Population-based and hybrid heuristic approaches for the bi-objective sustainable multi-vehicle traveling purchaser problem

This article examines a retailer's challenge in selecting sustainable suppliers, assigning orders, routing multiple capacitated vehicles to collect purchased products within a restricted travel distance, and choosing the vehicles' speed levels. It presents a bi-objective mixed-integer linear programming model that allows varying speed levels between arcs of the asymmetric network connecting suppliers and between vehicles on the same arc. Suppliers have different capacities and can supply various products to meet deterministic demands, with total supply capacity exceeding demand for each product. The retailer aims to select the optimal suppliers to minimize variable and fixed procurement costs, fuel and transportation costs, and CO2 social costs while maximizing the social and environmental worth of the procured goods. The study extends the pollution routing problem and the traveling purchaser problem by integrating environmental and social sustainability and accounting for the social cost of CO2 emissions. An exact approach and two suggested heuristic algorithms are used to solve the model. A comprehensive numerical analysis demonstrates that the proposed solution algorithms reliably approach the optimum within a practical amount of computation time for the instances considered.