A Mixed Integer Linear Programming Model for Packaged Drinking Water Distribution Routing Problem

Abstract

This study addresses the Vehicle Routing Problem with heterogeneous vehicles, simultaneous pickup and delivery, multiple trips, and time windows (HVRPSPDMTTW), formulated for the distribution of packaged drinking water (PDW) specifically gallon-packaged PDW. The model was developed to reflect real operational conditions of PDW depots which employs a heterogeneous fleet of pickup trucks and three-wheeled commercial motorcycles to deliver and collect gallon-packaged PDW within defined time windows. The mathematical model is constructed as a Mixed Integer Linear Programming (MILP) formulation with the objective of minimizing total transportation costs, consisting of both fixed and variable vehicle costs. Verification of the model was carried out using LINGO 18.0 software on hypothetical datasets generated through random numbers, with small-scale scenarios involving 5 customers. Computational results confirm that all constraints were satisfied and that the model produces logical and feasible routing solutions. The behavior verification further shows that the model accurately responds to parameter changes, such as reduced vehicle capacity and narrower time windows, demonstrating consistent and realistic results. This research validates the feasibility and reliability of the proposed MILP model in representing real-world distribution systems.