Multi-location stochastic inventory control with service level constraints and routing decisions

We study a multi-period distribution network where many nodes face non-stationary random demand. Nodes are replenished by a single truck from a central depot. Minimum service levels have to be met and are stated as a maximum admissible probability of stock-out at each node. We consider a fixed cost for dispatching the truck, traveling costs among nodes/the depot, unit variable replenishment costs and unit inventory holding costs at each node. We minimize expected total transportation, inventory replenishment and holding costs. We discuss a certainty equivalent MILP formulation for our problem.