Vehicle Fleet Sizing, Positioning and Routing Problem with Stochastic Customers

TL;DR

This paper introduces a novel two-stage stochastic programming approach for the Vehicle Fleet Sizing, Positioning, and Routing Problem with uncertain customer demand, integrating scenario generation, optimization techniques, and novel cuts to efficiently solve complex strategic and operational decisions.

Contribution

It develops a comprehensive methodology combining scenario-based stochastic programming with innovative cuts and activation strategies for the VFSPRP-SC, addressing demand uncertainty in fleet and routing decisions.

Findings

Solutions obtained within 1 to 6 hours for strategic planning.

75% of instances solved in less than 3 minutes for operational use.

Methodology effectively handles demand uncertainty and provides practical solutions.

Abstract

The Vehicle Fleet Sizing, Positioning and Routing Problem with Stochastic Customers (VFSPRP-SC) consists on pairing strategic decisions of depot positioning and fleet sizing with operational vehicle routing decisions while taking into account the inherent uncertainty of demand. We successfully solve the VFSPRP-SC with a methodology comprised of two main blocks: i) a scenario generation phase and ii) a two-stage stochastic program. For the first block, a set of scenarios is selected with a simulation-based approach that captures the behavior of the demand and allows us to come up with different solutions that could match different risk profiles. The second block is comprised of a facility location and allocation model and a Multi Depot Vehicle Routing Problem (MDVRP) assembled under a two-stage stochastic program. We propose several novel ideas within our methodology: problem specific cuts that serve as an approximation of the expected second stage costs as a function of first stage decisions; an activation paradigm that guides our main optimization procedure; and, a way of mapping feasible routes from one second-stage problem data into another; among others. We performed experiments for two cases: the first case considers the expected value of the demand, and the second case considers the right tail of the demand distribution, seeking a conservative solution. By using acceleration techniques we obtain solutions within 1 to 6 hours, reasonable times considering the strategic nature of the decision. For the ex-post evaluation, we solve 75% of the instances in less than 3 minutes, meaning that the methodology used to solve the MDVRP is well suited for daily operation.