Discrete optimization model for multi-product multi-supplier vehicle routing problem with relaxed time window

This study examines the complicated logistics optimization issue known as the vehicle routing problem for multi-product and multi-suppliers(VRP-MPMS), which deals with the effective routing of a fleet of vehicles to convey numerous items from multiple suppliers to a set of consumers. In this problem, products from various suppliers need to be delivered to different customers while considering vehicle capacity constraints, time windows, and minimizing transportation costs. We propose a hybrid approach that combines a generalized reduced gradient method to identify feasible regions with a feasible neighborhood search to achieve optimal or near-optimal solutions. The aim of the exact method is to get the region of feasible solution. Then we explore the region using feasible neighborhood search, to get an integer feasible optimal (suboptimal) solution. Computational experiments demonstrate that our model and method effectively reduce transportation costs while satisfying vehicle capacity constraints and relaxed time windows. Our findings provide a viable solution for improving logistics operations in real-world scenarios.