مدیریت موجودی با دو تامین کننده تحت عدم قطعیت عملکرد و ریسک گریزی

In this paper, we consider a single-product single-period inventory model in which the retailer can source from two suppliers. The primary supplier is cheaper but unreliable in the sense that it generates supply yield uncertainty, whereas the secondary supplier is perfectly reliable but more expensive. The reliable supplier's capacity is fixed and the retailer cannot order more than the quantity reserved in advance. We study the problem in the context of a risk-averse retailer who has to determine the optimal order quantity from the primary supplier and the optimal reserved quantity from the secondary supplier. We develop the model in the perspective of a low risk averse retailer and quantify the risk via an exponential utility function. We show by numerical experiments how the resulting dual sourcing strategies differ from those obtained in the risk-neutral analysis. We also examine the sensitivity of some model-parameters on the optimal decisions.

Many inventory models have been developed based on the assumption that items are replenished from a single supplier. However, in practice, the sole supplier often fails to meet the retailer's demand due to various reasons. These include insufficient supply of raw materials, production of poor quality products, machine breakdown, workers strike, and so on. Business organizations use a secondary supplier or multiple suppliers today to maintain a desirable service level or to reduce customer service time or even to reduce costs. Dual or multiple sourcing strategy is particularly very useful to retailers for newly launched products which undergo several changes and updates during their early stage of life cycle. In the supply chain literature, mainly two forms of supply uncertainty have been considered—supply disruption and yield uncertainty. Supply disruption refers to the complete inoperativeness of a portion of the supply chain whereas yield uncertainty refers to a form of supply uncertainty in which the quantity produced or received differs from the quantity ordered by a random amount. Supply disruption models have been studied extensively both for single supplier systems (Parlar and Berkin, 1991, Moinzadeh and Aggarwal, 1997 and Arreola-Risa and DeCroix, 1998) and two-supplier systems (Parlar and Perry, 1996, Gurler and Parlar, 1997 and Tomlin, 2006). But the majority of yield uncertainty models have been developed for single supplier systems, see Yano and Lee (1995) for a comprehensive review of yield uncertainty literature. Dual sourcing in the context of yield uncertainty has attracted the attention of only a few researchers. Gerchak and Parlar (1990) investigate a second sourcing option in an EOQ (Economic Order Quantity) setting to reduce the effective yield randomness of firm's purchase quantity and deduce conditions under which double sourcing (with distinct yield distributions to two suppliers) is preferable to single sourcing. Parlar and Wang (1993) compare single and double sourcing alternatives in the newsvendor model assuming that actual incoming quantities are a function of random yield. Agrawal and Nahmias (1997) consider a single period supplier selection and order allocation problem with normally distributed supply and show that for two non-identical suppliers, the expected profit function is concave in the number of suppliers. Anupindi and Akella (1993) address the operational issue of quantity allocation between two uncertain suppliers and its effects on the inventory policies of the buyer. Gurnani et al. (2000) simultaneously determine ordering and production decisions for a two component assembly system with random yield from two suppliers, each providing a distinct component. Chopra et al. (2007) develop a single period model integrating two types of supply uncertainty. One supplier is subject to both recurrent and disruption uncertainties and the other one is perfectly reliable. They show that bundling the two uncertainties results in an over-utilization of the unreliable supplier and under-utilization of the reliable supplier. The above works focus on characterizing the replenishment decisions which optimize the expected cost or profit. That is, the problems are studied from the point of view of risk-neutral decision makers. However, risks due to market fluctuation, high degree of uncertainties in demand and supply, etc. may have a significant impact on cost. For this reason, inventory managers sometimes accept a reasonably higher expected cost in order to reduce the variability of cost. So, there is a need to incorporate risk into the managerial decision making. Optimal decisions of a risk-averse retailer in the single-item single-period (newsvendor) problem setting have been extensively studied in the literature, see Eeckhoudt et al. (1995), Agrawal and Seshadri (2000), Keren and Pliskin (2006), Chen et al. (2007), and Chopra et al. (2007); multi-item single period setting (Gotoh and Takano, 2007 and Borgonovo and Peccati, 2009); single-item multi-period setting (Bouakiz and Sobel, 1992 and Ahmed et al., 2007). The above references utilize mean-variance criterion or expected utility theory to develop models under risk. The exceptions being Ahmed et al. (2007), Gotoh and Takano (2007) and Borgonovo and Peccati (2009) which are based on coherent risk measures. In this paper, we consider a single-period inventory model for a short-life product which is supplied by two suppliers, one is unreliable and cheaper and other one is reliable but more expensive. The underlying problem scenario is very close to Chopra et al. (2007) in which the delivery quantity from the unreliable supplier is assumed to follow a probability distribution having mean and variance independent of the order quantity. The authors develop the model for a risk-neutral retailer. In this paper, we consider an extended newsvendor model assuming that the mean and variance of random yield are dependent on the order quantity. We develop the model and derive the optimal dual sourcing strategy from the point of view of a risk-averse retailer. We investigate, by numerical experiments, how the resulting dual sourcing strategies differ from those obtained in the standard (risk neutral) mean cost analysis.

This paper has considered a single-product single-period inventory model in which the risk-averse retailer faces yield uncertainty from the primary supplier; the secondary supplier being reliable though capacity constrained. The random yield has been modeled with a probability distribution having mean and variance dependent on the order quantity and the risk aversion has been modeled via an exponential utility function. From the numerical study it has been observed that the risk aversion can reduce the cost variance significantly by allowing a reasonable small increase in the mean cost. Moreover, compared to the risk-neutral retailer, the risk-averse retailer always places lower order quantities from the primary supplier. This observation is similar to the ordering decision in a single sourcing newsvendor model where it has been shown that a risk-averse retailer's optimal order quantity is less than that of a risk-neutral retailer. Future research could solve the problem by developing a more general methodology based on expected utility theory. In that case, one can proceed to analyze the model with the expected disutility equation(12) View the MathML sourceE[u¯(s,R)]=∫0d−Ru¯[w1x+(w2+r)R+cu(d−R−x)]f(x)dx+∫d−Rdu¯[w1x+w2(d−x)+rR]f(x)dx+∫d∞u¯[w1x+c0(x−d)+rR]f(x)dx. Turn MathJax on Moreover, assumptions of two unreliable suppliers instead of one and/or other uncertainties such as demand and suppliers’ lead time uncertainties would be worthful contributions. Another direction of research may be the study of the proposed model under coherent risk measures such as mean-absolute deviation (MAD) (Ruszczyński and Shapiro, 2005), conditional value-at-risk (CVaR) (Rockafellar and Uryasev, 2002).