A Framework for Mathematical Development of a Location-Allocation Model for Recycling Facilities

Abstract

Unattractive travel distances and poorly located recycling collection points are significant barriers to public participation in recycling and source‑separation practices, making effective facility planning essential for improving service accessibility and coverage. This study proposes a capacitated facility location–allocation model that aims to maximize recyclable waste coverage while considering accessibility, fixed facility capacities, and operational constraints on the number of facilities. Building upon an existing facility location framework, the proposed model replaces the busyness‑level assumption with fixed capacity levels to better represent standardized recycling container capacities. The problem is formulated as a binary integer programming model on a network graph, in which demand locations are assigned to activated recycling facilities within a predefined travel‑time threshold, subject to capacity limitations and an upper bound on facility numbers. Numerical experiments conducted using randomly generated datasets examine the model’s behavior under varying travel thresholds, capacity levels, and facility limits. The results reveal clear trade‑offs between accessibility, capacity sizing, and facility quantity, demonstrating that increased travel thresholds and capacities improve demand coverage up to saturation points, while stricter facility limits significantly constrain achievable coverage. The study contributes a capacity‑based extension to recycling facility location modeling and provides practical decision‑support insights for improving recycling accessibility and infrastructure planning.