Robust mechanism design and production structure for assembly systems with asymmetric cost information

We consider the design of a robust procurement mechanism for an assembler who must procure multiple complementary components under limited information regarding the unit production costs of the potential suppliers. We abandon the standard assumption that there exists a common prior distribution for the suppliers’ costs and we employ the max-min criterion in which we design a mechanism to maximize the assembler’s worst-case expected profit when only the means of the suppliers’ costs are known. We formulate this problem using a linear semi-infinite programming model and we apply a primal-dual approach to reduce the problem to a single joint optimization model. We characterize the optimal procurement mechanism (payments and ordering quantities) under the assumption of balanced ordering and uncertain end-customer demand. We use these results to compare the performance of component production, under which the components are sourced from separate suppliers, and integrated production, under which the components are sourced from the same supplier. We find that component production is preferred when the production costs of the components are heterogeneous. We also propose two heuristic mechanisms which are easier to compute and implement in practice, particularly when the number of components is large. Finally, we extend our analysis to the case in which the average and variance of the suppliers’ costs are known.