DIVERSIFICATION UNDER SUPPLY UNCERTAINTY

Supply chain management is becoming an increasingly important issue, e specially when in most industries the cost of materials purchased comp rises 40-60% of the total sales revenue. Despite the benefits cited fo r single sourcing in the popular literature, there is enough evidence of industries having two/three sources for most parts. In this paper w e address the operational issue of quantity allocation between two unc ertain suppliers and its effects on the inventory policies of the buye r. Based on the type of delivery contract a buyer has with the supplie rs, we suggest three models for the supply process. Model I is a one-d elivery contract with all of the order quantity delivered either in th e current period with probability beta, or in the next period with pro bability 1 - beta. Model II is also a one-delivery contract with a ran dom fraction of the order quantity delivered in the current period; th e portion of the order quantity not delivered is cancelled. Model III is similar to Model Il with the remaining quantity delivered in the ne xt period. We derive the optimal ordering policies that minimize the t otal ordering, holding and penalty costs with backlogging. We show tha t the optimal ordering policy in period n for each of these models is as follows: for x greater-than-or-equal-to u(n)BAR order nothing; for v(n)BAR less-than-or-equal-to X < u(n)BAR, use only one supplier; and for x < v(n)BAR, order from both suppliers. For the limiting case in t he single period version of Model I, we derive conditions under which one would continue ordering from one or the other or both suppliers. F or Model II, we give, sufficient conditions for not using the second ( more expensive) supplier when the demand and yield distributions have some special form. For the single period version of Models II and III with equal marginal ordering costs we show that the optimal order quan tities follow a ratio rule when demand is exponential and yields are e ither normal or gamma distributed.