In this book, Andrew Harvey sets out to provide a unified and comprehensive theory of structural time series models. Unlike the traditional ARIMA models, structural time series models consist explicitly of unobserved components, such as trends and seasonals, which have a direct interpretation. As a result the model selection methodology associated with structural models is much closer to econometric methodology. The link with econometrics is made even closer by the natural way in which the models can be extended to include explanatory variables and to cope with multivariate time series. From the technical point of view, state space models and the Kalman filter play a key role in the statistical treatment of structural time series models. The book includes a detailed treatment of the Kalman filter. This technique was originally developed in control engineering, but is becoming increasingly important in fields such as economics and operations research. This book is concerned primarily with modelling economic and social time series, and with addressing the special problems which the treatment of such series poses. The properties of the models and the methodological techniques used to select them are illustrated with various applications. These range from the modellling of trends and cycles in US macroeconomic time series to to an evaluation of the effects of seat belt legislation in the UK.

Forecasting, Structural Time Series Models and the Kalman Filter

Publisher Summary This chapter reviews the supply chain coordination with contracts. Numerous supply chain models are discussed. In each model, the supply chain optimal actions are identified. The chapter extends the newsvendor model by allowing the retailer to choose the retail price in addition to the stocking quantity. Coordination is more complex in this setting because the incentives provided to align one action might cause distortions with the other action. The newsvendor model is also extended by allowing the retailer to exert costly effort to increase demand. Coordination is challenging because the retailer's effort is noncontractible—that is, the firms cannot write contracts based on the effort chosen. The chapter also discusses an infinite horizon stochastic demand model in which the retailer receives replenishments from a supplier after a constant lead time. Coordination requires that the retailer chooses a large basestock level.

Supply Chain Coordination with Contracts

Many companies have embarked on initiatives that enable more demand information sharing between retailers and their upstream suppliers. While the literature on such initiatives in the business press is proliferating, it is not clear how one can quantify the benefits of these initiatives and how one can identify the drivers of the magnitudes of these benefits. Using analytical models, this paper aims at addressing these questions for a simple two-level supply chain with nonstationary end demands. Our analysis suggests that the value of demand information sharing can be quite high, especially when demands are significantly correlated over time.

The Value of Information Sharing in a Two-Level Supply Chain

Perspectives in supply chain risk management

We incorporate information flow between a supplier and a retailer in a two-echelon model that captures the capacitated setting of a typical supply chain We consider three situations: (1) a traditional model where there is no information to the supplier prior to a demand to him except for past data; (2) the supplier knows the (s, S) policy used by the retailer as well as the end-item demand distribution; and (3) the supplier has full information about the state of the retailer Order up-to policies continue to be optimal for models with information flow for the finite horizon, the infinite horizon discounted and the infinite horizon average cost cases Study of these three models enables us to understand the relationships between capacity, inventory, and information at the supplier level, as well as how they are affected by the retailer's (S - s) values and end-item demand distribution We estimate the savings at the supplier due to information flow and study when information is most beneficial

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Value of Information in Capacitated Supply Chains

We study the optimal pricing of a finite quantity of a fashion-like seasonal good in the presence of forward-looking (strategic) customers. We distinguish between two classes of pricing strategies: contingent and announced fixed-discount. In both cases, the seller acts as a Stackelberg leader announcing his pricing strategy, while consumers act as followers taking the seller's strategy as given and determining their purchasing behavior. In each case, we identify a subgame-perfect Nash equilibrium and show that given the seller's strategy, the equilibrium in the consumer subgame is unique and consists of symmetric threshold purchasing policies. For both cases, we develop a benchmark model in which customers are nonstrategic (myopic). We conduct a comprehensive numerical study to explore the impact of strategic consumer behavior on pricing policies and expected revenue performance. We show that strategic customer behavior suppresses the benefits of price segmentation, particularly under medium-to-high values of heterogeneity and modest rates of decline in valuations. However, when the level of consumer heterogeneity is small, the rate of decline is medium-to-high, and the seller can optimally choose the time of discount in advance, segmentation can be used quite effectively even with strategic consumers. We find that the seller cannot avoid the adverse impact of strategic consumer behavior even under low levels of initial inventory. We argue that while the seller expects customers to be more concerned about product availability at discount time, he cannot use high-price “betting” strategies as he would in the case of low inventory and myopic customers. Under certain qualifications, announced fixed-discount strategies perform essentially the same as contingent pricing policies in the case of myopic consumers. However, under strategic consumer behavior, announced pricing policies can be advantageous to the seller, compared to contingent pricing schemes. Interestingly, those cases that announced discount strategies offer a significant advantage compared to contingent pricing policies. They appear to offer only a minimal advantage in comparison to fixed-pricing policies. Finally, when the seller incorrectly assumes that strategic customers are myopic in their purchasing decisions, it can be quite costly, reaching potential revenue losses of about 20%.

Optimal Pricing of Seasonal Products in the Presence of Forward-Looking Consumers

We consider a cooperative, two-stage supply chain consisting of two members: a retailer and a supplier. In our first model, called local forecasting, each member updates the forecasts of future demands periodically, and is able to integrate the adjusted forecasts into his replenishment process. Forecast adjustments made at both levels of the supply chain can be correlated. The supply chain has a decentralized information structure, so that day-to-day inventory and forecast information are known locally only. In our second model, named collaborative forecasting, the supply chain members jointly maintain and update a single forecasting process in the system. Hence, forecasting information becomes centralized. Finally, we consider as a benchmark the special case in which forecasts are not integrated into the replenishment processes at all. We propose a unified framework that allows us to study and compare the three types of settings. This study comes at a time when various types of collaborative forecasting partnerships are being experimented within industry, and when the drivers for success or failure of such initiatives are not yet fully understood. In addition to providing some managerial insights into questions that arise in this context, our set of models is tailored to serve as building blocks for future work in this emerging area of research.

The Effect of Collaborative Forecasting on Supply Chain Performance

This paper studies the potential benefits of collaborative forecasting (CF) partnerships in a supply chain that consists of a manufacturer and a retailer. To reflect the reality in production environments, we propose a scorecard that captures inventory considerations, production smoothing, and adherence-to-plans. We present a prescriptive convex-cost production planning model for the manufacturer, and a replenishment model for the retailer. We use our integrative reference model to study the potential benefits of CF partnerships. Overall, we find that the benefits of CF depend on the following key characteristics of the supply chain: the relative explanatory power of the supply chain partners, the supply side agility, and the internal service rate. CF is expected to bring high benefits to the supply chain when the manufacturer has the largest relative explanatory power. But quite disappointingly, in these cases a CF partnership does not appear to be valuable to the manufacturer. When the retailer is the dominant observer of market signals, CF typically yields a “win-win” outcome. In order to effectively act upon the information exchanged via CF, the supply side needs to be sufficiently agile. The benefits reported in this paper should be considered as conservative. This is because CF partnerships often bring better information, improved decision support technologies, as well as process improvement to the trading partners. Consequently, the supply side agility can be improved. If this indeed happens, the compound benefits of CF can be dramatically higher than our conservative estimates. Finally, we provide a qualitative discussion of the possible role of internal service rates in supply chains, either as planning parameters to improve performance, or as a mechanism for sharing the benefits of CF between the trading partners.

On the Benefits of Collaborative Forecasting Partnerships Between Retailers and Manufacturers

Consider a retailer announces both the regular price and the post-season clearance price at the beginning of the selling season. Throughout the season, customers arrive in accord with a Poisson process. In this paper we analyze the impact of two types of customer purchasing behavior and two common in-store display formats on the retailer’s optimal expected profit and optimal order quantity. We consider the case when all customers are either myopic (purchase immediately upon arrival) or strategic (either purchase at the regular price upon arrival or attempt to purchase at the clearance price after the season ends). In addition, we consider the case when the retailer would display either all available units or one unit at a time on the sales floor. When all customers have identical valuation, we show that, in equilibrium, each strategic customer’s purchasing decision is based on a threshold policy that depends on the inventory level at the time of arrival. We prove analytically that the retailer would obtain a higher expected profit and would order more when the customers are myopic. Also, we show analytically that the retailer would earn a higher expected profit and would order more under the display one unit format when the customers are strategic. We illustrate numerically the penalty when the retailer mistakenly assumes that the strategic customers are myopic. We extend our analysis to the case in which customers belong to multiple classes, each of which has a class-specific valuation, and also to the case in which the post-season clearance price depends on the actual end-of-season inventory level.

Optimal Markdown Pricing: Implications of Inventory Display Formats in the Presence of Strategic Customers

In this paper we consider a cooperative, two-level supply chain consisting of a retailer and a supplier. As in many practical settings, the supply chain members progressively observe market signals that enable them to explain future demand. The demand itself evolves according to an auto-regressive time series. We examine three types of supply chain configurations. In the first setting, the retailer and the supplier coordinate their policy parameters in an attempt to minimize systemwide costs, but they do not share their observations of market signals. In the second setting, resembling many original vendor-managed inventory (VMI) programs, the supplier takes the full responsibility of managing the supply chain's inventory, but the retailer's observations of market signals are not transferred to him. In our third setting, reminiscent of collaborative forecasting and replenishment partnerships, inventory is managed centrally, and all demand related information is shared. We propose a set of stylized models to study the three settings and use them to provide managerial insights into the value of information sharing, VMI, and collaborative forecasting.

Yossi Aviv

Papers

Optimal Pricing of Seasonal Products in the Presence of Forward-Looking Consumers

The Effect of Collaborative Forecasting on Supply Chain Performance

On the Benefits of Collaborative Forecasting Partnerships Between Retailers and Manufacturers

Optimal Markdown Pricing: Implications of Inventory Display Formats in the Presence of Strategic Customers

Gaining Benefits from Joint Forecasting and Replenishment Processes: The Case of Auto-Correlated Demand