Optimal production and rationing policy of two-stage tandem production system

The rationing literature has been so far oblivious to the fact that sellable items may not only be finished products, but also intermediate products to manufacture subsequent sellable products. We address this gap by considering an inventory rationing problem in a two-product tandem make-to-stock production/inventory system. Bulk demand arrives to a partial-batch production system with exponentially-distributed production time for each batch. The management has to decide whether to run or stop production and whether the various classes of demand for both products intermediate product (IP) and finished product or end product (EP) have to be satisfied from available inventory or not in which case demand is lost in order to maximize the firm's expected profit. We present the corresponding dynamic programming formulation and characterize the optimal policy. The resulting policy depends on dynamic switching curves, which define a) thresholds to continue or discontinue production, and b) thresholds to satisfy or turn down incoming orders. We identify the key value drivers and compare various heuristic policies through extensive numerical analyses.