  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.
