Managing stochastic demand in an Inventory Routing Problem with transportation procurement. (October 2015) - Bertazzi, Luca; Bosco, Adamo; Laganà, Demetrio
Abstract: We study an Inventory Routing Problem in which the supplier has a limited production capacity and the stochastic demand of the retailers is satisfied with procurement of transportation services. The aim is to minimize the total expected cost over a planning horizon, given by the sum of the inventory cost at the supplier, the inventory cost at the retailers, the penalty cost for stock-out at the retailers and the transportation cost. First, we show that a policy based just on the average demand can have a total expected cost infinitely worse than the one obtained by taking into account the overall probability distribution of the demand in the decision process. Therefore, we introduce a stochastic dynamic programming formulation of the problem that allows us to find an optimal policy in small size instances. Finally, we design and implement a matheuristic approach, integrating a rollout algorithm and an optimal solution of mixed-integer linear programming models, which is able to solve realistic size problem instances. Computational results allow us to provide managerial insights concerning the management of stochastic demand. Abstract : Highlights: We provide a mathematical formulation of the IRP with transportation procurement. We prove that a policy based just on the average demand can be very suboptimal. We provide a stochastic dynamic programming formulation of the problem. We implement an exact dynamic programming algorithm and a matheuristic. We provide managerial insights concerning the management of stochastic demand.