of crisp or stochastic ones studied in literature. At first, grey numbers and classical cooperative inventory games are recalled. Then, cooperative grey games are introduced and related results are given. Finally, an application is performed for three shotgun companies in Turkey. Originality/value – It is an effective approach for theoretical analysis of systems with imprecise information and incomplete samples. Therefore, grey system theory, rather than the traditional probability theory and fuzzy set theory, is better suited to model the inventory problems by using cooperative game theory. To the best of the knowledge no study exists modeling inventory situations by using cooperative grey games. From this point of view this study is a pioneering work on a promising topic.

<abstract><p>The Banzhaf value with grey data is a solution concept in cooperative grey games that has been extensively studied in the context of operations research. The author aims to define the traits of the Banzhaf value in cooperative grey games, where the values of coalitions are depicted as grey numbers within intervals. The grey Banzhaf value is defined by several axioms, including the grey dummy player, grey van den Brink fairness, and grey superadditivity. By presenting these axioms, this investigation contributes novel insights to the axiomatic characterization of the grey Banzhaf value, offering a distinct perspective. Finally, the study concludes by presenting applications in cooperative grey game models, thereby enriching the understanding of this concept.</p></abstract>

The location of facilities in order to provide service for customers is a well-studied problem in the operations research literature. In the basic model, there is a predefined cost for opening a facility and also for connecting a customer to a facility, the goal being to minimize the total cost. Often, both in the case of public facilities (such as libraries, municipal swimming pools, fire stations,....) and private facilities (such as distribution centers, switching stations, ....), we may want to find a 'fair' allocation of the total cost to the customers-this is known as the cost allocation problem. A central question in cooperative game theory is whether the total cost can be allocated to the customers such that no coalition of customers has any incentive to build their own facility or to ask a competitor to service them. We establish strong connections between fair cost allocations and linear programming relaxations for several variants of the facility location problem. In particular, we show that a fair cost allocation exists if and only if there is no integrality gap for a corresponding linear programming relaxation; this was only known for the simplest unconstrained variant of the facility location problem. Moreover, we introduce a subtle variant of randomized rounding and derive new proofs for the existence of fair cost allocations for several classes of instances. We also show that it is in general NP-complete to decide whether a fair cost allocation exists and whether a given allocation is fair.

The primary goal of this article is to develop a direct and simplified approach for computing triangular fuzzy Banzhaf values for a special class of cooperative games with coalitions' values represented by triangular fuzzy numbers, which are called triangular fuzzy cooperative games for short. Combining with the β-cut sets of coalitions' triangular fuzzy values, in this article, we can obtain a series of associated interval-valued cooperative games with the triangular fuzzy cooperative games. Hereby, we construct associated cooperative games with the interval-valued cooperative games. It is proven that the Banzhaf values of the associated cooperative games with interval-valued cooperative games are monotonic and nondecreasing functions under some size monotonicity-like conditions. Hence, the mean and the lower and upper limits of the triangular fuzzy Banzhaf values can be directly and explicitly attained through using only the mean, and the lower and upper limits of the coalitions' triangular fuzzy values, respectively. The developed approach does not use the subtraction of triangular fuzzy numbers and, hereby, can effectively avoid the irrational issues resulting from it. Furthermore, some important properties of the triangular fuzzy Banzhaf values are proven and the applicability and validity of the developed approach are illustrated with a numerical example.

Cooperative facility location games

Objective: The principles of marginalism and egalitarianism are handy tools for sharing worth among the players of a group in a TU game. Here, our objective is to combine two such solutions to generate a new value that keeps in mind the need of each player required for the survival of a group in a TU game. Methods: Here, the Banzhaf value and the equal division value were merged to establish a new consolidated solution. Method of induction is used over unanimity games and symmetric games to characterize the proposed value using some well-known as well as some freshly defined axioms of cooperative game theory. Findings: To describe the new value, we first looked at a number of intuitive axioms linked to it and the uniqueness of the value is obtained by characterizing it using the defined axioms. The value is then extended to the class of simple games. Novelty: The proposed solution is a non-efficient solution that allocates a portion of the total worth to the players and keeps a portion undistributed to use for the purpose of further investment by the group. Keywords: Cooperative game; Banzhaf value; Egalitarian Value; Null Player; Solution Concept

In this paper I consider the ordinal equivalence of the Shapley and Banzhaf values for TU cooperative games, i.e., cooperative games for which the preorderings on the set of players induced by these two values coincide. To this end I consider several solution concepts within semivalues and introduce three subclasses of games which are called, respectively, weakly complete, semicoherent and coherent cooperative games. A characterization theorem in terms of the ordinal equivalence of some semivalues is given for each of these three classes of cooperative games. In particular, the Shapley and Banzhaf values as well as the segment of semivalues they limit are ordinally equivalent for weakly complete, semicoherent and coherent cooperative games.

Purpose: This study aims to identify inventory control and costs incurred by the company, analyze inventory cost control for green spinach seeds using the EOQ model VII method, and analyze cost efficiency for green spinach seed inventory. Methodology: The analysis used the EOQ method to determine the optimal order quantity for green spinach seeds at CV Amatta Mulya Barizi. Results: The EOQ method resulted in an optimal order quantity of 2,280 grams per order. The inventory costs for green spinach seeds amounted to IDR 273,642.00 per order or IDR 3,283,704.00 per year. Findings: The study found that the EOQ method is more efficient compared to the company’s current method, allowing the company to save IDR 586,296.00 annually on green spinach seed inventory costs. Novelty: This research provides new insights into the application of the EOQ model VII for seed inventory management, highlighting significant cost savings. Originality: The study offers a detailed analysis of inventory control and cost efficiency for green spinach seeds, contributing to better inventory management practices. Conclusions: The EOQ method is more efficient for inventory management of green spinach seeds at CV Amatta Mulya Barizi, resulting in considerable cost savings. Type of Paper: Empirical Research Article

Existing literature on dealer liquidity provision and inventory management has focused on dealer inventory cost. I uncover a new inventory benefit channel: dealers strategically build inventory in order to compete for market share. The inventory benefit reduces the effective cost of dealer inventory holding, thereby lowering the price of liquidity provision. Using the TRACE data for the U.S. corporate bonds, I show that, excluding the 2008 crisis, the inventory benefit per trade is on average 8.4 basis points larger than the inventory cost. The result is reversed during the crisis, when dealers suffer significantly higher inventory cost.

: In RM 23, a proof was given that the nucleolus is continuous as a function of the characteristic function. This proof is not correct; the author, at least, does not know how to complete it. In the paper a correct proof for this fact is given. The proof is based on an alternative definition of the nucleolus, which is of some interest in its own right. (Author)

In this paper, the problem of sequential estimation and lifetime maximization of a wireless sensor network (WSN) is formulated in a cooperative game theoretic framework. This framework allows addressing problems of fair resource allocation for sequential estimation at the Fusion center (FC) of a wireless sensor network as a solution of a cooperative game. We propose a simple game theoretic solution to power allocation problem for sensor nodes such that the obtained solution leads to increased lifetime of the WSN. Simulation results show that the proposed solution achieves target estimation quality at the FC, and at the same time lifetime of the overall sensor network is increased.

In this paper, the problem of sequential estimation in a wireless sensor network (WSN) is formulated in a cooperative game theoretic framework. This framework allows addressing the issue of fair resource allocation for sequential estimation task at the Fusion center (FC) in a WSN as a solution of a cooperative game. We propose a simple game theoretic solution to the problem of power allocation for sensor nodes that are subjected to power constraints. Simulation results show that the proposed solution has the same performance trend (in terms of the estimator quality at the FC) as when all nodes transmit at their maximum powers, while our proposed solution leads to an overall improvement of the network lifetime.

India's quick service restaurant market has expanded significantly in recent years. For small-scale QSRs, inventory management continues to be an essential challenge. Inventory management enhances the efficiency of business operations by influencing the stockpile and supply of essential products and materials. The research aims to highlight the importance of inventory control and management in QSRs. Primary data was collected from 120 operational QSRs in Bangalore in Karnataka and 30 from Kottayam in Kerala. It was found that most of the respondents felt that proper inventory management and control could help to improve their service quality and help to reduce costs. It has been found that the factors service, savings, and risk have a strong positive correlation with inventory cost. Several techniques and strategies like techniques for cooking with no waste, menu planning with fewer ingredients, networks for local sourcing, matching demand and supply through seasonal planning have been identified to increase the performance of QSRs.

Incorporating quantity discounts and their inventory impacts into the centralized purchasing decision

In this paper we use classical and behavioral game theory to predict coalition behavior in a sequential three-person laboratory game. In the laboratory situation used for the three studies reported in this paper, each player seeks to maximize the rank of his final accumulated point score in relation to the total scores of the other members of his triad. We assume that, unable to solve the sequential game as a single supergame, each player forms a simplified representation of the situation by adopting short-run, surrogate objectives for the outcome of each game in the sequence. In particular, we assume that each player seeks to maximize the status of his current total score during each game in the sequence. Given these surrogate objectives, we represent each trial in the sequential game as a distinct game of status in characteristic set function form. Using this formal model of the situation, we extend a solution concept from n-person game theory to identify which of the possible outcomes of each game in the sequence are, in a game theoretic sense, stable. We then add the assumption that each player obeys a bargaining maxim prescribing that coalition members should agree to an outcome in which one partner outranks the other if and only if he also enjoys higher rank when the coalition forms. We modify the game theoretic solution by considering only outcomes that conform to the bargaining maxim. The behavioral modification substantially improves the success game theory achieves in predicting rank outcomes observed in the three laboratory studies. However, with or without the modification, the game theoretic solution concept fails to predict which coalitions form in these studies. Finally, we develop an alternative theory that predicts not only the rank outcomes of each game in the sequence but also the probability that each coalition forms. The empirical success enjoyed by this theory in predicting the ranks acquired on each game is greater than that attained by the unmodified game theoretic predictions, and is nearly comparable to that achieved by the behaviorally modified game theoretic solution. Moreover, the alternative theory's robust coalition predictions are strongly supported by the results from the three laboratory studies.