Rationing, defective inputs and Bayesian updates under central planning

The enterprise manager anticipates that he will be rationed in his input markets and is required to meet an output target. In order to avoid a penalty for missing the output target, he can purchase the inputs at an earlier time, when rationing is not in effect, but then he must incur an inventory cost. The inputs themselves are defective with a known mean rate but unknown variability; the manager has a prior density over this parameter. He can solve the relevant expected-cost minimisation problem in three ways: (a) by simultaneously determining the optimal amounts to be ordered on the two dates, (b) by dynamic programming, and (c) by dynamic programming combined with Bayesian learning. The paper investigates the properties of the optimal solution under the three scenarios with respect to variations in the defective rate, the level of uncertainty and the relative costs of inventories and of missing the target.We are indebted to the National Science, Olin and Guggenheim Foundations and the National Council on Soviet and East European Research for support. We are also indebted to Gregory C. Chow, J.-S. Pischke, and two referees for several insightful comments.