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Article Excerpt
1. Introduction
Over the past decade, the assemble-to-order (ATO) system has become a widely accepted business model in the electronic industry. Many high-tech firms that face shrinking product life cycles, increasing demand for product varieties, and rapid technology innovations, have successfully used ATO to broaden customized product offerings, to lower inventory cost, and to reduce time-to-market. In contrast to the traditional make-to-stock (MTS) system that keeps inventory at the end-product level, ATO keeps inventory at the component level. Components are acquired in advance. When a customer order arrives, required components are pulled from inventory and the end product is assembled and delivered to the customer. As such, ATO postpones the point of commitment of components to specific products and increases the probability of meeting customized demand on time. Furthermore, by using common components and modules in the final assembly, ATO is better protected against demand variability due to risk-pooling effect.
However, in the faster, better, and cheaper information age, rapid technology innovations have significantly increased the pace of product obsolescence. Empirical evidences show that the life cycles of most electronics are much less than one year (Billington et al. 1998). In particular, for an assembled product, its life cycle is directly determined by the life cycles of its constituent components; that is, technology obsolescence at the component level affects the entire product. It has been repeatedly observed that the price of an early-generation PC was drastically reduced after the introduction of a new technology of its major component. In 2001, Intel introduced the 2 GHz Pentium 4 processor and reduced the prices of slower chips by as much as 54%, which subsequently caused the prices of outdated PCs to plummet by 20% (Clark 2001).
ATO is an ideal system to hedge against the risk of component obsolescence. In MTS, technology innovation of a major component could force the firm to either dismantle the early-generation product for spare parts, or drastically slash the prices of or even write off the entire product line equipped with the old component. In ATO, because the final assembly of the end product is postponed until demand is realized, the impact of technology innovations is confined to the component level: The firm salvages the obsolete component and replaces it by a new one, which then is used, together with other components, to assemble a next-generation product. Because MTS salvages the obsolete products whereas ATO salvages obsolete components, ATO is better suited than MTS in the dynamic marketplace that faces rapid, component-based innovations.
Component obsolescence and price erosion due to rapid technology advances pose new challenges to the ATO firm. When products have relatively long life cycles, technology management and inventory control are often not coordinated. However, rapid technology innovations at the component level mean that product configurations need to be reviewed more frequently in the environment of time-based competition. This pushes technology management in ATO closer to the operational level and calls for the effective coordination between technology and inventory management. Anecdotal stories indicate that ineffective coordination between technology management and inventory control is costly. In 1989, Apple Computer Inc. stockpiled $300 millions worth of old memory chips, while several aggressive Korean memory chip suppliers accelerated the introduction of better memory chips; this caused Apple's profit in the first quarter of 1989 to fall by $21 million (Schlender 1989). The lesson from Apple suggests that technology management and inventory control have to be dynamically adjusted and effectively coordinated in today's ever-changing marketplace.
In this paper, we consider an ATO system with a single product assembled from several components. (1) Each component is subject to obsolescence due to the introduction of new technologies. We consider incremental innovations such as a new microprocessor with a faster speed and a new version of a software product with enhanced features (see [section]2 for a discussion of different types of innovations). Motivated by the phase characterization of R & D activities in the literature on new product development (NPD), (2) we model the incremental innovation process for a component as a discrete-time, phase-type (PH) renewal process, with its phases roughly corresponding to the development milestones of R & D activities. Hereafter, the phases of the innovation processes across different components are called the innovation state. At any time and for each component, two technologies, labelled as Generation (G0) for the latest technology and Generation 1 (G1) for the earlier technology, coexist. When an innovation occurs, the newly released technology is launched as a G0 technology. Subsequently, an existing technology becomes one generation older and a Generation 2 (G2) technology is immediately phased out. The cost parameters associated with each technology, such as selling price, procurement cost, and salvage value, are all state-and generation-dependent and evolve dynamically. In each period, the firm makes the technology decision (i.e., select a technology for each component) and the inventory decision (i.e., set the inventory level for each selected technology). The lead time for each component is negligible. Demand in each period depends on the offered configuration and innovation state. After demand is realized, the firm uses available inventory to assemble the product and satisfy demand. Unmet demand is lost.
We consider two technology-inventory coordination schemes. In the first scheme, technology-inventory coordination is deployed at the strategic level: A technology management plan is set at the beginning of the planning horizon contingent on the innovation state but independent of inventory information; the inventory policy is then determined based on the technology contingency plan. This problem will be formulated as a two-stage sequential optimization (SO) problem. Note that for the SO problem, technology and inventory management are coordinated in the following way: Each contingency plan determines an optimal inventory policy and the optimal contingency plan is selected that yields the best overall outcome. In the second coordination scheme, technology-inventory coordination is implemented at the operational level: technology and inventory decisions are made jointly at the beginning of each period using full information. This problem will be formulated as a joint optimization (JO) problem. The operational-level coordination is expected to outperform the strategic-level coordination, because the former jointly optimizes two decisions using full information. The performance gap between the two schemes quantifies the value of incorporating dynamic inventory information in technology management. Our objective is to develop effective approaches to solve both problems and investigate the structural properties of the optimal policies. The result will provide insights to and guidelines for when the strategic-level coordination is sufficient and when the operational-level coordination is necessary, and how to dynamically execute a contingency technology plan to achieve the performance of the optimal operational-level coordination.
Our research overlaps with three streams in the literature: the ATO system, the single-component (product) obsolescence model, and the technology-replacement model. Early work in ATO research studies the effects of component commonality (Baker et al. 1986, Gerchak et al. 1988). The general conclusion from this line of inquiry is that the total safety stock can be reduced by using the common component, as a result of risk pooling. Several authors extend the early work on component commonality by allowing different demand distributions, cost structures, and correlation among demands (Eynan and Rosenblatt 1996, Hillier 1998). The joint inventory replenishment and component allocation problem in the discrete-time setting is investigated by Gerchak and Henig (1989), Agrawal and Cohen (2001), Hausman et al. (1998), Swaminathan and Tayur (1998), and Akcay and Xu (2004). Several rule-based and optimization-based inventory-replenishment and component-allocation policies are proposed. There is also a significant literature related to continuous-review ATO systems. These studies are mostly concerned with performance evaluation under various assumptions (Song 1998, Song et al. 1999, Glasserman and Wang 1998, Dayanik et al. 2003) and optimizing inventory replenishment policies (Gallien and Wein 2001, Song and Yao 2002, Cheng et al. 2002, Lu et al. 2003, Hsu et al. 2006). We refer the reader to a survey paper by Song and Zipkin (2003) and references therein for further details. Our work is also related to product (with a single component) obsolescence. For a more comprehensive literature review on this topic, the reader is referred to survey papers by Raafat (1991) and Tekin et al. (2001). Obsolescence models consider the inventory policy in a single component (product) setting at either the supply or the demand side. When obsolescence occurs at the supply side (for example, blood products and perishable foods are discarded after their lifetimes), it effectively reduces inventory on hand (Nahmias 1975, Nansakumar and Morton 1993). When obsolescence occurs at the demand side, demand for the product diminishes over its lifetime (Song and Zipkin 1996, Angelus and Porteus 2002, Souza et al. 2004). The NPD and literature on technology replacement is also related to our work. In addition to the aforementioned NPD literature, Hopp and Nair (1994) consider the trade-off between technology improvement and machine deterioration and determine the optimal timing to replace the machine. Nair (1995), Rajagopalan et al. (1998) consider the equipment investment problems with sequential technological changes.
Our research distinguishes itself from others in several aspects. First, existing ATO models assume that cost parameters are fixed and do not consider technology innovations. Here, using information of the innovation process as a key driver, we capture the dynamic characteristics of cost parameters, overlapping life cycles of coexisting technologies and product introduction and disposition process, and answer the key questions on how technology management and inventory control can be effectively coordinated. Second, single-component (product) obsolescence models focus on determining the optimal inventory policy, treating the technology management decision as an exogenous input. In contrast, we consider the coordinated product rollover and inventory management. Technology replacement models do not consider technology adoption at the component level and do not have the inventory aspect, as we do in this paper. To the best of our knowledge, the joint technology management and inventory control optimization problem in the ATO setting with technology innovations and price erosion has not been addressed heretofore in the literature.
For the remainder of the section, we provide the reader with a road map of the major results of the paper and their managerial implications. Our solution procedure consists of two steps: (1) we first consider the zero salvage loss case, meaning a component can be salvaged at its procurement cost; and (2) we then consider the positive salvage loss case, meaning a component can be salvaged only at a price below its procurement cost. The zero salvage loss case deserves special attention in its own right. First, the assumption can be justified in certain situations, as discussed in [section]4. Second, zero salvage loss induces the optimal policy that is myopic, due to the temporal separation of system dynamics. The myopic policy is easy to compute and implement and often turns out to be a good approximation to the optimal solution. In addition, structural properties can be extracted from the myopic solution, which can provide guidelines for the development of effective heuristics for the positive salvage loss case.
With zero salvage loss, JO and SO reduce to the same problem. Hence, the strategic-level coordination can achieve the same performance as the operational-level coordination with zero salvage loss. We show that the optimal inventory policy for a fixed configuration is a balanced base-stock policy, under which the inventory level for each component should be set the same. Unfortunately, the configuration selection problem, which entails to select an appropriate technology for each component to form a final product, becomes a combinatorial optimization problem. Under some plausible conditions, we develop the interval partitioning algorithm (IPA) that can effectively identify the optimal configuration and optimal inventory level simultaneously of action for a given innovation state. We further propose sufficient conditions under which the myopic policy has monotone properties: As the innovation state increases, the new technologies used in the optimal configuration either increases or decreases, and the optimal base-stock level either increases or decreases. This allows us to gain insights on how the firm's cost structure determines its market position as an early or a late technology adopter, and how its inventory level is aligned with its market position.
We then study the SO and JO problems with positive salvage loss, focusing on the class of the balanced base-stock policy. For SO, the objective function for a fixed contingency plan is concave in initial inventory. Also, the optimal inventory is controlled by two limits that specify a range that the inventory level should be brought within. The number of contingency plans that need to be evaluated to determine the optimal one, unfortunately, grows exponentially fast. For JO, we show that the two-limit inventory policy remains optimal if the demand density function is log-concave. The optimal configuration problem can be solved by a modified IPA.
Both JO and SO cannot be easily evaluated with positive salvage loss, due to the curse of dimension. We develop two heuristics for SO, based on the decomposition and news-vendor principles. We also develop the one-step-improvement (OSI) heuristic for JO: It starts with a contingency plan in SO as a base policy and improve it by applying one round of the standard policy iteration algorithm in dynamic programming (DP). The managerial implication of OSI is that the firm can adopt a "hybrid" technology-inventory coordination strategy whereby it starts with a contingency plan, either optimally or heuristically, in advance, and then execute it dynamically via OSI.
Our work provides several managerial insights and general rules of thumb for managing an ATO system with technology innovations and price erosion:
* The increasing speed of technology innovations at the component level necessitates coordinated technology-inventory management. We study both the strategic- and operational-level technology-inventory coordination schemes. With positive salvage loss, our numerical results suggest that it is often sufficient to control technology and inventory sequentially: Technology management can be closely aligned with the innovation process, whereas inventory control is aligned with the technology contingency plan and also utilizes full inventory information. However, we also observe that the performance gap between the two schemes increases on demand variability and salvage loss rate, but appears insensitive to the profit margin rate and innovation speed.
* We propose a hybrid technology-inventory coordination scheme, whereby the firm executes a contingency plan dynamically using the OSI heuristic. The test cases show that if a good technology contingency plan is adopted, then OSI can virtually close the gap between the strategic- and operational-level coordination schemes; if a...
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