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Article Excerpt
1. Introduction
Collaborative planning, forecasting, and replenishment (CPFR) is a standard set of technology-enabled business processes that has been developed over the last decade by the Voluntary Interindustry Commerce Standards Association (VICS). CPFR's key objective is to provide trading partners with a roadmap for collaboration, via which they can integrate their demand and supply planning and execution processes (see CPFR 1999). A CPFR partnership may include extensive sharing of information, and the use of such information to drive operational planning and product replenishment processes. By exchanging demand data, supply chain members can improve their product fulfillment levels, reduce their inventories, and use their resources more efficiently and effectively.
The main objective of the present paper is to study the potential benefits that a supply chain can gain when its trading partners share advanced demand information--a practice to which we refer below as collaborative forecasting (CF). More specifically, our focus is on understanding the benefits of CF in decentralized supply chain configurations that include a retailer and a manufacturer. The manufacturer operates in an environment in which production smoothing, inventory levels, and the stability of the production schedule, are key metrics of concern (Graves et al. 1998). The consideration of the trade-offs characterizing production environments in the assessment of CPFR projects appears to be of substantial interest in practice; see, e.g., KJR Consulting (2002) and AMR Research (2001).
We develop a stylized reference model in which the supply chain members progressively collect information about the demand process. One key contribution of this paper lies in the adaptive production planning process it proposes for the manufacturer. The production strategy we devise is based on a class of policies that we derive by defining and solving a surrogate linear-quadratic Gaussian (LQG) problem. Another key contribution of this work is that it offers an optimization method for the retailer's inventory replenishment process, by taking into account the exact correlation pattern between the demand and the supply process (both are uncertain).
We use our model to study the potential benefits of CF partnerships, and the way the benefits naturally split between the trading partners. On average, CF leads to about 4% improvement in the overall supply chain scorecard performance. However, the benefits vary considerably across the different parameter combinations that were tested. We notice that three key characteristics of the supply chain affect the potential benefits of CF: (1) the relative explanatory power of the supply chain partners, (2) the supply side agility, and (3) the internal service rate. These properties need to be well understood and taken into account when trading partners consider CF partnerships. A detailed summary of our key results and insights are found in the concluding section of this paper.
The paper is organized as follows. In [section]2 we propose a stylized reference model for the supply chain. In [section]3 we describe the retailer's replenishment policy class. In [section]4, we develop a class of production planning and execution policies for the manufacturer. In [section]5, we describe a method for determining the policy parameters for the trading partners based on their local incentives, and we present the way in which we evaluate the supply chain performance with and without CF. This enables us to study the potential benefits of CF and the way these benefits naturally split between the retailer and the manufacturer; see our numerical study in [section]6. We conclude the paper with a detailed summary of results in [section]7.
1.1. Literature Review
The management science literature has focused on several important aspects of CPFR. Aviv (2001) proposed a stylized reference model for quantifying the inventory and service performance of supply chains in settings where forecasts are dynamically updated at more than one location in the system. Using this model, Aviv studied the potential benefits that the supply chain can gain through CF as well as the benefits derived from the coordination of the replenishment processes across the chain ("collaborative replenishment" (CR)). Aviv (2002) compared traditional vendor-managed inventory (VMI) and CPFR programs in settings with different levels of intertemporal correlation in the demand process. In both of these papers, Aviv's scope of analysis was limited to a discussion of the potential value of CPFR in a cooperative supply chain. The current paper bears some similarity to the above papers in the choice of the underlying descriptive demand model, and in the modeling of information exchange under CF. The key differences are the consideration of the manufacturer's production environment, and the explicit modeling and discussion of the internal service performance.
A few recent research papers examine incentive issues in CF settings. Miyaoka (2003) studied a procurement transaction taking place between a retailer and a seller. The paper examined the conditions under which collaborative forecasting alignment is achievable; in other words, the situation in which the trading partners have the right incentives to credibly share forecasts. Kurtulus and Toktay (2004) developed a game-theoretical model in which the supply chain partners can make investment choices that impact their forecasting capabilities. The authors identified important factors that affect individual and total forecasting effort and quality, and characterize conditions under which CF is sustainable. Other relevant papers that discuss self-interest behavior in uncertain environments characterized by asymmetric information include Cachon and Lariviere (2001), Mishra et al. (2001), and Ozer and Wei (2006). We refer the reader to a more detailed literature review in a recent book chapter by Aviv (2004).
To our knowledge, there is no work that studies CF in decentralized, information-rich environments, in which production capacities are explicitly modeled. Although researchers have studied the value of information sharing in capacity-constrained environments, they considered the upstream share of historical demand data (e.g., point-of-sale data) with the manufacturer; see, e.g., Aviv and Federgruen (1998), Gavirneni et al. (1999), and Simchi-Levi and Zhao (2003). Our paper is different from these papers in that it considers information-rich environments, in which the share of information is not limited to the transfer of historical demand figures, but encompasses other "information signals." Generally speaking, information signals are streams of data that the supply chain members may be privy to on an ongoing basis. These may include promotion plans, changes in weather conditions, advanced information about demand--essentially, any sort of data, other than past demand realizations, that correlate with future demand. As argued in Aviv (2001, 2002), and Kurtulus and Toktay (2004), the consideration of information signals is of significant importance for the understanding of CPFR's value proposition. Additionally, in the aforementioned papers, capacity is modeled as a fixed constraint. But in these models, a variable production path was not more costly than a stable one, and similarly, deviations from plans were not costly (thus, planning was not needed to be taken into account explicitly in their models).
Another approach to model the production environment is to consider metrics such as production smoothing, and plan stability (see, e.g., Sethi and Thompson 2000, Chapter 6). We adopt this approach, using a convex-cost smoothing formulation rather than a finite-capacity model in our analysis; we postpone the motivation and details to [section]2.2. Graves et al. (1998) proposes an elegant model of this type for production and inventory planning. Our paper is congruent with their work in the choice of the scorecard metrics (quadratic cost functions) for the manufacturer. However, there are some important differences. First, we allow for intertemporal correlations in the demand process. Second, our models allow us to consider different levels of expectation for product availability in the manufacturer-to-retailer link of the supply chain--in our terms--the internal service rate. The assumption in Graves et al. (1998) is that the internal level of service is high enough so that the supply chain is "decoupled" with inventory (we shall discuss this issue in significant detail later on). The third difference is that our paper considers different levels of information asymmetries, and that it explicitly studies the value of CF.
2. A Stylized Supply Chain Model
In this section we present three elements of our reference model: (i) the specification of the coevolution of demand and information ([section]2.1); (ii) a set of metrics, which we refer to as the supply chain scorecard ([section]2.2); and (iii) the mode of operations in the supply chain, as well as the notion of internal service rate used later in this work ([section]2.3).
Let us begin with a few preliminaries. We consider a retailer and a manufacturer who are responsible for producing and delivering a single product to the market. Let [I.sub.n.sup.r] denote the retailer's inventory position (=on hand, minus backlogs, plus all outstanding orders) at the beginning of period n, prior to order placement for that period. After placing the order for this period (denoted by [A.sub.n]), it takes L periods for the manufacturer to deliver the product, given that no shortages occur at the manufacturer's level. We refer to L as the nominal delivery lead time, or in short: the lead time.
We now turn to the manufacturer's facility. Define [q.sub.n, n] to be the production batch size prescribed for period n, and suppose that, in addition, the manufacturer specifies a production plan for the immediate planning horizon of T periods. Specifically, let ([q.sub.n, n+1], [q.sub.n, n+2],..., [q.sub.n, n+T]) be the production plan for periods n + 1 through n + T, set at the beginning of period n. Essentially, the manufacturer needs to determine the value of the column vector
[q.sub.n] [dot.=] ([q.sub.n, n], [q.sub.n, n+1], [q.sub.n, n+2],..., [q.sub.n, n+T])'
at the beginning of period n. We postpone the treatment of this challenging planning process to [section]4. Let [I.sub.n.sup.m] denote the manufacturer's net inventory (=on hand, minus backlogs) at the beginning of period n, just after completing the production of items during period n -1 (i.e., [q.sub.n-1, n-1]), and receiving the retailer's demand for that period. After the retailer places his order, the manufacturer ships to him as many units as possible to cover the current order plus all standing backorders.
Throughout this paper, we use the superscript or subscript notation "r" and "m" to refer to the retailer-specific and manufacturer-specific parameters, respectively.
2.1. Reference Autoregressive Demand Model
We use a classic first-order autoregressive process (denoted AR(1)) to represent the demand evolution. Let [d.sub.n] be the demand for the product, realized at the retailer's level, during period n, and suppose that it satisfies the dynamics
[d.sub.n] - [mu] = [alpha]([d.sub.n-1] - [mu]) + [[epsilon].sub.n], (1)
where {[[epsilon].sub.n]} is a white-noise process, and [less than or equal to] [alpha] < 1. The AR(1) time series pattern is commonly used in the inventory management literature; see, e.g., Kahn (1987), Lee et al. (2000), and Miyaoka and Hausman (2004). By varying the level of [alpha], one can capture a range of demand processes. For instance, [alpha] = corresponds with the case of i.i.d. demands. The larger the value of [alpha], the larger is the intertemporal correlation between demands in different periods.
To capture the parties' ability to collect advanced demand information, we consider the following linear-regression explanatory model. (1)
[[epsilon].sub.n] = [[tau].summation over (i=1)] [[delta].sub.n, i.sup.r] + [[tau].summation over (i=1)] [[delta].sub.n, i.sup.m] + [[epsilon].sub.n.sup.0]. (2)
This model reflects the fact that demand variations can be explained (statistically) in advance by using information collected by the supply chain members. But it holds several properties that are worth emphasizing. The first property is the fact that the information structure in the supply chain can be decentralized--this is an essential model feature for the study of CF. The superscript notation in the [delta]-values denotes which information is available to each individual member. The second property demonstrates the fact that advanced information is collected over time for each specific random component [[epsilon].sub.n]. This is reflected by the subscript index i in the explanatory variables: For each member a of the supply chain (a [member of] {r, m}), [[delta].sub.n, i.sup.a] is the information obtained about [[epsilon].sub.n] during period n - i. The value [tau] represents the maximal time in advance from which the supply chain members can start collecting information about a specific [epsilon]-component. A third property of the model is that it enables us to consider cross-correlation between the individual members' information processes. For instance, if both members observe the exact same information during each period, the correlation between [[delta].sub.n, i.sup.r] and [[delta].sub.n, i.sup.m] would be perfect. For the sake of tractability and elegance of presentation, we assume that a correlation Cor([[delta].sub.n, i.sup.r], [[delta].sub.n', i'.sup.m]) = [rho] applies only if n = n' and i = i', and it is zero otherwise. Taking a more complex intertemporal correlation pattern into account is certainly possible, but it makes the analysis, the experimental setup, and the notation excessively cumbersome. Instead, we assume that statistical dependency between [[delta].sub.n, i] values and future demands is reasonably reflected via the intertemporal correlation parameter [alpha] of the underlying auto-regressive time series (1). We will use...
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