A Multi-Period Production-Inventory-Routing Model with Farm and In-Store Production for Urban Agriculture Network

Abstract

As urban agriculture evolves into networks of farms and stores, production, inventory, and delivery must be coordinated at the network level. However, prior studies have mainly focused on individual facilities, with limited attention to integrated logistics and supply-demand balancing. This study develops a multi-period production-inventory-routing model that jointly determines farm production, in-store production, inventory, delivery, and inter-store redistribution. A deterministic mixed-integer programming model is formulated to determine production, routing, delivery, redistribution, sales, inventory, and shortages under deterministic demand. A Greedy Heuristic is proposed to efficiently solve large-scale instances, and its performance is evaluated through comparisons with the MIP model and sensitivity analyses. Results show that the Greedy Heuristic finds feasible solutions within 0.2 seconds for all instances, with gaps below 0.1% relative to the best lower bound in large cases. Sensitivity analyses indicate that the benefit of increasing vehicle capacity diminishes beyond a certain level, while greater in-store production enhances the effectiveness of inter-store redistribution in reducing shortages and improving service levels. These findings highlight the importance of jointly designing production capacity allocation and redistribution policies in urban agriculture networks, and demonstrate a practical solution approach for medium- and large-scale planning.