Min–Max exact and heuristic policies for a two-echelon supply chain with inventory and transportation procurement decisions

• We provide worst-case results for the optimal Min-Expected Value policy.
• We provide worst-case results for the optimal Min–Max policy.
• We formulate a dynamic programming model of the Min–Max problem.
• We apply an Exact DP algorithm to compare the two policies.
• We design a Min–Max Matheuristic algorithm to find near-optimal policies.
• We provide a lower bound on the optimal Min–Max cost.

We study the problem in which one supplier delivers a product to a set of retailers over time by using an outsourced fleet of vehicles. Since the probability distribution of the demand is not known, we provide a Min–Max approach to find robust policies. We show that the optimal Min-Expected Value policy can be very poor in the worst case. We provide a Min–Max Dynamic Programming formulation that allows us to exactly solve the problem in small instances. Finally, we implement a Min–Max Matheuristic to solve benchmark instances and show that it is very effective.