No abstract

Supply chain management is becoming an increasingly important issue, especially when in most industries the cost of materials purchased comprises 40--60% of the total sales revenue. Despite the benefits cited for single sourcing in the popular literature, there is enough evidence of industries having two/three sources for most parts. In this paper we address the operational issue of quantity allocation between two uncertain suppliers and its effects on the inventory policies of the buyer. Based on the type of delivery contract a buyer has with the suppliers, we suggest three models for the supply process. Model I is a one-delivery contract with all of the order quantity delivered either in the current period with probability \beta , or in the next period with probability 1 -- \beta . Model II is also a one-delivery contract with a random fraction of the order quantity delivered in the current period; the portion of the order quantity not delivered is cancelled. Model III is similar to Model II with the remaining quantity delivered in the next period. We derive the optimal ordering policies that minimize the total ordering, holding and penalty costs with backlogging. We show that the optimal ordering policy in period n for each of these models is as follows: for x \ge \bar{u} n, order nothing; for v\bar n \le x n , use only one supplier; and for x n , order from both suppliers. For the limiting case in the single period version of Model I, we derive conditions under which one would continue ordering from one or the other or both suppliers. For 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 quantities follow a ratio rule when demand is exponential and yields are either normal or gamma distributed.dual sourcing, supply uncertainty, inventory

We investigate the role of options (contingent claims) in a buyer-supplier system. Specifically using a two-period model with correlated demand, we illustrate how options provide flexibility to a buyer to respond to market changes in the second period. We also study the implications of such arrangements between a buyer and a supplier for coordination of the channel. We show that, in general, channel coordination can be achieved only if we allow the exercise price to be piecewise linear. We develop sufficient conditions on the cost parameters such that linear prices coordinate the channel. We derive the appropriate prices for channel coordination which, however, violate the individual rationality constraint for the supplier. Contrary to popular belief (based on simpler models) we show that credit for returns offered by the supplier does not always coordinate the channel and alleviate the individual rationality constraint. Credit for returns are useful only on a subset of the feasibility region under which channel coordination is achievable with linear prices. Finally, we demonstrate (numerically) the benefits of options in improving channel performance and evaluate the magnitude of loss due to lack of coordination.Supply Contracts, Real Options, Coordination, Flexibility

Classical reasons for carrying inventory include fixed (nonlinear) production or procurement costs, lead times, nonstationary or uncertain supply/demand, and capacity constraints. The last decade has seen active research in supply chain coordination focusing on the role of incentive contracts to achieve first-best levels of inventory. An extensive literature in industrial organization that studies incentives for vertical controls largely ignores the effect of inventories. Does the ability to carry inventory influence the problem of vertical control? Conversely, can inventories arise purely due to incentive effects? This paper explicitly considers both incentives and inventories, and their interplay, in a dynamic model of an upstream firm (supplier) and a downstream firm (buyer) who can carry inventories. In our model, none of the classical reasons for carrying inventory exists. However, as we prove, the buyer's optimal strategy in equilibrium is to carry inventories, and the supplier is unable to prevent this. These inventories arise out of purely strategic considerations not yet identified in the literature, and have a significant impact on the equilibrium solution as well as supplier, buyer, and channel profits. We prove that strategic inventories play a pivotal role under arbitrary contractual structures, general (arbitrary) demand functions and general (finite or infinite) horizon lengths. As one example, two-part tariff contracts do not lead to optimal channel performance, nor can the supplier extract away all of the channel profits, in our dynamic model. Our results imply that firms can and must carry inventories strategically, and that optimal vertical contracts must take the possibility of inventories into account.contracts, inventories, industrial organization, supply chain coordination