Week-13

THE EFFECT OF LEARNING ON THE MAKE/BUY DECISION*

EDWARD G. ANDERSON, JR.† AND GEOFFREY G. PARKER‡ † University of Texas, McCombs School of Business, Austin, Texas 78712, USA

‡ Tulane University, A.B. Freeman School of Business, New Orleans, Louisiana 70118, USA

By including the effects of learning over time on both the production of components and their integration into complete products, we develop an engineering-based model of outsourcing. This model provides an alternative explanation for much of what other outsourcing theories predict, as well as making several new predictions. In particular, we show that outsourcing decisions can create a path-dependent outsourcing trap in which a firm experiences higher long-run costs after an immediate cost benefit. We also describe conditions under which outsourcing a small fraction of component production may dominate either complete insourcing or complete outsourcing. Finally, we show that, with discounting, there is a convex, curvilinear relationship between the optimal outsourcing fraction and the rate of technological change. (LEARNING; INTEGRATION; LEARNING CURVE; PRODUCT DEVELOPMENT; VERTICAL INTEGRATION; MODULARITY; PRODUCT DESIGN)

1. Introduction

Economists, management scientists, and organizational theorists all recognize that the decision to make or buy product components and the resulting impact on industrial organi- zation is of paramount importance to firms. Theories put forward to explain sourcing decisions include transaction economics, market channel power, appropriability, and scale economies. However, these theories do not account for how learning interacts with product design over time, nor do they explain many interesting empirical observations concerning outsourcing behavior. The observations include dynamic outsourcing “traps,” expensive re-insourcing, and partial outsourcing (for reasons other than volatility protection). Below, we explain these observations in detail.

By including the effects of learning over time on boththe production of individual components and the integration of components into complete products, we propose an engineering-based model of outsourcing that can illuminate these unexplained observations, as well as provide an alternative explanation for much of what other theories predict. The model also makes several important new predictions. (1) Some outsourcing decisions that improve a firm’s short-run cost position can have a long-run cost penalty. This can create a path-dependent outsourcing trap in which a firm can find itself unable to recover from a

* Received February 2000; revisions received September 2000, March 2001, and June 2001; accepted June 2001.

PRODUCTION AND OPERATIONS MANAGEMENT Vol. 11, No. 3, Fall 2002

Printed in U.S.A.

313 1059-1478/02/1103/313$1.25

Copyright © 2002, Production and Operations Management Society

regime of low profit and high outsourcing once an initial outsourcing decision is made. (2) Under certain conditions described by the model, partial outsourcing may dominate all make or all buy strategies. (3) High discount rates and product modularity should lead to higher fractions of outsourcing. (4) If there is no cost-discounting, the long-run optimal outsourcing fraction increases monotonically with the speed of technological change; under cost-dis- counting, however, this result can actually reverse in slowly changing industries, creating a convex, curvilinear relationship between outsourcing and the rate of technological change.

We specifically propose that there are two critical learning curves that account for a product’ s cost over time. One curve represents the component cost. The component curve behaves in the expected manner, declining with the cumulative number of units pro- duced— or alternatively, the cumulative number of component design iterations. When the component is outsourced, learning accrues to the supplier rather than the original equipment manufacturer (OEM). The other curve represents the cost of integration. This cost includes learning from component design and production about how best to integrate the component into the overall product design and is extensively discussed in Fine and Whitney (1995). Learning about component integration only occurs, however, when a component is produced by the firm that integrates the product. Hence, like the component learning curve, the integration learning curve declines with the cumulative number of units produced in our model, but only for those units produced in-house. Once the component is outsourced, the learning benefits with respect to integration no longer accrue to either OEM or supplier. Figure 1 presents a schematic view of the model that shows the learning cycles for both system integration and component manufacturing. (Note that, for simplicity in presentation, the schematic does not separate the OEM knowledge stock for manufacturing from integration as is done later in the formal model.)

OEM learning improves both integration and component manufacturing cost. The supplier’ s component learning curve is driven by the buy fraction of OEM product demand and by other firms’ component demands. When the OEM buys components from the supplier, it immedi- ately reaps the benefit of the supplier’ s knowledge from producing components for other firms, which typically will reduce component acquisition cost. However, the integration and make costs are driven solely by the stock of OEM knowledge derived from component production. By buying the component, the OEM learns less about component production and less about system integration, driving up make and integration costs. Because knowledge changes are non-instantaneous, decisions that lead to short-term cost reductions can lead to long-term cost increases. The relative size of integration cost and component cost over time dictates the optimal make/buy proportion.

FIGURE 1. Effect of Make/Buy Proportion on OEM Knowledge, System Integration Cost, Component Make Cost, Component Buy Cost, and Total Product Cost.

314 EDWARD G. ANDERSON JR. AND GEOFFREY G. PARKER

A key feature of our model is that we explicitly link the component learning cycle to the system integration learning cycle. In dividing the learning curve between component man- ufacturing and product integration, we set up a tradeoff between lower component costs (which usually favors outsourcing) and lower integration costs, which generally favor retaining production in-house. The degree of product modularity also has an impact on these costs (Ulrich 1995). We assume that highly modular products have lower integration costs because the interfaces between components are well-understood and documented. We can predict that highly modular products should have a greater fraction of their components outsourced than highly integral products, and this is seen in our analysis.

Our focus on integration issues was originally motivated by examples in the automobile and electronics industries, with which both authors have substantial experience, and which has been studied extensively in the economics and operations management literatures (Monteverde and Teece 1982; Hayes and Wheelwright 1984; Womack, Jones, and Roos 1989). However, integration problems are not limited only to mature industries such as the automotive industry, but also to new businesses created by the rise of computing power and high-speed networks. Christopher McCleary, founder of USInternetworking—viewed by analysts and consultants as one of the premier information management application service providers (ASPs)— has noted that the hardest problem with internet commerce is “ putting all the [technical] pieces together” (Bruno 2000). Traditionally information management con- sultants have designed software solutions for clients and implemented them at client sites using the client’ s own software, computers, and maintenance personnel. Once the solution was up and running, however, the consultant would walk away. The problems associated with this hand-off implementation model are notorious. Forrester Research’ s survey of 150 information management consultant companies repeatedly showed inconsistent performance, botched or incomplete jobs, and general confusion among clients (Girard and Pickering 2000). Anderson (2000) describes these problems in detail in the implementation of enter- prise resource planning packages (ERP). We believe that the models we develop below can be applied just as usefully to internet commerce as to more traditional industries.

The rest of the paper proceeds as follows. In the next section, we discuss the previous literature on integration and learning. In Section 3 we develop our model. We then introduce three canonical examples, “ the outsourcing trap,” “ pain before gain,” and “ partial outsourc- ing,” in Section 4. In Section 5, we analyze the objective function to understand when these situations are likely to occur in equilibrium. In Section 6, we relax the simplifications necessary to achieve these analytic results and present a number of numerical results to explore the behavior of the objective function with respect to a large number of parameters. In Sections 7 and 8, we conclude and discuss possible follow-on work.

2. Literature

In general, we build on the tradition of stylized models of product design (e.g., Cohen et al. 1996) and technology (e.g., Loch and Huberman 1999). However, we also review the vertical integration and learning curve literature to place our model in context.

2.1. Vertical Integration Literature

In the economics discipline, outsourcing or insourcing decisions are basically equivalent to the question of optimal vertical integration. The main reasons put forward to explain the degree of vertical integration are asset specificity, incomplete contracts, heterogeneous competencies, and agency. Industrial organization theorists beginning with Coase (1937) and Williamson (1975) have argued that vertical integration may incur lower costs in areas such as negotiation, contract specification, monitoring, and dispute resolution. Monteverde and Teece (1982) and Novak (1999) find empirical justification for this insight. Farrell, Monroe, and Saloner (1998) argue that heterogeneous competencies drive firms to disaggregate and

315THE EFFECT OF LEARNING ON THE MAKE/BUY DECISION

compete at the component level rather than the system level. Fine (1998) builds on this to trace cycles of vertical and horizontal competition in multiple industries. Zenger (1994) suggests that smaller organizations are better able to attract and hold higher-performing employees, because they can better measure employee performance and can use stronger incentives. The idea should logically extend to components: disaggregating a supply chain into independent organizations can allow assembler firms to exploit the “ economies of smallness” in its supplier base.

In contrast, the operations management literature has focused primarily on cost, quality, and availability. Hayes and Wheelwright (1984) argue that outsourcing a component or product may lead to increased economies of scale both in the current period and in future periods through the learning curve. However, Hayes and Wheelwright also observe that if price (or supply) is volatile, it may benefit the OEM to control a captive supplier. This effect has been shown to be significant by Lieberman (1991) in the chemicals industry. Finally, Hayes and Wheelwright suggest that outsourcing may be advantageous if suppliers can produce a product of higher quality than the OEM (perhaps for the reasons suggested by Zenger).

The field of technology management has three concerns that somewhat overlap with the economics and operations approaches to the outsourcing decision: technological uncertainty, appropriability (the degree to which diffusion of a technology to competitors through reverse-engineering and other methods can be prevented), and product modularity. Hayes and Wheelwright (1984) suggest that vertical integration may be called for if there is technolog- ical uncertainty at the component level. If a technology is highly appropriable, a firm may create a competitive advantage by gaining control over the supplier (Teece 1987). In contrast, Balakrishnan and Wernerfelt (1986) argue that integration is disadvantageous in markets characterized by technological uncertainty because of the general decrease in expected profitability per firm. However, they did not control for appropriability in their analysis. Ulrich and Ellison (1998) argue and present evidence that the outsourcing decision must consider the component’ s modularity. They predict that firms will outsource both component production and design only if the component is modular and the technology is stable. Monteverde (1995) also finds empirical support for this idea.

2.2. Learning Curve Literature

Because of the dependence of our model on learning, we briefly review the literature on learning curves. Most of the relevant literature breaks down into firm-level models and models that describe horizontal rather than vertical integration. The firm-level literature is mostly descriptive and tries to determine the shape and strength of the learning curve as well as its causes. Since its discovery (Wright 1936), hundreds of studies have addressed this phenomenon (see Argote 1999 for a review). Most of these studies have detected a power-law relationship between cumulative output and cost; efforts to explain the power-law relation- ship are numerous (Levy 1965; Muth 1986; Huberman 1997). A stream in the theoretical economics literature, including Spence (1981), Fudenberg and Tirole (1983), and Ghemawat and Spence (1985), shows that learning curves tend to increase output and may raise barriers to entry. However, these effects may lessen as a result of spillover (knowledge diffusion). The most important recent studies in the area include papers such as Epple, Argote, and Devadas’ (1991) examination of an automotive assembly plant that explains the often-noted plateau effect first described by Conway and Schultz (1959) in studies of several start-ups in the electronics industry. These papers attribute the plateau to “ organizational forgetting”— the idea that knowledge gained through production or other activities loses relevance with time.

There is also a substantial body of normative work by management scientists and economists that accounts for learning in production planning, including Ebert’ s (1976) adaptation of the Holt-Modigliani-Muth-Simon (1960) model. Among others, Majd and

316 EDWARD G. ANDERSON JR. AND GEOFFREY G. PARKER

Pindyck (1989) model a firm’ s production under price uncertainty. Mazzola and McCardle (1996) use a Bayesian approach to dealing with uncertain parameters in the learning curve and how they affect optimal production. Jovanovic and Nyarko (1996) address switching between learning curves by developing a highly stylized one-firm Bayesian model of technology choice. Li and Rajagopalan (1998a) consider the optimal production path, assuming knowledge depreciation, although their example uses a learning curve that is not in the classic power-law form. Finally, many authors separate investment in learning from investment in production, including Dorroh, Gulledge, and Womer (1994), and Li and Rajagopalan (1998b).

2.3. Contribution

The theoretical contribution we make in this paper is twofold. First, we explicitly link the outsourcing and learning curve literatures to create a formal dynamic model of outsourcing. Second, we break apart the learning curve into production and integration components. We then use the resulting model to study path-dependent tradeoffs between integration and component costs using analysis and simulation.

3. Model Setup

3.1. Total Product Cost

We consider a product with one component that may either be manufactured in-house (made) or outsourced (bought). The cost to make and the cost to buy will generally differ. There is also a separate cost associated with integrating the component into the product system. Additionally, there will generally be associated with the product other variable costs which are unaffected by the learning curve. The total product cost will equal the sum of all these costs.

Let: c(t) � total product cost

cm(t) � component make cost cb(t) � component buy cost ci(t) � cost for OEM to integrate component cr(t) � other product manufacturing costs

� � insourcing percentage Total product cost at time t can then be written as:

c�t� � �cm �t� � �1 � ��cb �t� � ci �t� � cr �t� (1)

Note that the effective component acquisition cost will be a weighted sum of the make and buy costs. Because we are investigating the tradeoff between lower component costs through purchasing from a supplier versus lower integration costs through making components in-house (Fine and Whitney 1995), without loss of generality, we let cr(t) remain constant in the following analyses.

Of course, if high fixed costs need to be duplicated at both the OEM and its supplier, then pursuing this partial outsourcing strategy may not be feasible. For example, silicon wafer fabs cost several billion dollars and are unsuitable for low-volume production. Unless a semi- conductor company has a tremendous number of components, partial outsourcing in this industry is unlikely to be cost-effective. On the other hand, in the software design industry, the majority of fixed costs, such as providing high-end computers and internet access, are accrued per programmer. Hence, maintaining a small fraction of programming activities in-house is unlikely to duplicate fixed costs at the supplier.

317THE EFFECT OF LEARNING ON THE MAKE/BUY DECISION

3.2. OEM Component Manufacturing Cost

As a reminder, we first present the classic learning curve model (Wright 1936) used to describe the reduction of variable cost as a function of cumulative production output.

Let: � � initial cost to make product

Q(t) � cumulative output at time t Q(0) � cumulative output at time 0 q(t) � product demand at time t

Then the standard form for the learning curve model can be written as:

c�t� � �� Q�t�Q�0�� ��

(2)

Q(t) is cumulative output where:

dQ�t�

dt � q�t� (3)

and

� � � ln � progress ratio�

ln 2 (4)

Under a learning curve, each doubling of cumulative output leads to a constant fractional reduction in cost from its former value. Hence, a learning curve is often characterized by its “ progress ratio,” which describes the rate at which costs decline per doubling. Thus, an 80% progress ratio describes a process in which, with each doubling of output, variable costs decline to 80% of their previous value. In some literature, the progress ratio is termed a “ slope” because a curve described by the power-law above appears linear on a log-log graph.

To study the important effect of technological change on the outsourcing question, we adopt a modified version of Wright’ s learning curve that includes a “ forgetting” term to account for the empirical observation that knowledge gained from output or design iterations loses relevance after a period of time (Argote 1999). Numerous studies have shown that including this “ forgetting” term (summarized in Argote 1999) improves the explanatory power of the learning curve model. The forgetting rate can be driven by such factors as employee turnover, cognitive limitations, or—the most useful interpretation for this paper— technological obsolescence.

Let: cm(t) � cost for OEM to make component at time t

�m � initial cost to make component Km(t) � OEM knowledge stock at time t Km(0) � OEM knowledge stock at time 0 Km,min � minimum OEM manufacturing knowledge stock

qa(t) � OEM product demand at time t � � fractional obsolescence rate � � manufacturing learning rate

Following Epple et al. (1991), we write the OEM’ s cost to manufacture a component in-house as:

cm �t� � �m� Km �t�Km �0�� ��

(5)

318 EDWARD G. ANDERSON JR. AND GEOFFREY G. PARKER

Where

dKm �t�

dt � �qa �t� � ��Km �t� � Km,min � s.t. Km �0� � Km,min 0 (6)

As shown above, the forgetting rate is typically modeled as a constant fractional reduction of accumulated knowledge (Li and Rajagopalan 1998a). Hence, under a constant production rate, there will be a positive lower bound on costs that declines convexly in the production rate. This contrasts with the classic learning curve in which variable costs go to zero in the limit. Thus, in industries with higher obsolescence rates—that is, high-tech industries— learning curves will have less of an impact than in low-tech industries. This will have important consequences for the behavior of our model.

Finally, to correct for poor model behavior at zero knowledge, we include a minimum knowledge term. Our base assumption is that this is relatively insignificant once production is under way; hence, its absence in the standard forgetting model. However, given that the OEM in our model may cease production, its component knowledge stock without such a minimum would shrink to zero. This would drive costs toward the nonsensical value of infinity. By adding in a minimum term, we place a finite upper bound on cost while making the least restrictive assumption necessary.

3.3. OEM Product Integration Cost

Researchers have generally not included integration costs in their models, perhaps because of the inherent difficulty in measuring these costs. However, as Johnson and Kaplan (1987) note, failing to include integration costs leads to an estimate we know to be wrong: zero. Capturing integration costs, even within an order of magnitude of their true value, can help decision-makers choose better outsourcing policies. As an initial step toward modeling integration costs, we adopt the same form of the learning curve used for manufacturing costs to describe integration costs. In their study of technical projects, Boone and Ganeshan, (2001) finds empirical support for this form of learning curve (including depreciation). Because we believe that the tasks involved in integrating products will closely resemble those in Boone and Ganeshan’ s study, this lends support for our choice of model. We make the distinction between design iterations, which might not be expected to reduce costs (but instead lead to design convergence), and overall design projects. However, we note that design iterations can lead to lower cost if they improve product quality. We assume that integration and design teams improve their efficiency with each new project (subject to knowledge depreciation), as Boone found empirically.

To put this assumption into a shared context with the previous equations relating manu- facturing learning to cumulative production volume, we further assume that there is a constant number of component units produced per design iteration. From an examination of the aerospace or automobile industries, this is not an unreasonable first assumption on average (see Ward’ s 1993 Automotive Yearbook 1993).

Let: ci(t) � cost for OEM to integrate component at time t

�i � initial integration cost Ki(t) � OEM integration knowledge stock at time t Ki(0) � OEM integration knowledge stock at time 0 Ki,min � minimum OEM integration knowledge stock qa(t) � OEM product demand at time t

� integration learning rate Integration cost can then be expressed as:

ci �t� � �i� Ki �t�Ki �0�� �

(7)

319THE EFFECT OF LEARNING ON THE MAKE/BUY DECISION

Where:

dKi �t�

dt � �qa �t� � ��Ki �t� � Ki,min� s.t. Ki �0� � Ki,min 0 (8)

3.4. Supplier Component Cost

The last cost we need to define is the cost of purchasing components from a supplier. Let:

cb(t) � cost for OEM to purchase component at time t � � supplier price markup over supplier cost, � � 0

Ks(t) � supplier knowledge stock at time t Ks(0) � supplier knowledge stock at time 0 Ks,min � minimum supplier manufacturing knowledge stock qs(t) � other firms’ product demand being served by supplier at time t

We assume the supplier and the OEM have the same component learning rate and obso- lescence rate. Differences between the two costs are driven solely by different manufacturing volumes and previous production at time t � 0. We do not explicitly include other sources of cost difference, such as lower supplier labor costs, although these could be captured in �. We also include a constant percentage markup (1 � �) over the supplier’ s cost to obtain the price paid by the OEM to buy components. Such constant mark-up policies have been shown to be quite common in industry (Lilien, Kotler, and Moorthy 1992). Furthermore, in constant-elasticity demand models (as we assume), such mark-up policies can be optimal (Lilien, et al. 1992). Applying the mark-up to the learning curve yields:

cb �t� � �1 � ���m� Ks �t�Km �0�� ��

(9)

Where,

dKs �t�

dt � �1 � ��qa �t� � qs �t� � ��Ks �t� � Ks,min � s.t. Ks �0� � Ks,min 0. (10)

Note that the learning curve for the supplier is driven by two streams of demand: one from the OEM and another from the supplier’ s other customers. For simplicity, we will assume that qs(t) is a constant, although in reality it too may change over time. However, in either case, because the supplier gains production experience at a faster rate after the outsourcing decision, the buy cost will in fact reduce over time from the initial time of outsourcing to a lower steady-state level. Combined with the demand function specified in the section below, this increases the long-run attractiveness of outsourcing.

3.5. Demand

As can be imagined by the reader, the interaction of the market with the learning curve will have important consequences. Hence, for completeness, it is necessary to specify the product demand function faced by the OEM.

qa(t) � OEM demand curve qref(t) � reference component demand pref(t) � reference component price

� � price elasticity of demand, � � 1 cr(t) � other costs

� OEM price markup over cost, � 0 We assume that the OEM faces a constant elasticity demand curve as follows:

qa �t� � qref��1 � �c�t�pref � ��

(11)

320 EDWARD G. ANDERSON JR. AND GEOFFREY G. PARKER

The assumption that price elasticity (expressed as a positive number) is greater than one is important. Under falling costs, this assumption forces total market revenue and profit to increase even as the constant mark-up assumption causes unit price to decrease.

3.6. Objective

Finally, we require a criterion to judge the desirability of any given outsourcing policy. A myopic approach to the problem may lead to long-term mistakes. However, there is also a time cost associated with money that cannot be ignored. Hence, we adopt a net present value objective function.

Let: � � discount rate � OEM cost markup T � planning horizon

We can then express the OEM’ s objective function as

Z � max �

� 0

T

exp���t� c�t�qa �t�dt s.t. 0 � � � 1. (12)

We analyze this objective function in Sections 5 and 6. Before doing so, we introduce three canonical examples, “ the outsourcing trap,” “ pain before gain,” and “ partial outsourcing,” in the next section.

4. Canonical Examples

4.1. The Outsourcing Trap

The first situation we explore is the “ outsourcing trap” case. This case occurs when the OEM is attracted by the component cost savings offered by a supplier without considering the long-term effects on the OEM’ s ability to effectively integrate the component into the product. In Figure 2, we compute the time path of make, buy, and total product costs. We begin with � � 1 at t � 0. The OEM initially benefits from a steady reduction in component manufacturing costs as a function of the OEM’ s own learning curve, but decides it could do better by outsourcing component production to a supplier. At time t � 10, the OEM ceases

FIGURE 2. OEM Switches from 100% Internal Component Production to 100% Purchasing of Component at t � 10.

321THE EFFECT OF LEARNING ON THE MAKE/BUY DECISION

all production (� 3 0) of components and instead purchases the component from a supplier to take advantage of its lower costs. The situation we are first interested in is the “ outsourcing trap” case. This case models the situation in which the OEM is attracted by the component cost savings offered by a supplier without considering the long-term effects on the OEM’ s ability to effectively integrate the component into the product.

Parameter values for the base case shown in Figure 2 appear below. They are stylized values based on an automotive engine control module that is to be incorporated into an automotive electronic control system. The initial knowledge stock levels are chosen to represent pre-equilibrium levels so that the learning curve can be observed.

Initial cost to make component �m 50 $/unit Initial OEM mfg. knowledge stock Km(0) 80,000 units Initial supplier mfg. knowledge stock Ks(0) 320,000 units Minimum OEM mfg. knowledge stock Km,min 16,000 units Supplier price markup � 5 % per unit Manufacturing learning rate � 0.152* dimensionless Knowledge obsolescence rate � 33 % per year Initial cost to make component �i 10 $/unit Initial OEM integration knowledge stock Ki(0) 80,000 units Minimum OEM integration knowledge stock Ki,min 16,000 units Integration learning rate 0.510* dimensionless Other product costs cr(t) 30 $/unit OEM price markup 5 % per unit Reference OEM product demand qref 4,000 units/month Reference price for OEM product pref 90 $/unit Price elasticity of demand � 2 dimensionless Supplier component demand from other customers qs 16,000 units/month Discount rate � 5 % per year Time horizon T 200 years

* Learning rates of 0.152, 0.322, and 0.510 correspond to progress ratios of 90%, 80%, and 70%, respectively.

Just after the change to component outsourcing (t � 10�), total product costs are lower. In fact, component acquisition costs continue to decline in the short run because the additional manufacturing volume at the supplier will drive its production costs even lower than they were at the time of outsourcing. However, because internal component production has ceased, the OEM is no longer learning about those aspects of the component that are crucial to integrating it effectively into the product. Thus, with time, the integration knowledge stock deteriorates from obsolescence, which causes the integration cost to begin to creep upward. After about 5 years (t � 15), the total product cost is equal to the cost before the decision to outsource was made. After this time, increased integration costs exceed the component cost savings, causing the total product cost to climb even more. Thus, whereas outsourcing provided excellent short-run returns, it proved to have long-run drawbacks. Furthermore, if the OEM decides to re-insource once again, it will no longer have the in-house manufacturing experience it had at the time of the outsourcing decision and will have to climb the learning curve yet again before returning to the lower total product costs. Hence, the OEM has been caught in the outsourcing trap of seductive low initial supplier acquisition costs, and will find a return back to its prior cost levels to be quite costly.

Industrial experience from Chrysler seems to support our intuition of the potential for outsourcing traps with components or technologies that are highly integral to the product. Chrysler, which has relied heavily on suppliers (Parker 1993; Dyer 1996), has not been able to improve quality as quickly as its competitors (Gardner 1996). Many experts believe that most quality issues now result from the interaction of numerous components, that is, systems integration issues (e.g., Rajgopal et al. 1999). Hence, Chrysler’ s quality difficulties may stem in part from some weakness in its systems integration ability, resulting from its reliance on turn-key manufacturing systems that it no longer fully understands.

322 EDWARD G. ANDERSON JR. AND GEOFFREY G. PARKER

4.2. Re-Insourcing’ s Pain before Gain

In this section, we will show that bringing outsourced technologies back in house may be quite expensive. Consider the situation of an OEM that is outsourcing all production (� � 0) before time t � 10 for a highly integral component. Suppose at that time, the OEM pulls all component production back in house (� 3 1). The component cost, integration cost, and total product cost for the OEM are shown over time in Figure 3. The initial impact of the change is to incur a large expense as the OEM trades lower component costs from the supplier for the higher costs of components made internally. However, this negative effect is temporary. Eventually, an OEM with this set of parameters will begin to see lower component manufac- turing costs as it progresses down the component cost learning curve. As soon as insourcing begins, the OEM will also begin to climb down the integration cost curve, driving a reduction in integration costs. Whereas the OEM will never be able to acquire components internally as cheaply as from the supplier, for these parameter values, the reduction in integration costs will create an overall benefit from insourcing after year 12.

Parameter values that differ from the base case shown in Figure 2 appear below.

Initial OEM mfg. knowledge stock Km(0) 16,000 units Initial OEM integration knowledge stock Ki(0) 4,000 units Minimum OEM integration knowledge stock Ki,min 4,000 units

We believe that Toyota’ s recent investment in automotive electronics offers an example of a firm choosing to make components to capture integration benefits. In 1949, Toyota made the decision to outsource electronics components and sub-systems from Nippon-Denso (now Denso), which had spun off as a separate supplier. Recently, however, Toyota has reversed course and begun to reinvest in electronics production. For example, Toyota used to source its production of anti-lock braking systems (ABS) electronic control modules wholly from suppliers. In 1994, Toyota began to produce these components internally, planning to reach 20% internal production by 1996. Toyota has even gone so far as to invest in semiconductor fabrication facilities to support its electronics component manufacturing effort (Hansen 1994).

Why did Toyota do this? Forty years ago, electronics content in automobiles was small and relatively modular, confined primarily to radio, lighting, and starter systems. In recent years, however, the electronics content in automobiles has expanded dramatically; nearly every experience in a modern automobile from engine responsiveness to suspension behavior is

FIGURE 3. OEM Switches from 100% Purchasing of Components to 100% Internal Production at t � 10.

323THE EFFECT OF LEARNING ON THE MAKE/BUY DECISION

mediated by electronic systems (Fine 1998). The increasing electronics content in automo- biles suggests that the automotive integration problem, which might once have been primar- ily mechanical, is now substantially electro-mechanical. Thus, electronics have shifted from a modular to a much more integral component of the automotive system. Toyota is apparently betting that producing electronics components internally will offer it an advantage against other manufacturers, such as GM, who seem to be implementing the opposite strategy by selling off their electronics component suppliers (Ward’ s 1999).

The implication for firms in general of the pain before gain in insourcing is twofold. One is that the outsourcing trap can become permanent if a firm discounts heavily. Thus, outsourcing may be quite path dependent. Once a firm goes down this road, it may never be able to come back. On the other hand, as the stories from Ford and Toyota suggest, this pain may be worthwhile if the outsourced component is highly integral to the product. But the question then arises, might there be a way short of complete outsourcing that will realize most of the integration benefits of the pain-before-gain scenario, but without sacrificing the component acquisition benefit from outsourcing?

4.3. Virtues of Partial Outsourcing

Our model suggests that firms may be able to derive much of the integration learning benefit from a relatively small amount of internal component production. If so, for some situations, firms might wish to choose a level of outsourcing between all or none. In Figure 4, total component cost is plotted over time for three different levels of outsourcing: 0%, 90%, and 100%.

Parameter values that differ from the base case shown in Figure 2 appear below.

Minimum OEM integration knowledge stock Ki,min 2,000 units Integration learning rate 0.152 dimensionless

In this simulation, 100% outsourcing leads to the largest immediate cost improvement. However, the integration cost penalty eventually causes costs to nearly return to the level they were before outsourcing. For these parameter values, if the OEM outsources most of its production (90%), it receives most of the benefit of lower component costs from the supplier, but also retains some of the integration learning driven by component production. In the long run, this strategy can dominate both complete insourcing and complete outsourcing. This suggests that, for some components, partial outsourcing may be the optimal strategy.

FIGURE 4. OEM Maintains 100% Internal Production of Components or Switches to 90% or 100% Outsourcing at t � 10.

324 EDWARD G. ANDERSON JR. AND GEOFFREY G. PARKER

Toyota’ s practice with respect to transmissions and half-shafts provides anecdotal evi- dence that this strategy is practiced by some manufacturers. Toyota typically produces 30% of its transmissions in-house, while subcontracting the rest to its supply base (Nakagawa 1995). Toyota does the same thing with half-shafts for its drive train. Employees at Saginaw Steering report that Toyota is their most demanding customer and that Toyota has a much better sense of what it wants than other manufacturers, who are more willing to leave details to Saginaw (Whitney 1995). We suspect that because Toyota produces some of the half- shafts in house, it understands better than most of its competitors how to best integrate these components into the drive-train system. We further suggest that the reason Toyota retains a small percentage of half-shaft production in-house is to maintain this integration ability. It is important to note here, however, that Toyota does not outsource its engines. This suggests perhaps that Toyota pursues a regimen of partial outsourcing only for those parts that are of intermediate integrality to the system. We will explore this idea further in later sections of the paper.

In the next section, we develop a set of results to understand when the three canonical examples presented above happen in equilibrium.

5. Equilibrium Analysis

5.1. Total Insourcing versus Total Outsourcing

We now develop analytic results to show when firms would be better off pursuing a total insourcing or total outsourcing strategy. When there is market and price feedback, the analysis becomes extraordinarily difficult. To symbolically analyze the objective function specified in (12), we would have to solve a system of non-homogeneous, non-separable, non-exact partial differential equations. In the Appendix, we provide further detail on the exact set of partial differential equations involved in such an analysis. We now impose certain simplifying assumptions to ensure tractability, and we defer analysis of the com- pletely specified objective function until the next section. These assumptions are as follows.

● Demand is constant such that qa(t) 3 qa, qs(t) 3 qs. ● The outsourcing decision is made once. We now specify the instantaneous total costs and long-run total costs under both complete

insourcing and complete outsourcing. Assume that the firm changes from total internal component production to complete outsourcing of component production at time t1. Time t1

�

is just before this change, whereas time t1 � is just after the change. Then �(t1

�) � 1 and �(t1

�) � 0.

5.1.1. INSTANTANEOUS TOTAL COST COMPARISON. The immediate difference in cost can then be expressed as follows:

�c�t1 � � c�t1 �� � c�t1

�� � cb �t1 � � cm �t1 �

The difference in cost, �c(t1), is negative whenever the cost to purchase the component is lower than the internal component manufacturing cost at time t1. By substituting functional forms for cm(t1) and cb(t1), we can see that outsourcing is initially preferred (at time t � t1) if the following is true:

�m��Km,min � qa � ��1 � |�t1�� � Km �0�|�t1�

Km �0� �

��

�1 � ���m��Km,min � qs � ��1 � |�t1�� � Km �0�|�t1�

Km �0� �

��

(13)

325THE EFFECT OF LEARNING ON THE MAKE/BUY DECISION

If we assume that both the OEM and supplier begin manufacturing the component at t � 0, it is clear that the condition qs � qa � � � 0 is required for outsourcing to be preferable at t � t1. The difference � is determined by specific parameter values.

5.1.2. STEADY-STATE COST COMPARISON. Now consider the difference in steady-state costs. Using the differential equation that governs the evolution of manufacturing cost, we get:

cm �t� � �m��Km,min � �qa � ��1 � |�t�� � Km �0�|�t�

Km �0� �

��

Letting t 3 �, this becomes:

cm �t 3 �� � �m��Km,min � �qa � �

Km �0� �

��

(14)

Long run integration cost is found similarly:

ci �t 3 �� � �i�Ki,min � �qa �

Ki �0� �

�

(15)

The long-run cost to purchase the component from a supplier is determined as follows:

cb �t� � �1 � ���m��Km,min � qs � ��1 � |�t�� � Km �0�|�t�

Km �0� �

��

In steady-state, this simplifies to:

cb �t 3 �� � �1 � ���m��Km,min � qs � �1 � ��qa

� �

Km �0� �

��

(16)

We can now compare total costs in equilibrium when the component is insourced (� 3 1) and when it is outsourced (� 3 0). Long-run total costs for complete insourcing are as follows:

ct 3 � �� � 1� � �m��Km,min � qa � �

Km �0� �

��

� �i�Ki,min � qa �

Ki �0� �

�

(17)

Long-run total costs for complete outsourcing are as follows:

ct 3 � �� � 0� � �1 � ���m��Km,min � qs � qa

� �

Km �0� �

��

� �i�Ki,minKi �0�� �

(18)

In equilibrium, outsourcing is the superior strategy when the following relationship holds:

ct3� �� � 1� ct3� �� � 0�

326 EDWARD G. ANDERSON JR. AND GEOFFREY G. PARKER

Substituting (17) and (18) and rearranging, we see that outsourcing is preferred when the following inequality is true.

�m���Km,min � qa � �

Km �0� �

��

� �1 � ����Km,min � qs � qa

� �

Km �0� �

��

� �i��Ki,minKi �0�� �

� �Ki,min � qa �

Ki �0� �

�

� The LHS is almost always positive (when qs � 0 the supplier goes down the component manufacturing learning curve faster than the OEM); we assume that it is positive in our analysis. Similarly, when qa � 0, the RHS is also positive. Using these signs and rearranging terms, we can develop a relationship between �m and �i that determines when outsourcing is preferred. We define the ratio (�m/�i) as an index of modularity because it compares the initial component cost with the initial integration cost. The higher this ratio, the more modular the product.

�m �i

� Ki,minKi �0�� �

� �Ki,min � qa �

Ki �0� �

�

��Km,min � qa � �

Km �0� �

��

� �1 � ����Km,min � qs � qa

� �

Km �0� �

�� (19)

Because we are looking at knowledge stocks in equilibrium (where we would expect Ksteady-state � Kmin), we can approximate Ki,min and Km,min by zero when they are non-unique in an expression. This results in a somewhat simpler long-run test. Outsourcing is preferred in equilibrium when the following inequality is true.

�m �i

� Ki,minKi �0�� �

� � qa �Ki �0�

�� � qa �Km �0�

��� � �1 � ���qs � qa �Km �0�

��� (20) We summarize this result as a proposition.

PROPOSITION 1. As modularity increases, outsourcing will be preferred in equilibrium. Proof. Follows immediately from (20). ▫ Under the conditions described below, the modularity threshold defined in (20) will

increase in qa. The numerator strictly increases in qa. The denominator strictly decreases in qa if the following condition is met: (qa � qs)/qa � (1 � �)

1/(1��), or more loosely, if qs/qa � �. The interpretation is that as the OEM’ s demand increases, a higher modularity threshold is necessary to make the OEM prefer outsourcing in equilibrium.

We now introduce a proposition to show that outsourcing may be preferable in the short-term while insourcing is preferable in equilibrium.

PROPOSITION 2. When integration costs are sufficiently large, an assembler firm that has been making components in-house for a long time can reduce short-term costs, but may increase long-run costs by outsourcing component production to a supplier.

Proof. To show this, we must compare (13), the immediate cost difference at t � t1, and (20) to show that both inequalities need not be simultaneously true. For outsourcing to be preferred in the short run (assuming that both OEM and supplier began component production at t � 0), we showed above that the following relationship between qs and qa is necessary:

qs � qa � 0

327THE EFFECT OF LEARNING ON THE MAKE/BUY DECISION

Let qs � qa � � � 0, so that the short-term test is true. Note that the initial cost terms do not show up in the short-term test. However, in the long-run test, large initial integration costs (�i) or small initial component manufacturing costs (�m) make outsourcing increasingly less attractive. In the long run, even if qs � qa � � � 0, it is still possible for the long-run test to fail when �i is large enough or �m is small enough (as is shown in the canonical example). ▫

We can also analyze (20) to understand the effect of technological change on the long-run sourcing decision.

PROPOSITION 3. In equilibrium, the higher the rate of technological change, the more likely that complete outsourcing will be preferred over complete insourcing.

Proof. If we take the derivative of the RHS of (20) with respect to � (the rate of technological change), we get the following:

� qa �Ki �0�

� � � qa �Km �0�

� �� qa � qs �Km �0�

� �� Ki,minKi �0�� � ��� qa

�Ki �0� � � � � ���Ki,minKi �0��

� ���1 � ��� qa

�Km �0� �� � �qa � qs

�Km �0� ���

The first four terms in the numerator and the � in the denominator are positive. So the sign is determined by:

�� qa �Ki �0�

� � �� Ki,minKi �0�� �

� �Ki,minKi �0��

�1 � ��� qa �Km �0�

�� � �qa � qs �Km �0�

�� The denominator must be negative, or else outsourcing would never be beneficial, even in terms of component cost. In the numerator, the sum of the first two terms must be positive because the steady-state integration knowledge stock, qa/�, must be greater than the minimum knowledge Ki,min. The final term of the numerator is clearly positive, so the derivative is negative implying that as � rises, outsourcing is increasingly preferred. ▫

5.2. Partial Outsourcing in Equilibrium

In the previous subsection, we restricted � to values of zero or one, restricting ourselves to a “ bang-bang” control policy. We now allow � to take on values between zero and one to determine the optimal solution for � in equilibrium. The steady-state total cost then becomes:

ct3� ��� � cr �t� � �i�Ki,min � �qa �

Ki �0� �

�

� ��m��Km,min � �qa � �

Km �0� �

��

� �1 � ���1 � ���m��Km,min � �1 � ��qa � qs

� �

Km �0� �

��

If we assume that the OEM has been producing the component internally for a long time and is now deciding what the steady-state sourcing fraction should be, then we can simplify this expression by letting Ki(0) 3 qa/� and Km(0) 3 qa/�. Total steady-state costs then become:

328 EDWARD G. ANDERSON JR. AND GEOFFREY G. PARKER

ct3� ��� � cr �t� � �i�� � �Ki,minqa � �

� ��m�� � �Km,minqa � ��

� �1 � ���1 � ���m�qa � �qs � qs � �Km,minqa � ��

(21)

We now take the derivative of (21) with respect to � to find the first-order condition for a local minimum. We also simplify by approximating Km,min and Ki,min by zero when they are non-unique in an expression. This gives us the following relationship:

�1 � ����1 � ��� qsqa� �1��

� �1 � ��� qsqa� ��

� ���� � �Km,minqa � �1��

� �i �m

�� � �Ki,minqa � �1�

� �� � �Km,minqa � ��

(22)

Finding a closed form solution for � seems to be intractable. However, we can show how � behaves with respect to parameters of interest. We first state a lemma that will facilitate our analysis.

LEMMA 1. For Ki,min, Km,min small relative to qa/�, the optimal insourcing proportion � will either be:

� � 1

0 � � � �c

Where �c � (qs/qa)(1��/(1��)(1��(qa/qs))) 1/�.

Furthermore, if qs/qa e(1 � �) 1/�, �c 1.

Proof. There will be an interior solution for � if (22) holds. Rewriting (22) so that (�Ki,min/qa and (�Km,min/qa go to zero and letting m � xm/xi , we get:

��

�1�� �

m�1� �

1

�� � �1 � ����1 � ��� qsqa�

�1��

� �1 � ��� qsqa� ��

(23)

Simplify to get:

1 � �

�� �

m�1� � �1 � �1 � ��� qaqs��1 � ���

qa qs � � (24)

For (24) to be true, the following must hold:

� � � qsqa�� 1

1 � ��qaqs�� 1/�� 11 � ��

1/�

�1 � ��1/� (25)

Let �c equal the RHS of (25). Note that max�� 0,1� �1 � �� 1/� � e�1, and that as � 3 1,

(1 � (1 � �)�(qa /qs )) 3 1. Substituting these into (25) yields the required relation to guarantee that �c 1. Note that this result is independent of the integration cost. In fact, from (24), the upper bound on � should decrease in the integration learning rate and increase in component modularity. ▫

Earlier, we showed that outsourcing was more likely when the rate of technological change was higher, but we had restricted ourselves to equilibrium policies with � � {0, 1}. With this

329THE EFFECT OF LEARNING ON THE MAKE/BUY DECISION

lemma, we can show the more general case that higher degrees of technological change are associated with higher levels of outsourcing when � � [0, 1].

PROPOSITION 4. In equilibrium, as � 3 0 and Ki,min, Km,min small relative to qa/�, the optimal fraction outsourced will increase in the rate of technological change.

Proof. Examine (22), the first-order condition for a local total cost minimum. From the assumptions and Lemma 1, � is small. Therefore, the first terms of the LHS of the equation will approach zero, and the first factor of the first term of the RHS of the equation will approach unity. The only remaining terms affected by � will have partial derivatives in the same sign with respect to � and �. Therefore, as � increases (decreases), so too must � decrease (increase) to maintain equality with the RHS of (22). ▫

From Lemma 1, we know that the partial insourcing fraction is likely to be small. Further, from Proposition 3, we see that under these conditions, higher rates of technological change should lead to higher optimal outsourcing fractions.

In the next section, we relax the assumption that demand is constant and allow for non-zero discount rates. We then extend our analysis of the objective function by examining modu- larity, the discount rate, demand elasticity, and technological change.

6. Numerical Analysis

In the following subsections, we explore the sensitivity of the model to parameters of interest. We calculate the discounted net present value of the OEM’ s profit stream for the base case shown in the outsourcing trap in Section 4. We numerically solve for the optimal outsourcing fraction (to maximize NPV) as a function of the discount rate, demand elasticity, technological change, and product modularity. Under these parameters, the base case (see Figure 5) minimizes total long-run product cost through 100% insourcing. Numerous other scenarios have been tested. However, the outsourcing trap is by far the most interesting case because it yields the greatest sensitivity to various conditions. For example, increasing a component’ s modularity increases the likelihood of outsourcing because there is no long-run integration penalty.

6.1. Optimal Outsourcing Increases with Modularity

Figure 6 plots the optimal outsourcing fraction against an index of product modularity. We calculate modularity as the beginning component cost divided by the initial integration cost.

As we would expect (and saw analytically), higher degrees of modularity lead to higher

FIGURE 5. Base Case for Numerical Analysis.

330 EDWARD G. ANDERSON JR. AND GEOFFREY G. PARKER

levels of outsourcing. This makes sense because the integration cost penalty (relative to the component cost reduction) is greater when outsourcing integral components than modular ones. Perhaps the more interesting result is the confirmation of the tri-modal behavior discussed earlier: first, no outsourcing is optimal, then a relatively high level of outsourcing is optimal, and finally, complete outsourcing is optimal. For only a very small interval of modularity is low outsourcing (less than 50%) even potentially viable.

6.2. Optimal Outsourcing Increases with the Discount Rate

In Figure 7, we plot the percent change in the firm’ s profit versus the discount rate for three levels of outsourcing (75%, 90%, and 100%) relative to the base case of no outsourcing (0%) to examine the impact of different planning horizons.

For low discount rates under these parameter values, the highest profit can be achieved by

FIGURE 6. Optimal Outsourcing Fraction versus Product Modularity.

FIGURE 7. Profit as a Function of Outsourcing Fraction and Discount Rate. Outsourcing Improves Profit as Discount Rate Increases.

331THE EFFECT OF LEARNING ON THE MAKE/BUY DECISION

retaining all production in house. This makes sense because steady-state total cost is minimized by not outsourcing. However, at some point, the discount rate rises high enough that the immediate benefit of a cost reduction through outsourcing offsets the longer-term integration cost penalty. In the curves above, as the discount rate increases from zero, the highest profit is reached first through 0% outsourcing, then by 75%, 90%, and then finally 100%.

In Figure 8, we calculate the optimal outsourcing fraction as a function of the discount rate to test this hypothesis. In Figure 8, we indeed see three distinct regions of optimal outsourc- ing as a function of discount rate. As the discount rate rises, first, no outsourcing, then a steadily increasing partial outsourcing fraction, and finally, complete outsourcing is optimal. In simulations with other parameters, we have observed cases in which one of the three states might be absent. However, the states that do occur always follow the same pattern as above.

6.3. Optimal Outsourcing as a Function of the Demand Elasticity

In Figure 9, we calculate the optimal outsourcing percent versus demand elasticity for several discount rate scenarios. The results from Figure 9 require explanation. When looking at the lines for demand elasticities greater than one, there are two important features. First, the optimal outsourcing fraction increases with the discount rate, as discussed in the previous section. Second, outsourcing decreases in the demand elasticity. The intuition for this is as follows: cost declines convexly in production volume. Hence, an increase in volume will induce a greater percentage reduction in sales at lower volumes than at higher volumes. This reinforces itself because the reduced costs will further increase sales in a virtuous cycle. Additionally, any change in outsourcing will induce a greater percentage change in insourced volumes than outsourced ones. Thus, as the demand elasticity increases, the percentage reduction in component acquisition cost induced by the learning curve will be greater for insourcing than for outsourcing. On the other hand, the percentage increase in long-run integration cost will also increase with demand elasticity. Thus, as the demand elasticity rises, the short-term outsourcing benefit declines relative to the long-run outsourcing penalty.

6.4. Technological Environment (Rate of Knowledge Obsolescence)

We now consider the impact of technological change on the optimal outsourcing percent- age. In Figure 10, we plot the optimal outsourcing fraction against the obsolescence rate for

FIGURE 8. Optimal Outsourcing Fraction versus Discount Rate. The Optimal Outsourcing Percentage Increases with the Discount Rate.

332 EDWARD G. ANDERSON JR. AND GEOFFREY G. PARKER

several discount rates. We use the obsolescence time, which is the inverse of the obsoles- cence rate, for ease of presentation. Roughly speaking, the knowledge obsolescence time is the average length of the relevance of the experienced gained from production on future cost reductions.

As obsolescence time increases, the ultimate integration cost penalty from switching to outsourcing relative to the short-run component acquisition cost benefit increases because there is more integration knowledge to forget, as was demonstrated in the analysis in Section 5. This induces the initial reduction in optimal outsourcing. However, as the knowledge obsolescence time increases, integration knowledge takes longer to forget, hence postponing the effect of the ultimate integration penalty. Under higher discount rates, the integration cost penalty can be delayed for so long that its net present value becomes negligible. So, for highly stable technologies, it may be optimal for OEMs to move to 100% outsourcing, even after considering the integration cost penalty.

FIGURE 9. Optimal Outsourcing Fraction versus Demand Elasticity for Multiple Discount Rates. Optimal Outsourcing Fraction Decreases with Demand Elasticity � 1.

FIGURE 10. Optimal Outsourcing Fraction versus Obsolescence Time across Multiple Discount Rates. The Optimal Outsourcing Percentage is Curvilinear in Knowledge Obsolescence Time.

333THE EFFECT OF LEARNING ON THE MAKE/BUY DECISION

7. Conclusions

Previous theories to explain vertical integration do not account for how learning interacts with product design over time. Using an engineering-based learning curve model leads to several novel insights. We can offer an explanation for empirical phenomena such as the outsourcing trap, which is not predicted by earlier work, as well as offer an alternative explanation for much of what these other theories predict. Using this formulation, we can predict when firms will outsource as a function of product modularity, the discount rate, technological change, and demand characteristics. A major result from the model is that outsourcing policies that seek immediate cost savings can increase costs in the long run. Another result is that high degrees of modularity and high discount rates are likely to lead to more outsourcing. We also find that partial outsourcing can dominate all-make or all-buy strategies. A final result is that the optimal sourcing fraction is monotonically decreasing in the speed of technological change if there is no profit discounting. However, if there is, the optimal outsourcing fraction can become curvilinear in the speed of technological change.

The analysis suggests several potential managerial insights. One is that normally the component learning curve favors outsourcing, even to the extent that it may make sense for a firm to support a higher cost new supplier with greater learning opportunities than the firm. Even more promising is the idea of spinning off internal suppliers of highly modular components. If a component’ s integration cost is high, however, a rational firm may attempt to increase its component volume by soliciting business from other assembler firms to increase its integration capability.

Our results also suggest that partial outsourcing may dominate complete insourcing or complete outsourcing, and this is seen in a number of industries. The agency literature suggests that some firms retain a portion of component production in house to know their suppliers’ cost structures and derive bargaining leverage over them, or to use the outside suppliers as leverage to discipline their internal units. Other reasons to partially outsource come from the business cycle; firms may prefer to make a steady-state fraction of compo- nents while outsourcing unusually high demand to suppliers. Anderson, Fine, and Parker (2000) discuss this phenomenon with respect to the machine tool industry. Our story about integration costs provides an equally plausible reason for partial outsourcing behavior that is based on the engineering costs incurred when designing and producing new products.

8. Further Research

There are three promising areas for further research. First, the formulation presented above may, with sufficient simplification, prove tractable in a more elaborate analytic model. Second, results from the model provide a rich set of hypotheses for empirical testing by future researchers. (1) There should be a delay between outsourcing component acquisition benefits and systems integration penalties and vice versa. (2) The optimal outsourcing fraction seems to be tri-modal: 0%, 100%, or nearly 100%. With the absence of scale effects, we would accordingly expect to observe outsourcing fractions only between 60% and 100%. (3) All else being equal, we would expect firms to more readily outsource those components that exhibit very high and very low rates of technological change. We would expect firms to less readily outsource components that exhibit a moderate rate of technological change. (4) All else being equal, we would expect firms to outsource components less readily in markets with high demand elasticities. (5) All else being equal, we would expect firms to outsource more readily if they use higher discount rates in less predictable technological regimen or during standards competitions. A third, final line of research would describe mechanisms with which

334 EDWARD G. ANDERSON JR. AND GEOFFREY G. PARKER

firms may attempt to explicitly invest in an integration capability even when they pursue a total outsourcing strategy. Parker and Anderson (2002) explore this last idea through research in the computer and semiconductor industries.1

Appendix

Recall that the objective function of interest is

Z � max � �

0

T

exp���t� c�t�qa �t�dt s.t. 0 � � � 1.

In Section 5, we present an instantaneous and equilibrium analysis of the sourcing decision. It would be preferable to solve for the time path of the control, �(t). However, this proves to be a difficult problem. Below are the necessary equations that must be solved for the candidate for an optimal path under the infinite horizon version of Z. Note that qa(t) and all c(t) terms have been eliminated in favor of �(t), the three knowledge stock variables and their co-states. The co-state for Ki(t) is mi(t). The first equation is the current-value minimizing condition. Note that there are of course three initial conditions (OEM manufacturing knowledge, OEM integration knowledge, and supplier manufacturing knowledge).

��1 � ���1 � ���pref � qref�m�Km t�Km 0��

��� Ks t�Km 0�� ���� � �i�Ki t�Ki 0��

�

� �m� t��Km t�Km 0�� ��

� �1 � ���m ��1 � � t��� Ks t�Km 0�� �������1 � ���Km t�Km 0��

�

� � Ks t�Km 0�� ��

� qref��1 � ��� � �i� Ki t�

Ki 0� �� � �m� t��Km t�Km 0��

��

� �1 � ���m ��1 � � t��� Ks t�Km 0�� ���

pref �

��

�mi t� � mm t� � ms t�� � � 1

pref ���1 � �qref�m��Km t�Km 0��

��

� �1 � ��� Ks t�Km 0�� ���

� ��1 � ��� � �i� Ki t�

Ki 0� �� � �m� t��Km t�Km 0��

��

� �1 � ���m ��1 � � t��� Ks t�Km 0�� ���

pref �

�1��

�� t��mi t� � mm t�� � ��1 � � t��ms t��� The three state equations after qa(t) and c(t) have been eliminated are:

K�i t� � � �Ki � �Ki t� � qref� t�

� ��1 � ��� � �i� Ki t�

Ki 0� � � � �m� t�� Km t�Km 0��

��

� �1 � ���m ��1 � � t��� Ks t�Km 0�� ���

pref �

��

1 We thank Charlie Fine for early comments and inspiration for this line of work. We thank Dan Whitney for helpful comments on the concept and Larry Wein for suggestions on how to handle integration costs. We thank participants of the MIT and Boston University Operations Management seminars for their helpful comments and suggestions. We thank participants at the 1999 and 2000 INFORMS Conferences and the 2000 System Dynamics Winter Conference for their participation and feedback. Finally, we thank two anonymous reviewers and the special editor for their close reading and suggestions to improve the manuscript. This research has been generously supported by the A. B. Freeman School of Business and the McCombs School of Business.

335THE EFFECT OF LEARNING ON THE MAKE/BUY DECISION

K�m t� � � �Km t� � qref� t�

� � 1pref��1 � � � �� � �i� Ki t�

Ki 0� � � � �m� t�� Km t�Km 0��

��

� �1 � ���m ��1 � � t��� Ks t�Km 0�� ���������

K�s t� � � qs � �Km � �Ks t� � qref ��1 � � t��

� � 1pref ��1 � ��� � �i� Ki t�

Ki 0� �� � �m� t��Km t�Km 0��

��

� �1 � ���m ��1 � � t��� Ks t�Km 0�� ���������

The knowledge state equations are the simplest of the seven necessary conditions for the optimal solution. However, even these equations are nonlinear because of the presence of � in the exponent as well as the multiplicative relationships of �(t) and the three knowledge state variables. In general, as stated in Boyce and DiPrima (1977), “ the analytic determination of a first-order non-linear equation is usually very difficult, and often impossible.” The three main types of nonlinear equations that can be solved are homogenous, separable, or exact. The equations we must analyze are clearly not separable, i.e., such that the different variables can be isolated on opposite sides of the equation. Neither are the equations homogenous, i.e., they depend strictly on the ratios of the state variables to each other. Nor are they exact, i.e., there exists no function �(Ki(t), t) such that �t(Ki(t), t) equals the right-hand side of the equation and �Ki(t)(Ki(t), t) equals the coefficient of K�i(t).

Hence, all these equations taken together comprise an intractable set of partial differential equations. This is not surprising given that we are working with empirically derived functional forms. As stated by Farlow (1993): “ There is one major advantage to numerical solutions, and it is that many problems do not have analytic solutions. Practically all nonlinear PDEs (partial differential equations) must be solved by numerical methods, and in fact, most realistic problems in physics, chemistry, biology, and so forth, are nonlinear in nature . . . Hence, the general attack for most nonlinear problems (and some linear ones) involves the use of numerical solutions.”

For completeness, we give the current value adjoint or co-state equations (where mi(t) is the co-state for Ki(t) etc.) below.

Integration co-state equation:

m�i t� � �� � � � 1pref Ki t� �� �1 � �qref�i� t�� Ki t�Ki 0�� �

� ��1 � ��� � �i� Ki t�

Ki 0� �� � �m� t��Km t�Km 0��

��

� �1 � ���m ��1 � � t��� Ks t�Km 0�� ���

pref �

��1���

�� mi t� �

1

Ki t� � qref�i����1 � ���1 � ���pref� �Ki t�Ki 0��� �� � �i�Ki t�Ki 0��� � �m� t��Km t�Km 0����

� �1 � ���m ��1 � � t��� Ks t�Km 0�� ����� � ���Km t�Km 0���� Ks t�Km 0���

� ��1 � ��� � �i� Ki t�

Ki 0� �� � �m� t��Km t�Km 0��

��

� �1 � ���m ��1 � � t��� Ks t�Km 0�� ���

pref �

��

��� t�mm t� � ��1 � � t��ms t��� ����1 � ���m ��1 � � t���Ki t�Ki 0��

�Km t�Km 0�� �

� ��m� t��Ki t�Ki 0��

� ��i � ��Ki t�Ki 0�� ��Km t�Km 0��

��� Ks t�Km 0�� ����

336 EDWARD G. ANDERSON JR. AND GEOFFREY G. PARKER

OEM manufacturing knowledge co-state equation:

1

Km t� ����1 � ���1 � ���pref� qref�m� t��Km t�Km 0��

���� � �i�Ki t�Ki 0�� �

� �m� t��Km t�Km 0�� ��

� �1 � ���m ��1 � � t��� Ks t�Km 0�� ������ � m�m t� � �� � ��mm t� � ���qref�m� t��Ki t�Ki 0��

� Ks t�Km 0�� �

��1 � ��� � �i� Ki t�

Ki 0� �� � �m� t��Km t�Km 0��

��

� �1 � ���m ��1 � � t��� Ks t�Km 0�� ���

pref �

��

� ��� t��mi t� � mm t�� � ��1 � � t��ms t�����Km t����1 � ���m ��1 � � t���Ki t�Ki 0�� �Km t�Km 0��

�

� ��m� t��Ki t�Ki 0��

� ��i � ��Ki t�Ki 0�� ��Km t�Km 0��

��� Ks t�Km 0�� ���

Supplier manufacturing knowledge co-state equation:

1

Ks t� ���1 � ���pref� qref� Ki t�Ki 0��

� � Km t�Km 0�� ����m� t�� Ki t�Ki 0��

� ��i � �� Ki t�Ki 0�� �� Km t�Km 0��

�� � �� � �i� Ki t�Ki 0��

�

� �m� t�� Km t�Km 0�� ��

� �1 � ���m ��1 � � t��� Ks t�Km 0�� ������ � m�s t�

� 1

Ks t� ����1 � ���1 � ���pref� qref�m ��1 � � t��� Ks t�Km 0��

���� � �i�Ki t�Ki 0�� �

� �m� t��Km t�Km 0�� ��

� �1 � ���m ��1 � � t��� Ks t�Km 0�� ������ � 1Ks t� ���1 � ���pref� qref�

Ki t�

Ki 0� �� �Km t�Km 0��

��� Ks t�Km 0�� ��

� �� � �i�Ki t�Ki 0�� �

� �m� t��Km t�Km 0�� ��

� �1 � ���m ��1 � � t��� Ks t�Km 0�� ��������1 � ���m ��1 � � t��

� �Ki t�Ki 0�� �Km t�Km 0��

�

� ��m� t��Ki t�Ki 0��

� ��i � ��Ki t�Ki 0�� ��Km t�Km 0��

��� Ks t�Km 0�� ���

� �ms t� � �ms t� � 1

pref Ks t� ����1 � ���1 � �qref�m ��1 � � t��

� � Ks t�Km 0�� ����1 � ��� � �i�

Ki t�

Ki 0� �� � �m� t��Km t�Km 0��

��

� �1 � ���m ��1 � � t��� Ks t�Km 0�� ���

pref �

�1��

� �� t��mi t� � mm t�� � ��1 � � t��ms t��� References

ANDERSON, E. G. JR. (2000), Managing the Impact of High Market Growth and Learning on Knowledge Worker Productivity and Service Quality, Working Paper, McCombs School of Business, University of Texas, Austin, TX.

———, C. H. FINE, AND G. G. PARKER (2000), “ Upstream Volatility in the Supply Chain: The Machine Tool Industry as a Case Study,” Production and Operations Management, 9, 3, 239 –261.

ARGOTE, L. (1999), Organizational Learning: Creating, Retaining and Transferring Knowledge, Kluwer Academic Publishers, Boston, MA.

BALAKRISHNAN, S. AND B. WERNERFELT (1986), “ Technical Change, Competition, and Vertical Integration,” Strategic Management Journal, 7, 347–359.

BOONE, T. AND R. GANESHAN (2001), “ The Effect of Information Technology on Learning in Professional Service Organizations,” Journal of Operations Management 19, 4, 485–495.

BOYCE, E. B. AND R. C. DIPRIMA (1977), Elementary Differential Equations and Boundary Value Problems, Wiley, New York.

337THE EFFECT OF LEARNING ON THE MAKE/BUY DECISION

BRUNO, L. (2000), “ Clear Sailing Ahead,” Red Herring, September 1, 2000, No. 82, 378 –381. COASE, R. H. (1937), “ The Nature of the Firm,” Economica, 4, 386 –405. COHEN, M. A., J. ELIASHBERG, ET AL. (1996), “ New Product Development: The Performance and Time-to-Market

Tradeoff,” Management Science, 42, 2, 173–186. CONWAY, R. W. AND A. SCHULTZ (1959), “ The Manufacturing Progress Function,” Journal of Industrial Engineer-

ing, 10, 39 –53. DORROH, J. R., T. R. GULLEDGE, AND N. K. WOMER (1994), “ Investment in Knowledge: A Generalization of

Learning by Experience,” Management Science, 40, 8, 947–958. DYER, J. H. (1996), “ How Chrysler Created an American Keiretsu,” Harvard Business Review, 74, 4, 42–56. EBERT, R. J. (1976), “ Aggregate Planning with Learning Curve Productivity,” Management Science, 23, 2, 171–182. EPPLE, D., L. ARGOTE, DEVADAS, R. (1991), “ Organization Learning Curves: A Method for Investigating Intra-Plant

Transfer of Knowledge Acquired through Learning by Doing,” Organization Science, 2, 1, 58 –70. FARLOW, S. J. (1993), Partial Differential Equations for Scientists and Engineers, Dover, New York. FARRELL, J., H. K. MONROE, G. SALONER (1998), “ The Vertical Organization of Industry: Systems Competition

versus Component Competition,” Journal of Economics and Management Strategy, 7, 2, 143–182. FINE, C. H. (1998), Clockspeed: Winning Industry Control in the Age of Temporary Advantage, Perseus Books,

Reading, MA. ——— AND D. WHITNEY (1995), Is the Make/Buy Decision a Core Competence? Massachusetts Institute of

Technology, Cambridge, MA. FUDENBERG, D. AND J. TIROLE (1983), “ Learning-by-Doing and Market Performance,” Bell Journal of Economics,

14, 2, 522–530. GARDNER, G. (1996), “ The Cloud Over Chrysler,” Ward’s Auto World, 25–28. May 1996 Vol. 36, No. 6. GHEMAWAT, P. AND A. M. SPENCE (1985), “ Learning Curve Spillovers and Market Performance,” Quarterly Journal

of Economics, 100(Issue Supplement), 839 –852. GIRARD, K. AND C. PICKERING (2000), “ A Confederacy of Consultants,” Business 2.0, August 22, 2000, 170 –196. HANSEN, P. (1994), “ The Company Profile: Nippondenso.” The Hansen Report on Automotive Electronics. Spetem-

ber 1994. HAYES, R. H. AND S. C. WHEELWRIGHT (1984), Restoring Our Competitive Edge: Competing Through Manufac-

turing, John Wiley & Sons, New York. HOLT, C. C., F. MODIGLIANI, J. F. MUTH, AND H. A. SIMON (1960), Planning Production, Inventories, and Work

Force, Prentice-Hall, Englewood Cliffs, NJ. HUBERMAN, B. A. (1997), “ The Dynamics of Organizational Learning,” Xerox Palo Alto Research Center, May 15,

1997 1–13. JOHNSON, H. T. AND R. S. KAPLAN (1987), Relevance Lost: The Rise and Fall of Management Accounting, Harvard

Business School Press, Boston, MA. JOVANOVIC, B. AND Y. NYARKO (1996), “ Learning by Doing and the Choice of Technology,” Econometrica, 64, 6,

1299 –1310. LEVY, F. K. (1965), “ Adaptation in the Production Process,” Management Science, 11, 6, B136 –B154. LI, G. AND S. RAJAGOPALAN (1998a), “ A Learning Curve Model with Knowledge Depreciation,” European Journal

of Operational Research, 105, 143–154. ——— AND ——— (1998b), “ Process Improvement, Quality, and Learning Effects,” Management Science, 44,

11(Part 1), 1517–1532. LIEBERMAN, M. B. (1991), “ Determinants of Vertical Integration: An Empirical Test,” Journal of Industrial

Economics, 39, 5, 451–466. LILIEN, G. L., P. KOTLER, K. S., MOORTHY (1992), Marketing models, Prentice-Hall, Englewood Cliffs, NJ. LOCH, C. H. AND B. A. HUBERMAN (1999), “ A Punctuated-Equilibrium Model of Technology Diffusion,” Manage-

ment Science, 45, 2, 160 –177. MAJD, S. AND R. S. PINDYCK (1989), “ The Learning Curve and Optimal Production under Uncertainty,” RAND

Journal of Economics, 20, 3, 331–343. MAZZOLA, J. B. AND K. F. MCCARDLE (1996), “ A Bayesian Approach to Managing Learning-curve Uncertainty,”

Management Science, 42, 5, 680 –692. MONTEVERDE, K. (1995), “ Technical Dialog as an Incentive for Vertical Integration in the Semiconductor Industry,”

Management Science, 41, 10, 1624 –1638. ——— AND D. J. TEECE (1982), “ Supplier Switching Costs and Vertical Integration in the Automobile Industry,”

Bell Journal of Economics, 13, 1, 206 –213. MUTH, J. F. (1986), “ Search Theory and the Manufacturing Progress Function,” Management Science, 32, 948 –962. NAKAGAWA, S. (1995), Developing Core Technologies for Automotive Components. Creating and Managing

Corporate Technology Supply Chain Partners, Massachusetts Institute of Technology, Cambridge, MA. NOVAK, S. (1999), Sourcing by Design: Product Architecture and the Supply Chain, Sloan School of Management

Thesis, Massachusetts Institute of Technology, Cambridge, MA. PARKER, G. G. (1993), Interviews with Chrysler Employees, MIT Sloan School of Management, Cambridge, MA.

338 EDWARD G. ANDERSON JR. AND GEOFFREY G. PARKER

——— AND E. G. ANDERSON (2002), “ From Buyer to Integrator: The Transformation of the Supply-Chain Manager in the Vertically Disintegrating Firm.” Production and Operations Management, 11, 1, 75–91.

SPENCE, A. M. (1981), “ The Learning Curve and Competition,” The Bell Journal of Economics, 12, 1, 49 –70. TEECE, D. J. (1987), Profiting from Technological Innovation: Implications for Integration, Collaboration, Licensing

and Public Policy. The Competitive Challenge: Strategies for Industrial Innovation and Renewal, Center for Research in Management, School of Business Administration, University of California, Berkeley, Berkeley, CA.

ULRICH, K. (1995), “ The Role of Product Architecture in the Manufacturing Firm,” Research Policy, 24, 419 –440. ——— AND D. J. ELLISON (1998), Beyond Make-Buy: Internalization and Integration of Design and Production,

University of Pennsylvania, Sept. 1, 1998. 1–40. WARD’ S (1999), “ Delphi’ s Battenberg Eager for GM Split,” Ward’s Auto World, 35, 3, 33–34. WHITNEY, D. (1995), “ Toyota Relationship with Saginaw Steering,” MIT Leaders for Manufacturing Program

Report. Massachusetts Institute of Technology, Cambridge, Mass. WILLIAMSON, O. E. (1975), Markets and Hierarchies: Analysis and Antitrust Implications: A Study in the Economics

of Internal Organization, Free Press, New York. WOMACK, J. P., D. T. JONES, D. ROOS (1990), The Machine that Changed the World, Rawson Associates, New York. WRIGHT, T. P. (1936), “ Factors Affecting the Cost of Airplanes,” Journal of Aeronautical Sciences, 3, 122–128. ZENGER, T. R. (1994), “ Explaining Organizational Diseconomies of Scale in R&D: Agency Problems and the

Allocation of Engineering Talent, Ideas, and Effort by Firm Size,” Management Science, 40, 6, 708 –729.

Dr. Anderson is an Assistant Professor of Operations Management at the University of Texas McCombs School of Business. He received his doctorate from the Massachusetts Institute of Tech- nology and his bachelor’ s degree in electrical engineering and history from Stanford University. His research interests include supply chain management (especially service supply chains), outsourced product development, knowledge management, and system dynamics. He has published articles in such journals as Management Science, Production and Operations Management, and The Systems Thinker. Dr. Anderson won the prestigious Wickham Skinner Early-Career Research Award from the Production and Operations Management Society. He sits on the editorial review board of Production and Operations Management and has received research grants from SAP and Hewlett-Packard. Professor Anderson has consulted with Ford, Dell, Hewlett-Packard, Frito-Lay, and Atlantic-Richfield. Prior to his academic work, he was a product design engineer at the Ford Motor Company, from which he was granted three U.S. patents.

Dr. Parker is an Assistant Professor of Management at the A.B. Freeman School of Business at Tulane University. Parker’ s primary research interests are in the areas of learning, integration, and supply chain design. Parker has additional research interests in network and information economics. Parker’ s recent projects include a case study of supply chain integration practices in the electronics industry, an exploration of why firms choose to give away information products, and an examination of the interaction between product design and supply chain design in learning and competitive settings. Parker received a B.S. in Electrical Engineering and Computer Science from Princeton University, and an M.S. in Electrical Engineering (Technology and Policy Program) and a Ph.D. in Management Science from the Massachusetts Institute of Technology. Prior to graduate school, Parker held positions in engineering, finance, and business development at the General Electric Company.

339THE EFFECT OF LEARNING ON THE MAKE/BUY DECISION