OPTIMIZATION MODEL FOR MULTI-DEPOT ELECTRIC VEHICLE ROUTING PROBLEM WITH SOFT TIME WINDOWS WITH SCENARIO-BASED ANALYSIS

The adoption of electric vehicles has increased due to their cost-efficiency and environmental impact. However, limited battery capacity requires careful route planning to ensure vehicles complete deliveries efficiently. This study focuses on the Multi-Depot Electric Vehicle Routing Problem with Soft Time Windows (MDEVRPSTW), where electric vehicles can depart from and return to multiple depots, while serving customers within predefined time windows that allow limited violations with penalty costs. The model is formulated using Mixed Integer Linear Programming (MILP) and solved using the exact branch-and-bound method in Lingo 20.0. Two operational scenarios are considered: (1) vehicles must return to their original depot, and (2) vehicles are allowed to return to any depot. Hypothetical data is used to simulate delivery routes with varied time windows and battery capacity constraints. Results show that both scenarios produce feasible, cost-minimizing solutions. Allowing flexible depot return (scenario 2) consistently reduces total travel cost, highlighting the practical benefit of depot flexibility in real-world logistics. This model contributes to the EV routing literature by integrating multiple depots—both fixed and flexible return options—soft time windows, and battery constraints into a single formulation. However, it assumes constant travel speeds and does not account for charging durations, which presents an opportunity for future research.