Shapley value: its algorithms and application to supply chains

Introduction− Coalitional game theorists have studied the coalition struc-ture and the payoff schemes attributed to such coalition. With respect to the payoff value, there are number ways of obtaining to “best” distribution of the value of the game. The solution concept or payoff value distribution that is canonically held to fairly dividing a coalition’s value is called the Shapley Value. It is probably the most important regulatory payoff scheme in coali-tion games. The reason the Shapley value has been the focus of so much interest is that it represents a distinct approach to the problems of complex strategic interaction that game theory tries to solve. Objective−This study aims to do a brief literature review of the application of Shapley Value for solving problems in different cooperation fields and the importance of studying existing methods to facilitate their calculation. This review is focused on the algorithmic view of cooperative game theory with a special emphasis on supply chains. Additionally, an algorithm for the calcu-lation of the Shapley Value is proposed and numerical examples are used in order to validate the proposed algorithm. Methodology−First of all, the algorithms used to calculate Shapley value were identified. The element forming a supply chain were also identified. The cooperation between the members of the supply chain ways is simulated and the Shapley Value is calculated using the proposed algorithm in order to check its applicability. Results and Conclusions− The algorithmic approach introduced in this paper does not wish to belittle the contributions made so far but intends to provide a straightforward solution for decision problems that involve supply chains. An efficient and feasible way of calculating the Shapley Value when player structures are known beforehand provides the advantage of reducing the amount of effort in calculating all possible coalition structures prior to the Shapley.Introducción: Los teóricos del juego cooperativos han estudiado la estructura de coalición y los esquemas de pago atribuidos a esas coaliciones. En relación al valor del pago, hay varias maneras de obtener la “mejor” distribución del valor del juego. El concepto de solución o la distribución del valor de recompensa que se mantiene canónicamente para dividir justamente el valor de una coalición se llama Valor de Shapley. Es probablemente el esquema de pago más importante en los juegos cooperativos. La razón por la cual el valor de Shapley ha sido el foco de tanto interés es que representa un acercamiento distinto a los problemas de la interacción estratégica compleja que la teoría del juego intenta resolver.Objetivo: Este estudio tiene como objetivo hacer una breve revisión bibliográfica de la aplicación del Valor de Shapley para resolver problemas en diferentes campos de cooperación y la importancia de estudiar los métodos existentes para facilitar su cálculo. Esta revisión se centra en la visión algorítmica de la teoría cooperativa de juegos con un énfasis especial en las cadenas de suministro. Adicionalmente se propone un algoritmo para el cálculo del Valor de Shapley y se utilizan ejemplos numéricos para validar el algoritmo propuesto.Metodología: En primer lugar, se identificaron los algoritmos utilizados para calcular el valor de Shapley. También se identificó los elementos que forman una cadena de suministro. Luego se simula la cooperación entre los miembros de las vías de la cadena de suministro y se calcula el valor de Shapley utilizando el algoritmo propuesto para comprobar su aplicabilidad.Resultados y Conclusiones: El enfoque algorítmico introducido en este documento no pretende menospreciar las contribuciones hechas hasta ahora, pero tiene la intención de proporcionar una solución directa para problemas de decisión que involucran cadenas de suministro. Una manera eficiente y factible de calcular el valor de Shapley cuando las estructuras de jugador se conocen de antemano proporciona la ventaja de reducir la cantidad de esfuerzo en el cálculo de todas las estructuras de coalición posibles antes del Shapley

El valor de Shapley: sus algoritmos y aplicación en cadenas de suministro

Introduction: Coalitional game theorists have studied the coalition structure and the payoff schemes attributed to such coalition. With respect to the payoff value, there are number ways of obtaining to “best” distribution of the value of the game. The solution concept or payoff value distribution that is canonically held to fairly dividing a coalition’s value is called the Shapley Value. It is probably the most important regulatory payoff scheme in coalition games. The reason the Shapley value has been the focus of so much interest is that it represents a distinct approach to the problems of complex strategic interaction that game theory tries to solve.Objective: This study aims to do a brief literature review of the application of Shapley Value for solving problems in different cooperation fields and the importance of studying existing methods to facilitate their calculation. This review is focused on the algorithmic view of cooperative game theory with a special emphasis on supply chains. Additionally, an algorithm for the calculation of the Shapley Value is proposed and numerical examples are used in order to validate the proposed algorithm.Methodology: First of all, the algorithms used to calculate Shapley value were identified. The element forming a supply chain were also identified. The cooperation between the members of the supply chain ways is simulated and the Shapley Value is calculated using the proposed algorithm in order to check its applicability.Results and Conclusions: The algorithmic approach introduced in this paper does not wish to belittle the contributions made so far but intends to provide a straightforward solution for decision problems that involve supply chains. An efficient and feasible way of calculating the Shapley Value when player structures are known beforehand provides the advantage of reducing the amount of effort in calculating all possible coalition structures prior to the Shapley.Introducción: Los teóricos del juego cooperativos han estudiado la estructura de coalición y los esquemas de pago atribuidos a esas coaliciones. En relación al valor del pago, hay varias maneras de obtener la “mejor” distribución del valor del juego. El concepto de solución o la distribución del valor de recompensa que se mantiene canónicamente para dividir justamente el valor de una coalición se llama Valor de Shapley. Es probablemente el esquema de pago más importante en los juegos cooperativos. La razón por la cual el valor de Shapley ha sido el foco de tanto interés es que representa un acercamiento distinto a los problemas de la interacción estratégica compleja que la teoría del juego intenta resolver.Objetivo: Este estudio tiene como objetivo hacer una breve revisión bibliográfica de la aplicación del Valor de Shapley para resolver problemas en diferentes campos de cooperación y la importancia de estudiar los métodos existentes para facilitar su cálculo. Esta revisión se centra en la visión algorítmica de la teoría cooperativa de juegos con un énfasis especial en las cadenas de suministro. Adicionalmente se propone un algoritmo para el cálculo del Valor de Shapley y se utilizan ejemplos numéricos para validar el algoritmo propuesto.Metodología: En primer lugar, se identificaron los algoritmos utilizados para calcular el valor de Shapley. También se identificó los elementos que forman una cadena de suministro. Luego se simula la cooperación entre los miembros de las vías de la cadena de suministro y se calcula el valor de Shapley utilizando el algoritmo propuesto para comprobar su aplicabilidad.Resultados y Conclusiones: El enfoque algorítmico introducido en este documento no pretende menospreciar las contribuciones hechas hasta ahora, pero tiene la intención de proporcionar una solución directa para problemas de decisión que involucran cadenas de suministro. Una manera eficiente y factible de calcular el valor de Shapley cuando las estructuras de jugador se conocen de antemano proporciona la ventaja de reducir la cantidad de esfuerzo en el cálculo de todas las estructuras de coalición posibles antes del Shapley.

Real-time optimization of an integrated production-inventory-distribution problem.

In today\u27s competitive business environment, companies face enormous pressure and must continuously search for ways to design new products, manufacture and distribute them in an efficient and effective fashion. After years of focusing on reduction in production and operation costs, companies are beginning to look into distribution activities as the last frontier for cost reduction. In addition, an increasing number of companies, large and small, are focusing their efforts on their core competencies which are critical to survive. This results in a widespread practice in industry that companies outsource one or more than one logistics functions to third party logistics providers. By using such logistics expertise, they can obtain a competitive advantage both in cost and time efficiency, because the third party logistics companies already have the equipment, system and experience and are ready to help to their best efforts. In this dissertation, we developed an integrated optimization model of production, inventory and distribution with the goal to coordinate important and interrelated decisions related to production schedules, inventory policy and truckload allocation. Because outsourcing logistics functions to third party logistics providers is becoming critical for a company to remain competitive in the market place; we also included an important decision of selecting carriers with finite truckload and drivers for both inbound and outbound shipments in the model. The integrated model is solved by modified Benders decomposition which solves the master problem by a genetic algorithm. Computational results on test problems of various sizes are provided to show the effectiveness of the proposed solution methodology. We also apply this proposed algorithm on a real distribution problem faced by a large national manufacturer and distributor. It shows that such a complex distribution network with 22 plants, 7 distribution centers, 8 customer zones, 9 products, 16 inbound and 16 outbound shipment carriers in a 12-month planning period can be redesigned within 33 hours. In recent years, multi-agent simulation has been a preferred approach to solve logistics and distribution problems, since these problems are autonomous, distributive, complex, heterogeneous and decentralized in nature and they require extensive intelligent decision making. Another important part in this dissertation involved a development of an agent-based simulation model to cooperate with the optimal solution given by the optimization model. More specifically, the solution given by the optimization model can be inputted as the initial condition of the agent-based simulation model. The agent-based simulation model can incorporate many other factors to be considered in the real world, but optimization cannot handle these as needed. The agent-based simulation model can also incorporate some dynamics we may encounter in the real operations, and it can react to these dynamics in real time. Various types of entities in the entire distribution system can be modeled as intelligent agents, such as suppliers, carriers and customers. In order to build the simulation model more realistic, a sealed bid multiunit auction with an introduction of three parameters a, ß and y is well designed. With the help of these three parameters, each agent makes a better decision in a simple and fast manner, which is the key to realizing real-time decision making. After building such a multi-agent system with agent-based simulation approach, it supports more flexible and comprehensive modeling capabilities which are difficult to realize in a general optimization model. The simulation model is tested and validated on an industrial-sized problem. Numerical results of the agent-based simulation model suggest that with appropriate setting of three parameters the model can precisely represent the preference and interest of different decision makers

Collaboration and information sharing in dyadic supply chains: A literature review over the period 2000–2012

Information sharing and coordination between the agents of a supply chain are considered to be an effective strategy for improving its global performance. This paper presents an updated review of current literature examining the impacts of information sharing and collaboration strategies on supply chain dynamic performance, with particular focus on dyadic structure. To achieve this, a systematic review approach is followed over the period 2000–2012, intending to ensure that the process is reproducible and auditable. A comprehensive taxonomy is also presented, highlighting strategic and operational impacts of collaborative structures. The analysis revealed that collaborative and information sharing issues underlined 10 years ago still require further attention from researchers

Genetic Algorithm for Solving the Integrated Production-Distribution-Direct Transportation Planning

This paper proposes a model of integrated production, distribution and transportation planning for 4-echelon supply chain system that consists of a manufacturer using a continuous production process, a distribution center, distributors and retailers. By means of time-dependent demand at all retailers and direct transportation from one echelon to its successive echelons, the purpose of this paper is to determine production/replenishment and transportation policies at manufacturer, distribution center, distributors and retailers in order to minimize annually total system cost. Due to the proposed model is classified as a mixed integer non-linear programming so it is almost impossible to solve the model using the exact optimization methods and a lot of time is needed when the enumeration methods is applied to solve only a small scale problem. In this paper, we apply the genetic algorithm for solving the model. Using integer encoding for constructing the chromosome, the best solution is going to be searched. Compared with enumeration method, the difference of the result is only 0.0594% with the consumption time is only 0.5609% time that enumeration methods need

Key Factors to Increasing Free Cash Flow for Manufacturers Utilizing Lean Production: An AHP-DEMATEL Approach

This paper aims to apply AHP and DEMATEL to analyze the key factors and interrelationships of lean production to increase free cash flow for manufacturers. The AHP hierarchy was determined through literature and interviews with leading management experts. The assessment criteria were categorized into five major criteria and 15 sub-criteria, including production, sales, human resources, R&D, and finance. According to the AHP results, the first eight key factors were identified as the key factors to increasing cash flow for manufacturers who utilized lean production. DEMATEL was used to identify the interactions among the eight key factors and further identify the four more important ones. The four key factors are strategic planning, strategic deployment, leadership, and goal orientation. This paper proposes management implications and improvement suggestions for the four key factors and their interactions