Assessing the Difference Between Shock Sharing and Demand Sharing in Supply Chains

We consider the problem of assessing value of demand sharing in a multi-stage supply chain in which the retailer observes stationary autoregressive moving average demand with Gaussian white noise (shocks). Similar to previous research, we assume each supply chain player constructs its best linear forecast of the leadtime demand and uses it to determine the order quantity via a periodic review myopic order-up-to policy. We demonstrate how a typical supply chain player can determine the extent of its available information under demand sharing by studying the properties of the moving average polynomials of adjacent supply chain players. Hence, we study how a player can determine its available information under demand sharing, and use this information to forecast leadtime demand. We characterize the value of demand sharing for a typical supply chain player. Furthermore, we show conditions under which (i) it is equivalent to no sharing, (ii) it is equivalent to full information shock sharing, and (iii) it is intermediate in value to the two previously described arrangements. We then show that demand propagates through a supply chain where any player may share nothing, its demand, or its full-information shocks with an adjacent upstream player as quasi-ARMA in - quasi-ARMA out. We also provide a convenient form for the propagation of demand in a supply chain that will lend itself to future research applications.NYU Stern School of Business; Syms School of Business, Yeshiva UniversityStatistics Working Papers Serie

Inventory Policies and Information Sharing: An Efficient Frontier Approach

We consider a two-tier inventory management system with one retailer and one supplier. The retailer serves a demand driven by a stationary moving average process (of possibly infinite order) and places periodic inventory replenishment orders to the supplier. In this setting, we study the value of information sharing and its impact on the retailer’s optimal ordering strategy. We argue that information sharing affects performance through two key cost drivers: (i) on-hand inventory variability and (ii) replenishment order variability. We characterize a “Pareto frontier” between these two sources of variability by identifying optimal inventory replenishment strategies that trade-off one type of variability for the other in a cost efficient way. For the case in which the retailer is able to share her complete demand history, we provide a full characterization of the efficient frontier, as well as of an optimal replenishment policy. On the other hand, when the retailer is not able (or willing) to share any demand information we provide a partial characterization of an optimal solution and show that information sharing does not always add value. We also show that the question of identifying conditions under which information sharing does offer value reduces to a delicate analysis of the invertibility (in a time series sense) of a specific stationary process.Operations Management Working Papers Serie

Forecasting and Information Sharing in Supply Chains Under Quasi-ARMA Demand

In this paper, we revisit the problem of demand propagation in a multi-stage supply chain in which the retailer observes ARMA demand. In contrast to previous work, we show how each player constructs the order based upon its best linear forecast of leadtime demand given its available information. In order to characterize how demand propagates through the supply chain we construct a new process which we call quasi-ARMA or QUARMA. QUARMA is a generalization of the ARMA model. We show that the typical player observes QUARMA demand and places orders that are also QUARMA. Thus, the demand propagation model is QUARMA-in-QUARMA-out. We study the value of information sharing between adjacent players in the supply chain. We demonstrate that under certain conditions information sharing can have unbounded bene¯ts. Our analysis hence reverses and sharpens several previous results in the literature involving information sharing and also opens up many questions for future research.Sy Syms School of Business, Yeshiva University; Department of Information, Operations and Management Science, Stern School of Business, NYU; McCombs School of Business, University of Texas at AustinStatistics Working Papers Serie

Possible Sharing Arrangements in ARMA Supply Chains

We introduce a class of new sharing arrangements in a multi-stage supply chain in which the retailer observes stationary autoregressive moving average demand with Gaussian white noise (shocks). Similar to previous research, we assume each supply chain player constructs its best linear forecast of the leadtime demand and uses it to determine the order quantity via a periodic review myopic order-up-to policy. We demonstrate how a typical supply chain player can create a sequence of partial information shocks (PIS) from its full information shocks FIS and share these with an adjacent upstream player. We go on to show how such a sharing arrangement may be benecial to the upstream player by characterizing the player's FIS in such a case. Hence, we study how a player can determine its available information under PIS sharing, and use this information to forecast leadtime demand. We characterize the value of FIS sharing for a typical supply chain player. Furthermore, we show conditions under which a player is able to form and share valuable PIS without (i) revealing its historic demand sequence or (ii) revealing its FIS sequence. We also provide a way of comparing various PIS sharing arrangements with each other and with conventional sharing arrangements involving demand sharing or FIS sharing. We show that demand propagates through a supply chain where any player may share nothing or a sequence of PIS shocks with an adjacent upstream player as quasi-ARMA in - quasi-ARMA out.Statistics Working Papers Serie

Robust Analysis of Variance: Process Design and Quality Improvement

We discuss the use of robust analysis of variance (ANOVA) techniques as applied to quality engineering. ANOVA is the cornerstone for uncovering the effects of design factors on performance. Our goal is to utilize methodologies that yield similar results to standard methods when the underlying assumptions are satisfied, but also are relatively unaffected by outliers (observations that are inconsistent with the general pattern in the data). We do this by utilizing statistical software to implement robust ANOVA methods, which are no more difficult to perform than ordinary ANOVA. We study several examples to illustrate how using standard techniques can lead to misleading inferences about the process being examined, which are avoided when using a robust analysis. We further demonstrate that assessments of the importance of factors for quality design can be seriously compromised when utilizing standard methods as opposed to robust methods.Statistics Working Papers Serie

Impact of Exponential Smoothing on Inventory Costs in Supply Chains

It is common for firms to forecast stationary demand using simple exponential smoothing due to the ease of computation and understanding of the methodology. In this paper we show that the use of this methodology can be extremely costly in the context of inventory in a two-stage supply chain when the retailer faces AR(1) demand. We show that under the myopic order-up-to level policy, a retailer using exponential smoothing may have expected inventory-related costs more than ten times higher than when compared to using the optimal forecast. We demonstrate that when the AR(1) coefficient is less than the exponential smoothing parameter, the supplier’s expected inventory-related cost is less when the retailer uses optimal forecasting as opposed to exponential smoothing. We show there exists an additional set of cases where the sum of the expected inventory-related costs of the retailer and the supplier is less when the retailer uses optimal forecasting as opposed to exponential smoothing even though the supplier’s expected cost is higher. In this paper, we study the impact on the naive retailer, the sophisticated supplier, and the two-stage chain as a whole of the supplier sharing its forecasting expertise with the retailer. We provide explicit formulas for the supplier’s demand and the mean squared forecast errors for both players under various scenarios.College of Business Administration, Department of Information Systems and Supply Chain Management, Rider University; Sy Syms School of Business, Yeshiva University; Department of Information, Operations, and Management Science, Leonard N. Stern School of Business, New York UniversityOperations Management Working Papers Serie

Possible Sharing Arrangements in ARMA Supply Chains

We introduce a class of new sharing arrangements in a multi-stage supply chain in which the retailer observes stationary autoregressive moving average demand with Gaussian white noise (shocks). Similar to previous research, we assume each supply chain player constructs its best linear forecast of the leadtime demand and uses it to determine the order quantity via a periodic review myopic order-up-to policy. We demonstrate how a typical supply chain player can create a sequence of partial information shocks (PIS) from its full information shocks FIS and share these with an adjacent upstream player. We go on to show how such a sharing arrangement may be benecial to the upstream player by characterizing the player's FIS in such a case. Hence, we study how a player can determine its available information under PIS sharing, and use this information to forecast leadtime demand. We characterize the value of FIS sharing for a typical supply chain player. Furthermore, we show conditions under which a player is able to form and share valuable PIS without (i) revealing its historic demand sequence or (ii) revealing its FIS sequence. We also provide a way of comparing various PIS sharing arrangements with each other and with conventional sharing arrangements involving demand sharing or FIS sharing. We show that demand propagates through a supply chain where any player may share nothing or a sequence of PIS shocks with an adjacent upstream player as quasi-ARMA in - quasi-ARMA out.Statistics Working Papers Serie

Forecasting and Information Sharing in Supply Chains Under Quasi-ARMA Demand

In this paper, we revisit the problem of demand propagation in a multi-stage supply chain in which the retailer observes ARMA demand. In contrast to previous work, we show how each player constructs the order based upon its best linear forecast of leadtime demand given its available information. In order to characterize how demand propagates through the supply chain we construct a new process which we call quasi-ARMA or QUARMA. QUARMA is a generalization of the ARMA model. We show that the typical player observes QUARMA demand and places orders that are also QUARMA. Thus, the demand propagation model is QUARMA-in-QUARMA-out. We study the value of information sharing between adjacent players in the supply chain. We demonstrate that under certain conditions information sharing can have unbounded bene¯ts. Our analysis hence reverses and sharpens several previous results in the literature involving information sharing and also opens up many questions for future research.Sy Syms School of Business, Yeshiva University; Department of Information, Operations and Management Science, Stern School of Business, NYU; McCombs School of Business, University of Texas at AustinStatistics Working Papers Serie

Assessing the Difference Between Shock Sharing and Demand Sharing in Supply Chains

We consider the problem of assessing value of demand sharing in a multi-stage supply chain in which the retailer observes stationary autoregressive moving average demand with Gaussian white noise (shocks). Similar to previous research, we assume each supply chain player constructs its best linear forecast of the leadtime demand and uses it to determine the order quantity via a periodic review myopic order-up-to policy. We demonstrate how a typical supply chain player can determine the extent of its available information under demand sharing by studying the properties of the moving average polynomials of adjacent supply chain players. Hence, we study how a player can determine its available information under demand sharing, and use this information to forecast leadtime demand. We characterize the value of demand sharing for a typical supply chain player. Furthermore, we show conditions under which (i) it is equivalent to no sharing, (ii) it is equivalent to full information shock sharing, and (iii) it is intermediate in value to the two previously described arrangements. We then show that demand propagates through a supply chain where any player may share nothing, its demand, or its full-information shocks with an adjacent upstream player as quasi-ARMA in - quasi-ARMA out. We also provide a convenient form for the propagation of demand in a supply chain that will lend itself to future research applications.NYU Stern School of Business; Syms School of Business, Yeshiva UniversityStatistics Working Papers Serie

Aggregated Information in Supply Chains

We study a two-stage supply chain where the retailer observes two demand streams coming from two consumer populations. We further assume that each demand sequence is a station- ary Autoregressive Moving Average (ARMA) process with respect to a Gaussian white noise sequence (shocks). The shock sequences for the two populations could be contemporaneously correlated. We show that it is typically optimal for the retailer to construct its order to its supplier based on forecasts for each demand stream (as opposed to the sum of the streams) and that doing so is never sub-optimal. We demonstrate that the retailer’s order to its supplier is ARMA and yet can be constructed as the sum of two ARMA order processes based upon the two populations. When there is no information sharing, the supplier only observes the retailer’s order which is the aggregate of the two aforementioned processes. In this paper, we determine when there is value to sharing the retailer’s individual orders, and when there is additional value to sharing the retailer’s individual shock sequences. We also determine the supplier’s mean squared forecast error under no sharing, process sharing, and shock sharing.Operations Management Working Papers Serie