The Vehicle Routing Problem (VRP) is a classical problem of routing a fleet of vehicles from a center to service a set of customers at minimum cost. VRP has been studied over several decades due to its numerous applications in the industry. Such real life routing problems contain a high degree of uncertainty. Most of the current methods to address uncertainty in VRP either require strong assumptions or increase the complexity of the model significantly. Robust optimization has recently emerged, increasingly in this decade, as a novel approach to model uncertainty: optimize against the worst-case scenario. This study contributes to the literature by proposing a routing model that uses robust optimization with simple assumptions to model uncertainty in demand and travel times without increasing the complexity of the formulation. We adapt this model for a real life courier delivery problem with stochastic service times and time windows (via robust optimization), and with probabilistic customers (via a recourse action). We then develop a heuristic for this large scale problem and obtain improved solutions than used in practice at a leading company in the industry.

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