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 ۵۱ 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 =۰.۸۴۱. The findings offer significant managerial insights for balancing operational efficiency, cost reduction, and customer satisfaction in rebar supply chains.

Keywords:

Rebar Supply Chain , Delivery Scheduling , Vehicle Routing Problem (VRP) , Multi-Objective Optimization , Mixed-Integer Linear Programming (MILP) , Fuzzy Programming