Inventory Design for Mobile Food Markets Considering Customer Purchasing Behavior

Abstract

Food insecurity remains a pressing challenge in the United States, driven in part by limited access to affordable and nutritious food. Mobile markets - vehicles that sell healthy food directly to underserved communities - offer a promising solution. However, many mobile markets face operational and financial challenges due to complex interactions between inventory decisions, customer purchasing behavior, and logistical constraints.

In this project, we propose a bilevel optimization framework to design inventory strategies for mobile markets operating multiple stops on a single trip. The upper-level (leader) problem models the operator's inventory decisions under vehicle capacity constraints, aiming to maximize the total utility of all customers. The lower-level (follower) problem models individual customer purchasing behaviors, which depend on available inventory and budget constraints at the time of their visit. Our model captures the interdependencies between customers, as purchases made at earlier stops affect product availability for later customers.

We provide an exact reformulation and develop a heuristic solution method to address computational complexity. Theoretical performance bounds for the heuristic are established. Numerical experiments demonstrate the efficiency and robustness of our proposed approach and provide insights into how mobile markets can improve customer satisfaction and operational outcomes through strategic inventory planning.

This work lays the foundation for future studies that will incorporate additional operational decisions, such as pricing, routing, and the inclusion of stochastic customer behavior, to further support the financial and social sustainability of mobile market programs.