کنترل موجودی در یک مجموعه فروش از دست رفته با اطلاعات در مورد "زمان انجام سفارش" عرضه

Supply chain collaboration using advancements in information technology is on the rise and this includes sharing of information between suppliers and buyers. In this paper we study the value of information about the development of supply lead times from a buyer's perspective. We consider a periodically reviewed single-item inventory system in a lost sales setting where at most one order can be outstanding at a time. We compare the performance of an inventory model assuming informed lead times to a model assuming uninformed independent and identically distributed lead times. We employ the dynamic programming approach to find the best state-dependent ordering policy to minimize the expected average total cost per time unit. Our numerical results show that acquiring information about the development of supply lead times is of value. In general the best policy suggested by the model assuming informed lead times causes lower average cost than the model assuming uninformed lead times.

The crucial part of inventory management is to make replenishment decisions in the face of uncertainties at upstream and downstream stages of the supply chain. Demand uncertainty represents uncertainty in the downstream supply chain, whereas lead-time uncertainty captures the uncertainty of the supply system, i.e. the upstream part of the supply chain. As discussed in an empirical examination by Wagner and Bode (2008), such variations can be equated to supply chain risks which lower its performance. One way to mitigate supply chain risk is by improving confidence between decision-makers through collaboration and better information sharing (Christopher and Lee, 2004). An empirical study by Li et al. (2009) suggests that effective use of information technology has a positive effect on supply chain integration and hence on its performance. Advancements in information technology and its role in supply chain management provides managers with an opportunity to relatively easily obtain dynamic information about demand and supply variations. Similar to demand variations, major variations in supply lead times may have identifiable sources, such as equipment breakdown and workload conditions. These sources of variation reflect the condition of the supply system, and replenishment lead times evolve as the system evolves over time. Inventory models which consider the evolution of demand and use advance information in decision making are widely studied, for example Hariharan and Zipkin (1995), Karlin and Fabens (1959), Song and Zipkin (1993) and Gallego and Özer (2001). However, more sparsely studied are the models with shared information about upstream supply conditions. The hypothesis test by Cannon and Homburg (2001) shows that an increasing number of suppliers share information to reduce acquisition and operation costs for the customer, thus emphasizing a need for further study of such systems. Since the mid-1990s some results for inventory control models with information about supply conditions have been available, such as Song and Zipkin (1996). In these models, stockouts are backordered. However, stockouts may also result in lost sales. The lost-sales case has considerable practical significance. The study by Corsten and Gruen (2004) shows that in the retail industry unmet demands result in lost sales not backorders in almost half of the cases. Lost sales also appear to be a common mechanism for handling shortages in some spare parts industries. The purpose of this paper is to investigate the performance of the value of advanced lead-time information under lost sales. We study a single-item inventory control model with lost sales and ubiquitous demand uncertainty, controlled by a periodic review inventory replenishment policy with at most one order outstanding at any given time. The inventory is supplied by a system with evolving replenishment lead times which are informed in advance and with certainty at every ordering decision epoch. The assumption of no more than one outstanding replenishment order at a time can be justified from a practical standpoint. The likelihood of placing a new order while awaiting the arrival of an existing order can be negligible due to, for example, terms in the supplier-buyer contract or due to the buyer's internal ordering policy. Moreover, allowing for simultaneously outstanding orders makes the model numerically intractable in general (Zipkin, 2008a and Zipkin, 2008b). We assume that the supply system is exogenous, i.e. its development is independent of our demands and replenishment orders (Zipkin, 2000, Section 7.4). Hence, replenishment order lead time is independent of the size of our order and only depends on the conditions of the supply system. However, the system is transparent in the sense that it is assumed to be possible to obtain information about its current state and about the development of its supply lead times. Hence, changes in lead times are characterized by a Markov chain. Thus, with a reliable estimate of current lead time, information of the development of future lead times is available through the Markovian dependence. The performance of the model with information about the development of supply lead times is compared to the model with independent and identically distributed (i.i.d.) lead times. The latter model represents the case where the supplier is not sharing information about the development of the supply lead times. We consider an infinite time horizon inventory problem and formulate it as a dynamic program with finite and discrete state space. We assume that ordering, inventory holding and lost sales penalty costs are linear and the objective is to minimize expected average total cost per time unit over an infinite time horizon. Through numerical experiments, we observe the significance of information about the development of lead times. By changing the evolutionary pattern, we are able to study its qualitative effect on the inventory performance assuming either informed lead times or i.i.d. lead times. Such comparisons enable us to estimate the value of information available about the development of lead times compared to knowing only their long-term distribution. The rest of the paper is organized as follows. In Section 2 we give a brief survey of the literature related to inventory systems with lost sales and information about supply conditions. Analytical models used for our numerical study are introduced in Section 3 and computational experiments are specified and reported in Section 4. Finally, Section 5 summarizes the results and concludes the paper.

Unlike the conventional assumption in inventory models that supply lead times are independent and/or identically distributed, we have considered a model in which lead times are dependent and where information about the development of lead times is available. These lead times are modeled as a Markov chain and the information about their development is represented by transition probabilities. We have studied a periodically reviewed lost-sales inventory model with stochastic demand and compared the performance of the model assuming dependent and informed lead times with the model assuming i.i.d. lead times. Our numerical results show that information regarding the development of lead times may have a significant effect on inventory replenishment decisions. Using information about lead times can considerably improve the performance of the inventory control model compared to considering lead times only to be i.i.d. Informed lead times seem to have the most significance when the demand rate is neither too low nor too high (cf. Fig. 4) and when the steady-state distribution of the lead time has a high probability mass at a low lead time. Also, using information about lead times seems to be most beneficial when lost sales are relatively costly. Inspired by the integrated single-vendor–single-buyer production inventory model studied in Glock (2012), an interesting extension study could be to assume that the lead time of an order depends on its size and the lead time of an order can be reduced for an extra cost. Moreover, as discussed in Glock and Ries (2012) and Guiffrida and Jaber (2008) there are ways to reduce supply chain variances by investing in extra resources and a big impact can be achieved by doing so. This could be a potential extension of the paper. Also, when considering longer lead times, allowing multiple outstanding orders will significantly increase the complications in solving this problem. Hence, a small improvement step could be to consider at most two orders outstanding instead of only one. Finally, using the discounted cost criterion instead of the average cost criterion will provide a further dimension to the analysis.