Cost allocations in interval inventory situations: the SOC and Shapley approaches

TL;DR

This paper introduces interval-based cost allocation methods, the SOC and Shapley approaches, for inventory management under demand uncertainty, demonstrating their theoretical properties and practical effectiveness in a real-world case study.

Contribution

It develops and analyzes new interval-based cost-sharing rules, extending classical models to better handle demand uncertainty in collaborative inventory management.

Findings

Interval-based models enable fairer cost distribution under uncertainty.

The case study shows practical applicability in airport perfume inventory coordination.

Theoretical analysis confirms desirable properties of the proposed allocation rules.

Abstract

Uncertainty in demand and supply conditions poses critical challenges to effective inventory management, especially in collaborative environments. Traditional inventory models, such as those based on the Economic Order Quantity (EOQ), often rely on fixed parameters and deterministic assumptions, limiting their ability to capture the complexity of real-world scenarios. This paper focuses on interval inventory situations, an extension of classical models in which demand is represented as intervals to account for uncertainty. This framework allows for a more flexible and realistic analysis of inventory decisions and cost-sharing among cooperating agents. We examine two interval-based allocation rules, the interval SOC-rule and the interval Shapley rule, designed to distribute joint ordering costs fairly and efficiently under uncertain demand. Their theoretical properties are analyzed, and their practical applicability is demonstrated through a case study involving the coordination of perfume inventories across seven Spanish airports, based on 2023 passenger traffic data provided by AENA. The findings highlight the potential of interval-based models to enable a robust and equitable allocation of inventory costs in the face of operational uncertainty.