Optimal order split between local and global suppliers under stochastic yield and demand

Consider a firm facing an infinite horizon inventory problem with two suppliers, a local one with zero lead time and a global one with positive lead time. Assume that both suppliers have variable yields with known mean and standard deviation of yields, but no assumption made about the distribution of yield. Order cycle length is assumed to be a given industry standard supply window of unit length. Depending on the lead time taken t by the global supplier, the unit period is divided into two segments, 0 to t and t to 1. Demand is independent and uniform with different parameters for each of the two segments. The firm also has different holding and shortage costs in each segment and has the same selling price per unit for the entire period. We solve the problem of finding the optimal order quantities for each supplier that maximises the expected discounted profit for the entire horizon. We also solve an extension of this problem, where the length of the period along with order quantities are decision variables by proposing a robust heuristic procedure.