A Polynomial Dynamic Programming Algorithm for Crude Oil Transportation Planning

Crude oil transportation is a central logistics operation in petrochemical industry because its cost represents a significant part in the cost of petrochemical products. In this paper, we consider the transportation by tankers or trucks. We show that under some realistic assumptions, this problem can be transformed into a single item lot sizing problem with limited production and inventory capacities. We develop a strongly polynomial dynamic programming algorithm to solve it. The problem of crude oil transportation is very difficult. There are few efficient methods in this domain. In the model considered in this paper, crude oil is directly shipped from a supplier port to n client ports to satisfy customer demands over T future periods. The supplier port disposes a fleet of identical tankers with limited capacity. The inventory capacities of customers are limited and time-varying. The backlogging is admitted. The objective is to find an optimal shipment plan minimizing the total cost over the T-period horizon. When the number of tankers is unlimited and customer demands are independent, shipment plans of different customers become independent. This problem can be considered as n independent problems. Each of them can be transformed into a single item lot sizing problem with limited production and inventory capacities, where tanker capacity corresponds to production capacity in classical lot sizing models. The main contributions of this paper are: 1) transformation of a transportation planning problem into a lot-sizing problem; 2) an O(T-3) algorithm is proposed to solve it; and 3) the results can also be applied to terrestrial transportation with direct deliveries. Note to Practitioners-This paper addresses a real-life crude oil transportation planning problem with direct delivery. Based on mathematical properties, the problem is transformed into a lot sizing problem with limited production and inventory capacity. This latter problem is shown to be exactly solvable in polynomial time with dynamic programming. In other words, an optimal solution of this problem can be obtained within a very short amount of computation time, even for large sized instances. Furthermore, the algorithm can be easily implemented with Excel tables and a case study with real-life data shows that the proposed algorithm yields a solution reducing very significantly (by more than 25%) the transportation cost, compared with the classical solution with immediate deliveries.