Allocating Benefits Due to Shared Resources Using Shapley Value and Nucleolus in Dynamic Network Data Envelopment Analysis

Abstract

Shared resources are common among supply chain partners and also occur in multiple linked stages of an internal network. The sharing of these resources impacts the organization’s profits. This study is focused on the potential benefits of resource sharing on a three-stage network system and on the profit improvement allocation. Previous treatments concentrate on defining optimal proportions to allocate resources and disregard the impacts of allocations to promote cooperation and are limited to static evaluations. Data Envelopment Analysis performs the decision-making units (DMUs) efficiency measurement. Methodological advances have resulted in models that analyze their internal structure and temporal impacts on efficiency. We propose an integrated cooperative game and dynamic network DEA that considers known quantities of resources used in each stage and the time effects to optimize the system’s profit. Each DMU stage is a player, and we investigate performance before and after resource sharing. Using Shapley value and Nucleolus, it is possible to allocate the benefits obtained based on the marginal contributions of each stage, providing incentives to motivate and maintain cooperation. A numerical example is used to illustrate the method. The results confirm the identification of inefficient DMUs and that sharing resources allows for profit increase for all of them.