1 A Robust Optimization Approach for the Milk Run Problem with Time Windows under Inventory Uncertainty- An Auto Industry Supply Chain Case Study

In this paper we introduce a robust optimization approach to solve the milk run system with time window with inventory uncertainty. This approach yields routes that minimize transportation costs while satisfying all inventory in a given bounded uncertainty set. The idea of Milk Run problem has been used in the context of logistic and supply chain problems in order to manage the transportation of materials. Since the resulted problem formulation is NP-Hard, In order to solve the underlying problem, a novel algorithm entitled robust optimization has been proposed. We apply the model to solve some numerical examples to show robust solution efficiency versus deterministic. Since the resulted problem illustrate that grows up time in this method is progressively, In order to solve problem in large scale, particle swarm optimization has been proposed. We also observe that the robust solution amounts to a clever management of the remaining vehicle capacity compared to uniformly and non-uniformly distributing this slack over the vehicles