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Shapley Value for Shortest Path Routing in Dynamic Networks
Version 1
: Received: 27 April 2023 / Approved: 28 April 2023 / Online: 28 April 2023 (04:53:07 CEST)
How to cite: Masimli, A. Shapley Value for Shortest Path Routing in Dynamic Networks. Preprints 2023, 2023041115. https://doi.org/10.20944/preprints202304.1115.v1 Masimli, A. Shapley Value for Shortest Path Routing in Dynamic Networks. Preprints 2023, 2023041115. https://doi.org/10.20944/preprints202304.1115.v1
Abstract
Transportation is a crucial component of supply chain management, responsible
for delivering goods and services to customers. This paper explores the
application of game theory concepts, precisely the Shapley value, to cost allocation
in transportation operations involving drones and trucks.
Our focus is on shortest-path games in which agents own nodes in a network
and seek to transport items between nodes at the lowest possible cost. We
provide a comprehensive literature review of the Shapley value and its use in
shortest-path games, with particular emphasis on transportation networks.
Our proposed model includes sets of customers, drones, and trucks and uses
binary decision variables to indicate whether a drone or truck serves a given
customer. The objective is to minimize the total cost of serving all customers
while adhering to capacity and synchronization constraints. We use the Shapley
value to determine the contribution and cost-sharing of each drone and truck in
serving the customers.
Through a combination of de nitions, theorems, and examples, we explore
the formal meaning of the Shapley value and its relationship to shortest-path
games in transportation networks. We highlight exceptional cases and considerations
that must be taken into account when applying the Shapley value in
such scenarios.
Keywords
Shapley value, shortest-path games, transportation networks, drones, trucks.
Subject
Business, Economics and Management, Business and Management
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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