We propose and analyze a general periodic-review model in which the firm has access to a set of potential suppliers, each with specific yield and price characteristics. Assuming that unsatisfied demand is backlogged, the firm incurs three types of costs: (i) procurement costs, (ii) inventory-carrying costs for units carried over from one period to the next, and (iii) backlogging costs. A procurement strategy requires the specification, in each period, of (i) the set of suppliers to be retained, (ii) their respective shares in this period's replenishments, as well as (iii) the traditional aggregate order placed (among the various suppliers).
We show how the optimal procurement strategy can be obtained with an efficient algorithm. A base-stock policy is no longer optimal, but in each period there exists a maximum inventory level, such that orders are placed if and only if the starting inventory is below this threshold. In each period it is optimal to retain a given number of suppliers that are cheapest in terms of that period's effective cost rates, i.e., the expected cost per usable unit. The optimal number of suppliers to be retained in a given period depends on all current and future parameters and distributions, but this dependence can be aggregated into a single so-called benchmark cost measure. Under Normal yield and demand distributions, the suppliers' market shares are determined by a single aggregate score, itself the product of a simple reliability score and a cost score.
Federgruen, Awi, and Nan Yang. "Procurement Strategies with Unreliable Suppliers." Operations Research 59, no. 4 (2011): 1033-1039.
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