Article ID: | iaor201527029 |
Volume: | 56 |
Issue: | 6 |
Start Page Number: | 112 |
End Page Number: | 121 |
Publication Date: | Oct 2015 |
Journal: | Omega |
Authors: | Bertazzi Luca, Lagan Demetrio, Bosco Adamo |
Keywords: | combinatorial optimization, stochastic processes, vehicle routing & scheduling, demand, transportation: general, production, decision, programming: dynamic |
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.