an integrated multi-objective milp model for rebar delivery scheduling and vehicle routing: a case study

This study addresses the critical challenge of optimizing rebar delivery in heavy logistics industries by proposing an integrated multi-objective mixed-integer linear programming (milp) model for simultaneous delivery scheduling and vehicle routing. the model aims to minimize three conflicting objectives: the overall makespan of deliveries, the weighted customer dissatisfaction from delivery time windows based on customer priority, and the total transportation costs. a fuzzy multi-objective optimization approach, based on the principles of bellman and zadeh and zimmermann’s method, is employed to transform this complex problem into a single-objective maximization problem of an overall satisfaction level. the efficacy and practical applicability of the proposed model are validated through a real-world case study from amir kabir khazar steel company in gilan province, iran. the case study involves 51 customer orders to be delivered over a three-day planning horizon, incorporating realistic constraints such as specific time windows and customer priority levels. computational results, obtained using gams with the cplex solver, demonstrate that the model successfully achieves a high overall satisfaction level of λ =0.841. the findings offer significant managerial insights for balancing operational efficiency, cost reduction, and customer satisfaction in rebar supply chains.