A heuristic based on quadratic approximation for dual sourcing problem with general lead times and supply capacity uncertainty

We study a single-product, periodic-review dual sourcing inventory system with demand and supply uncertainty, where the replenishment lead times can be arbitrary and the expedited supplier has a shorter lead time with a higher unit price than the regular supplier, unmet demand is fully backlogged. Even for the general dual sourcing problem without supply risks, the optimal stochastic policy has been unknown for over 50 years and several simple heuristics have been proposed in the literature. Moreover, the consideration of supply uncertainty brings another challenge, where the objective functions characterized by the dynamic programming recursions are not convex in the ordering quantities. Fortunately, a powerful transformation skill is recently proposed to successfully address the problem above and shows that the value-to-go function is L♮ convex. In this article, we design a Linear Programming greedy (LP-greedy) heuristic based on the quadratic approximation of L♮ convex value-to-go function and convert the problem into a convex optimization problem during each period. In an extensive simulation study, two sets of test instances from the literature are employed to compare the performance of our LP-greedy heuristic with that of some well-known policies in dual sourcing system, including Tailored base-surge, Dual index, Best vector base-stock. In addition, to assess the effectiveness of our heuristic, we construct a lower bound to the exact system. The lower bound is based on an information-relaxation approach and involves a penalty function derived from the proposed heuristic. We show that our proposed LP-greedy heuristic performs better than other heuristics in the dual sourcing problem and it is nearly optimal (within 3%) for the majority of cases.