The multi-period fleet size and mix vehicle routing problem with stochastic demands

Abstract

The multi-period fleet size and mix vehicle routing problem with stochastic demands is a new optimization problem that arises from the need to make strategic fleet sizing decisions while taking into consideration tactical planning and operational uncertainty. The setting is a distribution company that delivers goods to a set of customers and where the expected demand for different customers vary from period to period. The actual demand in a given period is stochastic, and is only revealed when visiting the customer. The objective is to minimize total expected costs, consisting of vehicle acquisition costs, routing costs, and the expected cost of route failures. Route failures occur when a vehicle arrives at a customer with an insufficient amount of goods, resulting in the need to refill the vehicle at the depot. The problem is formulated as a mixed integer programming problem. A heuristic for solving the problem is described and implemented, and a computational study is conducted on a set of varied test instances.