یادداشتی پیرامون بازده تصادفی از دیدگاه زنجیره تامین

Keren [The single-period inventory problem: extension to random yield from the perspective of the supply chain. Omega 2009;37:801–10] considers a supply chain in which the distributor faces a known demand and orders from the producer subject to a random production yield, and shows that the distributor may find it optimal to order more than what is needed due to supply uncertainty under a uniform distribution. However, Keren (2009) does not address the questions whether it is always optimal for the distributor to order more, or when to order more. In this note, we point out that ordering more is not always an optimal strategy and specify the condition under which this strategy becomes optimal. We also examine the profit losses of the supply chain members resulting from the random yield supply, which is another question not considered in Keren (2009). The producer is found to possibly benefit from this production yield uncertainty, although the performances of the distributor and of the entire supply chain are always undermined. Our results are obtained under a more generalized yield distribution, and can thus be applied to wider industrial domains.

A recent paper by Keren [1] analyzes a two-tier supply chain, in which a distributor facing a deterministic demand procures a product from a producer confronting a random production yield under the wholesale price contract. An analytical solution to the distributor's ordering decision is derived when the production yield follows the uniform distribution, and the optimal ordering quantity is shown possibly more than the known demand through numerical examples. In this note, we revisit this problem and obtain new results by further examining supply chain decisions and profits for the generalized distribution of yield randomness. Our contribution mainly lies in the following areas: (1) We derive analytical solutions to the optimal decisions for supply chain members, and provide explicit conditions under which the distributor should order more than the demand. These conditions are found relevant in different ways to the yield distribution for the cases of additive risk and multiplicative risk, which indicates the importance of recognizing the type of production yield risk. These results surpass those of Keren [1]. (2) We derive analytical solutions of the profit losses for supply chain members due to the random production yield, and verify that the performances of the distributor and the entire supply chain are always worse off. However, the producer could benefit from this random yield under certain conditions, which indicates the importance of deriving a more effective risk-sharing mechanism rather than the simple wholesale price scheme. This issue is not addressed by Keren [1]. (3) All of our results are based on the generalized distribution of yield randomness, thus bearing significance in both theoretical and practical domains. In contrast, Keren [1] only provides analytical solutions for the uniform distribution. The problem in this paper stands on the research interface between random yield and supply chain management, both of which have generated a large body of literature, including the studies of Gerchak et al. [2], Anupindi and Akella [3], Erdem and Ozekici [4], Gupta and Cooper [5], and Mukhopadhyay and Ma [6], among others, on production planning under random yield, and Taylor [7], Cachon and Lariviere [8], Kaya [9], Jornsten et al. [10], and Hosoda and Disney [11], among others, on decision interaction in the supply chain. Aside from the aforementioned studies, more related publications involve supply chain models under the supplier's random yield, which are briefly reviewed below. Zimmer [12] investigates the supply chain coordination issue between a buyer facing deterministic demand and a supplier facing uncertain capacity that is equal to the sum of newly built capacity and a random leftover. He and Zhang [13] consider the risk-sharing problem between a retailer and a supplier subject to random production yield and a more expensive emergency production option. In a subsequent work, He and Zhang [14] further explore a supply chain with random yield production and a yield-dependent secondary market, in which the product is acquired or disposed of. Serel [15] considers a supply chain in which the retailer orders products from an unreliable supplier and a reliable manufacturer, analyzing the retailer's ordering problem in conjunction with the manufacturer's pricing problem. Xu [16] investigates a supply chain model in which the retailer adopts an option contract and the supplier conforms with random yield production and a more expensive emergency procurement. In addition, a number of recent studies explore issues of supply chain coordination of an assembly system with random yield supply. Such studies include those by Gurnani and Gerchak [17], Guler and Bilgic [18], and Yan et al. [19]. The reader can also refer to Keren [1] and the references therein for more literature. The rest of this paper is organized as follows. In Section 2 we restate the model and define the notations in use. Section 3 focuses on the optimal decisions of the supply chain members, and Section 4 explores the impacts of yield randomness on the system profits. Section 5 concludes the paper.

This note extends and provides new results on the supply chain model with producer's random yield proposed by Keren [1]. Keren gives the decision solutions under uniformly distributed yield and shows by numerical examples that the distributor may order more than the deterministic demand. In this note, we derive analytic solutions of the supply chain decisions under generalized yield distribution, and point out that whether the distributor should order more than the demand is conditional. That is, the distributor should order more than the demand if and only if her marginal profit from selling this product exceeds a threshold. The differences in the cases of additive risk and multiplicative risk are also shown, suggesting the importance of identifying yield risk type. We also explore the impacts of the yield randomness on the profits of supply chain members, which is not studied by Keren [1]. We find that although the performances of the distributor and the entire supply chain are always undermined by the yield uncertainty, the producer can be even better off when the distributor's marginal profit is adequately large. This result once again demonstrates the crucial role of the distributor's marginal profit, and further shows the possible need for other mechanisms rather than the simple wholesale price contract for a more effective yield risk sharing. The design of such mechanisms is an interesting topic for future research.