A stochastic programming approach for the operational fleet composition problem

This paper introduces the operational fleet composition problem with stochastic demands (OFCP-SD), which is commonly faced by e-commerce companies in the context of short-term capacity planning for freight transportation. We propose a two-stage stochastic programming formulation, in which the planned fleet size and mix decisions constitute the first stage, while recourse actions are taken in the second stage to hire extra vehicles or to make vehicle cancellations according to the observed demands. Hiring extra vehicles incurs additional costs, while vehicle cancellations involve financial restitutions. The objective is to minimize the fleet overall cost, which comprises the first-stage planned cost as well as the expected cost or restitution stemming from the fleet adjustments made in the second stage. A scenario generation procedure is devised, and a variable-fixing matheuristic is suggested for the OFCP-SD. A case study conducted within the Brazilian middle-mile operation of the leading e-commerce company in Latin America shows the advantages of explicitly modeling the stochastic demands and underlines the benefits of the proposed approach for the business. Compared to a simplified deterministic approach, the use of the OFCP-SD demonstrated a yearly potential cost avoidance of more than USD 2.5 million as well as an annual reduction of more than 20 thousand pallets transported by means of extra vehicles.