42 (2006) 1684–1696www.elsevier.com/locate/dss

Decision Support Systems

A decision support model for optimal timing of investments ininformation technology upgrades

Nivedita Mukherji a, Balaji Rajagopalan b,⁎, Mohan Tanniru c

a Department of Economics, School of Business Administration, Oakland University, Rochester, MI 48309, United Statesb Department of Decision and Information Sciences, School of Business Administration, Oakland University, Rochester, MI 48309, United States

c Department of Management Information Systems, Eller College of Management, University of Arizona, Tucson, AZ 85721, United States

Received 26 May 2003; received in revised form 16 February 2006; accepted 22 February 2006Available online 19 April 2006

Abstract

In an environment of continuous change, organizations are faced with the challenge of deciding when to invest in informationtechnology upgrades. While investing frequently is costly and at times risky, waiting too long can lead to lost competitiveness.Further, investing at a given time can preclude a firm from taking advantage of better technologies in the future. In the context ofsoftware upgrades, this study proposes and illustrates a decision support model to determine the optimal timing and choice ofupgrades. Analysis confirms that even if continuous upgrading is feasible, it is not an optimal strategy when adoption costs aresignificant. Simulations show that investments in upgrades are best made when the gap between new technology and currenttechnology reaches a critical threshold. Among other factors, this threshold is influenced by technology cost, change managementcost and opportunity cost.© 2006 Elsevier B.V. All rights reserved.

Keywords: Investment in IT upgrades; Technology adoption costs; Opportunity costs; Dynamic decision support model; Optimal timing oftechnology adoption

1. Introduction

In an environment of continuous technologicalchange, organizations are frequently faced with thechallenge of deciding when to invest in new andupgraded information technology (IT). Consider thereleases of operating systems (OS) by Microsoft—Windows 95 in August 1995, Windows 98 in June1998, Windows 98 Second edition in 1999, WindowsME and Windows 2000 in the year 2000 and

⁎ Corresponding author.E-mail addresses: mukherji@oakland.edu (N. Mukherji),

rajagopa@oakland.edu (B. Rajagopalan), mtanniru@eller.arizona.edu(M. Tanniru).

0167-9236/$ - see front matter © 2006 Elsevier B.V. All rights reserved.doi:10.1016/j.dss.2006.02.013

Windows XP in 2002. With this continuous streamof upgrade releases, individuals and organizations arefaced with the decision to upgrade their OS. Typically,few would upgrade to a new version every time arelease is announced; instead they would leapfrog toadopting a subsequent release [40]. Making suchtechnology investments continuously (i.e., every timea new release of a technology is announced) can bevery expensive.

While investing frequently is costly and at timesrisky, waiting too long can put an organization at the riskof losing first mover advantages associated withintroducing competitive products and services. Howev-er, by waiting, the firm can purchase a superiortechnology than the one available now. Clearly, in this

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context, it is critical for a firm to determine whether itshould incur the adoption costs now to take advantage ofthe productivity and competitiveness gains that thecurrently available new or upgraded technology pro-vides or wait for a better technology. This studyexamines how a firm can determine this optimal intervalbetween adoptions and thereby its optimal choice oftechnology.

The primary focus is on the case of software upgradedecisions. Cases of acquiring a technology for the firsttime are not considered. Unlike new technologyadoption, in the case of upgrade the question is moreof “when” to adopt than “whether” to adopt. Further-more, in contrast to new technologies, the uncertaintiesassociated with benefits and costs are relatively small inthe case of upgrades. First time investments in newtechnologies have received a lot of attention in theliterature and models like net present value and optionsbased evaluation have been developed for decisionsupport. On the other hand, few studies have focused onupgrade situations.

The choice of upgrade situations is motivated byseveral reasons. First, periodic upgrade investments areincreasingly becoming a significant percentage of totalIT budgets and hence, an area of utmost interest toresearchers and technology managers. Second, organi-zations seem to time the upgrades rather arbitrarilywithout a systematic analysis. Third, even in the case ofupgrades, where reasonably accurate predictions abouttechnological change can be made, it is not clear howdifferent costs involved with technology adoption affectthe intervals (timing) at which adoption decisions aremade. Finally, despite the importance of the topic it hasremained largely unexplored. To this end, the objectiveof this research is twofold:

(1) To develop a decision support model to determinethe optimal time and choice of upgrade invest-ment, and

(2) To study the impact of various costs on theoptimal upgrade time and upgrade choice.

It is worth noting that based on the type oftechnology under consideration, there can be substantialdifferences in factors that drive adoption decisions. Forexample, the primary driving force behind an upgradedecision might be lack of vendor support for one firmbut compatibility with competitors' or users' softwaremight be the critical factor for another. Clearly, these areopportunity costs associated with not adopting theupgrade and can be incorporated as such in decisionsupport models.

A decision support model must include a consider-ation of the dynamic context to take full account of theimpact of current upgrade decisions on future ones. In acompetitive landscape, technological improvementsoccur rapidly and investing at a given time maypreclude a firm from taking advantage of bettertechnologies at a later date. Thus, adoption decisionsmust consider the future impact of current decisions.

Interestingly, widely applied investment evaluationmethods in information systems (IS) research like netpresent value (NPV) do not take into account thedynamics discussed above as these methods do notconsider the impact on future decisions. In the case ofcontinuous upgrades, it is important for firms to decidethe frequency at which its technology must be replaced.Thus, unlike other types of investment decisions, firmswould benefit from a long term “plan” for investment inIT upgrades. Conducting disjoint static analysis ignoresthe element of inter-temporal interdependence of theinvestments—a critical consideration for technologyupgrades.

To address the interdependent nature of the decisions,this study draws upon models that have specificallyaddressed this issue (for e.g., see [2,3,11]). [3]developed a model that examined the problem oftechnology adoption that allows the state of nature tochange at a stochastic rate. They apply an impulse-control method to determine the intervals at whichdecisions are made. This framework is most suitable forthis study since it has been developed to solve exactlythe type of dynamic problem IT decision-makers face.That is, the framework allows us to examine how a firmshould optimally spread its investment over time in anenvironment of continuous change.

Other dynamic models have been used to studytechnology adoption decisions. The applicability ofalternative dynamic models, such as, options-pricingand the proposed model are, however, quite different.The main motivation for using options pricing in articlessuch as [4] is that the benefits from investment in thetechnology are uncertain. By using real options, a firmdelays adoption to gather valuable information regard-ing the investment. The question addressed in this studyis quite different. This study's model is applicable whenuncertainties regarding benefits or costs are not the keyfactors. The main concern is that firms understand thatadopting something new today implies that very soon aneven better technology will become available. Should itwait for that better technology or adopt now? Should itadopt every time a new or upgraded technology isreleased? How do the different costs involved withadoption affect the adoption decision? These questions

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cannot be answered by options pricing type models. Infact, the impulse control model was developed toaddress exactly these questions.

2. Literature Review

A critical issue in any IT investment evaluation,particularly true in the case of upgrades, is the timingof adoption. The investment decision, in upgradesituations, is usually less focused on the question of“whether” to acquire a technology or not but more on“when” to acquire it. Several studies in economics haveexamined the timing of adoption of new technologies.Some of the seminal studies include [20,21,32–34].These studies highlight the role of competition betweenfirms in the technology adoption and timing ofadoption decisions. More competitive industries seemto adopt new technologies faster than others. A morerecent study by [14] showed the importance of productmarket competition in the adoption decision of newtechnologies in the context of the airline industry.

Another issue of importance in adoption timing is theuncertainty associated with new technologies. Theuncertainty may take various forms, ranging fromuncertain benefits of new technologies to uncertaintiesregarding how soon it will become obsolete. Increaseduncertainty often delays adoption. When firms havelimited knowledge about the various features of a newtechnology or its ability to enhance productivity, bydelaying adoption, a firm may be able to gain additionalinformation. In this context [16,28,29,35,38] study therole of uncertainty in returns and costs in adoptiondecisions. While these articles did not study uncertaintyin IT investments, others such as [9,12,19,26] did. Theyrecognized that investments in IT have “option-like”characteristics. Building on this, [4] demonstrated theuse of option pricing models, such as Black–Scholes, tostudy the timing of deployment of a particular service bya banking network. By delaying adoption, the firmgathers valuable information to reduce uncertainty.

In addition to gathering information regarding anuncertain investment, by delaying adoption, a firm maybe able to either purchase an existing technology at amuch lower price (particularly true in the case ofhardware upgrades) or purchase a better technology. [7]studied the equipment replacement decision problemwhen successively improved machines become avail-able over time with certainty. [31] proposes a dynamicprogramming approach to study the upgrade problem inthe presence of technological uncertainty. [1,10,17,30]are examples of studies that illustrate using machinereplacement decisions of single or multiple machines

both in deterministic and stochastic models. It isimportant to note that in the case of upgrade situationsthere is relatively low uncertainty regarding the benefitsas the firm already has experience with other versions ofthe technology.

In cases of both new investments and upgrades, thedecision of whether to stay with the current technologyor leapfrog is influenced, among other factors, by thecompetitiveness of the market in which the firmoperates. Two complementary perspectives emergefrom research examining the decision of a firm to investin new technologies in the context of actions of othersimilar firms. One view is that of product marketcompetition that shows increased competition reducesthe time to adoption. The second view, based onresearch on network externalities, examines cooperationbetween firms in technology adoption. [13,22–24,37,8]highlighted the role of network externalities in adoptiondecisions. [25] provide empirical support for thenetwork externality effect and [27] used networkexternality and switching costs (barrier) to explainwhy in certain industries firms may be reluctant to adopta new and superior technology.

In sum, the literature on technology adoptiondecisions examines the role of factors such ascompetition, uncertainty, network externality, andprice changes on adoption decisions by firms. However,sufficient attention has not been devoted to examine theimpact of various costs on adoption timing ofinformation technology upgrades.

3. Model description

This study considers the technology upgrade deci-sion of a single firm. New upgrades appear at a steady,deterministic pace. For example, every year, output canbe increased by 100,000 units by implementingupgrades to the technology in use. In such anenvironment of continuous improvement, unless a firmadopts new upgrades immediately upon release, the gapbetween the technology in use and the most advancedavailable increases continuously. The firm has threealternatives: (i) adopt new upgrades as they becomeavailable, (ii) wait and adopt at a later time, or (iii) neveradopt upgrades. Generally, firms neither upgradecontinuously nor do they completely refrain fromdoing so since the direct or opportunity cases becomeprohibitive. Thus, the first and third cases are ratherunrealistic. Also in these two extreme cases, there is noneed for a model to make upgrade decisions. Thus, thestudy's focus is primarily on the more interesting “waitand adopt later” case.

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In addition to significant costs, adoption at the rateof release of new upgrades may not be optimal if themost recent release is not well suited for the firm. Forexample, new upgrades typically introduce newfunctionalities. These may not be productive for afirm if its other supporting software and hardware donot allow it to make use of these new features. It isalso possible that even if the firm itself may gain byupgrading, the output format may be incompatiblewith other user applications. Thus, for a variety ofreasons, the latest release may not be the mostsuitable level at which a firm would prefer to operate.However, assuming that all technologies change at acontinuous rate, these incompatibility issues are likelyto be transitory in nature. As new hardware andsoftware become available, an upgrade that hadcompatibility problems earlier may become thepreferred choice. If the firm does not upgrade, itwould begin to incur costs related to forgoneproductivity gains and lost competitiveness.

The most suitable upgrade is defined to be the onewhich has the optimal combination of functionalitiesgiven other supporting software and hardware capa-bilities and the needs of the firm's customers. That is,it is possible that a firm by adopting a newtechnology produces a product that is incompatiblewith the technologies used by its customers. In thatcase even if the internal needs of the firm makeadoption of the new technology optimal, the externaldemands may not. Thus, the most suitable technologyis the one that has the optimal combination offunctionalities given all the internal support andexternal needs. Further, it is assumed that due toreleases of new upgrades and changes in supportinghardware, software, and user technologies, the gapbetween a firm's existing technology and the mostsuitable one for it widens over time if the firm doesnot adopt new upgrades. This gap is measured interms of the productivity of the two technologylevels. To illustrate, suppose the current technologyallows a user to complete 250 operations per unit oftime and the upgrade increases that to 350, then bystaying with the older version, a firm gives up theopportunity to increase productivity of each user by100 units per period. Assuming that both time andproductivity are continuous variables and defining thedifference between the technology used at any giventime t and the most suitable available at that time tby x(t), it is assumed that

dxðtÞdt

¼ �g: ð1Þ

Eq. (1) shows that by not increasing its technologylevel to the most suitable level, the firm incurs aproductivity loss at a rate of g per unit time. g gives thechange in the productivity gap per unit of time. It isnoted that, if the firm is using a version that is older thanthe most suitable technology available, x(t)<0. Con-versely, if the firm uses a version that is higher than whatis most suitable at that time, x(t)>0. This is likely to bethe case when a firm adopts a new upgrade that it cannottake full advantage of given hardware and softwareconstraints or its needs.

As discussed earlier, although changes in productiv-ity may occur at a steady rate, the firm may not upgradeto the most suitable level at the rate at which that level ischanging. Due to cost considerations, it may prefer toupgrade after a minimum amount of time elapses afterthe last upgrade. Thus, the firm is assumed to upgrade itstechnology only at discrete intervals denoted by ti, i≥1.To determine these intervals, the various costs associ-ated with the decision must be considered.

3.1. Costs of adoption and the optimization problem

The costs of adoption have two components: (i) thecost of purchasing the upgrade for all the necessarymachines and (ii) the costs associated with installing,training, and transitioning people completely to thenew technology. The cost of purchasing an upgradedversion of the technology is assumed to be K. This isthe total cost for the organization to purchase theupgrade. Thus, for a given size of the organization ornumber of machines that need to be upgraded, thisvalue is assumed to be constant for all upgrades.Although in reality this may vary for different versionsand in some cases may even decrease over time, afixed value of K is assumed to keep the analysis moretractable.

In addition to this fixed cost, the firm is expected toincur change-management costs. These costs relate tothe deployment of the upgrades, the training andlearning costs associated with adoption, and anyadditional hardware and/or software purchases neces-sary to make full use of the new technology. Sinceretraining of workers takes time, it is assumed change-management cost is incurred over a span of some n>1periods, with the cost decreasing over time. In addition,the cost depends on how large the change is from thecurrent to the new version and the ease with which theworkers learn the new version. This captures the ideathat when an upgrade is adopted and workers learn touse it, training adds to the current cost of adjustment.However, the knowledge and experience gained helps

1688 N. Mukherji et al. / Decision Support Systems 42 (2006) 1684–1696

reduce the cost of future adoptions. Similarly, largechanges require more training and adjustment than smallchanges. Training adds to individual's knowledge andreduces the amount of future training.

If an upgrade occurs at time ti, the change-management cost is incurred over the following nconsecutive discrete intervals. Denoting the cost perinterval by cj, where, j=1, 2, …n and assuming that thecost decreases over time, 0<cj<cj�1, ∀j≤n and cj=0,∀j>n, the change-management cost is represented by:

Xnj¼1

cjuie�Aui�1j ð2Þ

This expression shows that the cost is distributed over nperiods, progressively decreasing over time. Further,the cost is higher if the current change to the upgrade ishigher. However, as discussed above, larger changesmake future change less costly. This is captured bydiscounting the current cost by the size of the previouschange, ui�1. The cost also shows that it decreases withthe interval j. A is a constant.

Summing the purchase cost of new technology andchange-management cost, total cost of adoption is givenby:

K þXnj¼1

cjuie�Aui�1j ð3Þ

If a firm chooses not to adopt the new technology, thiscost is zero. However, in that case it must consider theopportunity cost of not using the most suitable upgrade.This lost opportunity may be in the form of lostrevenue if the firm's competitors are using moreadvanced technology, or it may be in terms of lostopportunity to increase productivity. It may also meanthe cost of continuing with a technology that isunsupported by the vendor, in case a firm decides tocontinue using a technology beyond the time for whichvendor support is available. If a firm chooses to adopt atechnology more advanced than the most suitable forits purpose, it may lose revenue due to factors such asincompatibility with other firms it interacts with,incompatibility with other hardware and software ituses and so on. If p and r are the per unit ofproductivity costs of not using the most suitabletechnology, the cost of x≠0 is given by:

IðxðtÞÞ ¼ �pxðtÞ; xðtÞ < 0rxðtÞ; xðtÞ > 0

�ð4Þ

Thus, if the cost of lost competitiveness equals $1.5 peroperation between the current and most suitable

technology levels and the most suitable technologycan increase productivity by 100,000 operations, then bynot adopting that technology the firms loses $150,000.The interpretation of r parallels the interpretation of p.

In case a firm adopts no upgrades, its gap with themost suitable technology level will rise continuouslyand so will the cost I(x). Over the infinite horizon, thefirm continuously incurs the opportunity cost given by I(x(t)) but incurs the adoption cost discussed above onlyat discrete intervals given by ti's. The firm's objective isto minimize the sum of this opportunity cost and theadoption cost by appropriately choosing the upgradetimes, ti's and selecting the levels of upgrades, ui. Usingα as the discount factor, the firm's value function isrepresented as:

V ðxÞ ¼ minfui;tig

"Z l

0IðxðtÞÞeatdt

þXi>1

"K þ

Xnj¼1

cjuieAui�1j

#e�ati

#ð5Þ

subject to Eq. (1):

dxðtÞdt

¼ �g

The solution to this optimization problem is discussednext.

3.2. Trigger-target solution

At any time t, the firm has two options: it can upgradeor postpone adoption to a later period: t+ t′. If it choosesto postpone till time t+ t′ (leapfrog) then the valuefunction V(x) is bounded above by the cost ofpostponement:

V ðxÞVZ tþt V

tIðxðsÞÞe�aðs�tÞdsþ V ðxðt þ t VÞÞe�at V ð6Þ

If the firm chooses to adopt, the value function isbounded above by the cost of adoption:

V ðxÞVminu

"K þ

Xnj¼1

cjue�Auj þ V ðxþ uÞ

#ð7Þ

Since V(x) is the optimal solution, one of the aboveinequalities will be satisfied with an equality.

Research has shown that solutions to problems of thisnature follow a simple trigger-target rule. Existence ofsuch solutions was proven by [11] and other examples ofsuch problems can be found in [2,3,39] among others.

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The trigger-target type of solution has the characteristicthat no changes are made by the firm to its technologylevel until the difference between the technology in useand the most suitable level is less than a certain value,called the trigger. Once the difference hits the triggervalue, τ, the firm purchases new technologies and bringsthe difference to some target value, T. Thus, the changeu becomes T�τ.

Applying this rule, as long as the gap x is less than thetrigger τ, no action is taken and Eq. (6) is satisfied withan equality. Once the gap equals the trigger τ, the firmpurchases an upgrade and increases the gap to T. In thiscase, Eq. (7) is satisfied with an equality. Finding thesolutions to Eqs. (6) and (7) in these two cases yields thefollowing solutions for τ and T:1

�ðrT þ psÞ ¼ Kaþ aðT � sÞXnj¼1

cje�AjðT�sÞ ð8Þ

r þ p¼ reaT=g þ peas=g � aXnj¼1

cje�AjðT�sÞ

� ½AjðT � sÞ � 1�½eaT=g � eas=g� ð9ÞSince closed form solutions cannot be obtained,numerical simulations are conducted in the followingsection to gain insights into the solutions for the triggerand target.2

4. Numerical analysis and discussion

4.1. Overview of simulations

Simulations were conducted to arrive at numericalsolutions and for analyzing the sensitivities of the resultsto changes in technology cost, change-managementcost, and opportunity cost.3 The choice of range ofvalues for the parameters was based on typical upgradescenarios examined, one of which is presented here.

Operating system upgrade data from Microsoft wasused to create the scenarios.4 Parameter values werechosen to encompass a range of values for operatingsystem upgrade to Windows XP from a variety of

1 Derivations of the equations are available upon request from theauthors.2 Note that if K and c tend to zero, that is, the adoption costs

approach zero, T and τ also approach zero. Thus, the firm will upgradecontinuously.3 Programming was carried out in Mathematica 4.1 to arrive at

solutions using Newton's method.4 While it is acknowledged that this data may have a vendor bias, it

is still a valuable guide to creating real world scenarios.

environments including Windows 95, 98, and 2000 for1000 personal computers.

In the Microsoft case, for example, the sum of ITbenefits and business benefits represent opportunitycosts (p ·x); engineering, deployment, training andmaintenance costs represent change management costsand direct investment in the technology is the cost ofacquiring it (K). A productivity growth (g) of $40,000per year is used by averaging the benefits of a sequenceof releases of the operating system. The discount rate (α)is fixed at 10% and r at 10 for all numerical analysesconducted. While the model description section of thearticle gives a general form in which change-manage-ment cost varies over the transition period, that is,Pn

j¼1 cjuie�Aui�1j with 0<cj<cj�1, ∀j≤n, where n denotes

the number of periods over which the transition occurs, forthe purpose of numerically analyzing the solutions of themodel, it is necessary to specify how cj changes as jchanges. It is assumed that the change-management costequals

P9j¼1

0:1cj uie

�0:00001ui�1j. For the simulations, cvaries from 0.5 to 24 and p varies from 1 to 200.

2.1.1. Technology cost (K)Table 1 shows the results of simulation runs for

variations in upgrade investment. Results from theproposed model support the proposition that an increasein technology costs will result in a larger adjustment.This larger adjustment or size of leapfrogging means thefirm has to wait longer as a result of a decrease in thetrigger τ and an increase in target (T) values.

For example, as K changes from $70,000 to $2.99million, the optimal time to upgrade increases from2.26 years to 13.4 years. (The table presents only thetime to upgrade

T � sg

� �for clarity of exposition.)

Although this means firms should wait six times longer,the increase in cost that brought about this change isalmost 40-fold. Fig. 1a and b are used to get someinsights into how optimal adoption time responds tochanges in costs.

Fig. 1a plots the ratio of the percentage change intime to the percentage change in K, or the elasticity oftime with respect to changes in K, against K. This graphshows that this ratio varies within a small range 0.4 to0.55. That is, for every 1% increase in K, optimal timeincreases by 0.4% to 0.55% only, or, the percentagechange in time is about half the percentage change incost. In other words, time is inelastic to changes in K.

An alternative way of looking at the changes is toexamine the impact on time as the proportion of K intotal cost changes. Fig. 1b plots the ratio of thepercentage change in time to the percentage change inthe share of K in total upgrade-related costs (or the

Table 1Simulation results for impact of technology cost

Technologycost (K)

Optimal time toupgrade (OTU)

Percent change in optimaltime to upgrade (PCOTU)

Elasticity of time w.r.t. K:PCOTU/(percent change in K)

K/totalcost a

(PK)

Percent changein PK (PC-PK)

Elasticity of time w.r.t. K/total cost: PCOTU/PC-PK

50,000 1.941 0.000 Indeterminate 0.217 0.000 Indeterminate70,000 2.262 16.544 0.414 0.255 17.725 0.93390,000 2.535 12.098 0.423 0.287 12.563 0.963110,000 2.777 9.547 0.430 0.315 9.627 0.992⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮510,000 5.623 1.896 0.465 0.571 1.276 1.485530,000 5.725 1.826 0.466 0.578 1.211 1.508550,000 5.826 1.760 0.466 0.585 1.150 1.530⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮1,010,000 7.796 0.981 0.485 0.691 0.485 2.0241,030,000 7.871 0.963 0.486 0.694 0.471 2.0451,050,000 7.946 0.945 0.487 0.697 0.458 2.066⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮1,510,000 9.516 0.674 0.502 0.755 0.266 2.5331,530,000 9.580 0.666 0.502 0.757 0.261 2.5531,550,000 9.643 0.658 0.503 0.759 0.256 2.573⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮2,030,000 11.069 0.514 0.516 0.797 0.169 3.0482,050,000 11.125 0.509 0.517 0.798 0.166 3.0672,070,000 11.181 0.505 0.517 0.799 0.164 3.087⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮2,510,000 12.370 0.424 0.528 0.824 0.121 3.5162,530,000 12.422 0.421 0.529 0.825 0.119 3.5352,550,000 12.474 0.418 0.529 0.826 0.118 3.554⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮2,970,000 13.535 0.365 0.539 0.844 0.092 3.9602,990,000 13.583 0.3631 0.539 0.845 0.091 3.979a Total cost= technology cost+change management cost.

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elasticity of time with respect to K's share in totalupgrade costs) against the share of K in total cost.Observe from Table 1 that when K equals $70,000 it isabout 25% of the total cost and the percentage change intime equals 0.93% for a 1% increase in K's share in totalcost. However, as K takes the majority of the upgraderelated cost, for example 85% at $2.99 million, timechanges by 3.9% for a 1% increase in K's share in totalcost.

It is also worth noting that Fig. 1b shows that thepercentage change in time as a ratio of the percentagechange in K's share of total cost is increasing at anincreasing rate while the graph of the percentage changein time as ratio of the percentage change is K increases ata decreasing rate. Thus, even though the percentagechange in time as a fraction of the percentage change inK does not change much as K changes, the percentagechange in time is not only generally greater than thepercentage change in K's share in total cost, the ratioincreases at an increasing rate as K's share in total costrises. To understand the impact of a change in K on time,it is then more instructive to examine how it changes

with respect to the total upgrade cost. It is important tonote that two firms incurring identical technology costs(K) and the same percentage changes in K would havedifferent impacts on the optimal time to upgrade if theshare of K in the total budget is not the same.

These results suggesting that organizations shouldwait longer as K increases are consistent with the [5]study that found lower upgrade investment costs ledorganizations to adopt early. This is also echoed by TilLassance, Vice President of information systems atHeartland Financial USA Inc., as he points out that withan annual IT budget of about $250,000 they could endup spending all of it on just the upgrades to Windows2000 [36]. For the scenario described just the technol-ogy costs of upgrading is in the order of $189,000.Indeed, for reasons of high costs of technology,companies like Heartland will in all likelihood delaythe deployment of the upgrade.

If the cost of technology is very high (relative tothe size of IT budget), the adoption time in some casesmay be long enough to be beyond the foreseeablefuture and hence, the decision could be almost

0.4

0.42

0.44

0.46

0.48

0.5

0.52

0.54

0 500000 1000000 1500000 2000000 2500000 3000000 3500000

Cost of Technology

Ela

sticity o

f O

ptim

al T

ime t

o

Upgra

de w

.r.t.

Cost

of

Technolo

gy

1

1.5

2

2.5

3

3.5

4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Cost of Technology /Total Cost

Ela

sticity o

f O

ptim

al T

ime t

o U

pgra

de

w.r

.t.

Cost

of

Technolo

gy

a

b

Fig. 1. Impact of cost technology (K) on optimal time to upgrade.

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equivalent to not adopting. The DEC alpha processoris an example of such a scenario. When the promisingalpha processor was put forth by DEC, few computermanufacturers were willing to invest in the retoolingof the manufacturing facility at a cost of $50 millionas most of these facilities had installed bases for Inteland Motorola chips [18].

4.1.2. Change management costsTable 2 shows the results of the simulation runs for

various values of the change management costs. As thechange management cost varies from about $14,379 to$942,000, the resulting adjustment is a change in theoptimal time to adoption from 3.6 to 6.12years. It isclear that higher change management costs result in alonger wait to upgrade. This is consistent with [6]finding that high change management costs (specifical-ly, training cost) can be a disincentive to switch orupgrade.

Fig. 2a shows that for every 1% increase in change-management cost, the percentage change in time variesfrom 0.01 to 0.43, with the percentage change in timeincreasing at a decreasing rate. Thus, like the change inK, time is inelastic to changes in change-management

cost. Unlike K, however, the change occurs over a widerrange: 0.01 to 0.4 compared to K's 0.4 to 0.55.

Plotting the elasticity to time with respect tochange-management cost's share in total cost, orratio of the percentage change in time to percentagechange in share of change-management cost in totalcost, Fig. 2b shows that when change-managementcost is only about 9% of the total upgrade cost, a 1%increase in it causes an insignificant 0.01% increase intime. When the ratio rises to about 25% of the totalcost, time increases by 0.08% in contrast to K's 0.93%for the same 1% increase in cost. However, at a highershare such as above 70%, time is elastic to changes inchange-management cost's share in total cost. Com-paring Tables 1 and 2, it can be concluded thatoverall, adoption time responds less to changes inchange-management cost than it does to the directinvestment cost.

4.1.3. Opportunity costsResults shown in Table 3 clearly show that if an

organization has a high opportunity cost associated withan upgrade it is of benefit to conduct the upgrade sooner.As reflected in the results, a change in the opportunity

Table 2Simulation results for impact of change management cost

Changemanagementcost (CMC)

Optimal timeto upgrade(OTU)

Percent change inoptimal time to upgrade(PCOTU)

Elasticity of time w.r.t. CMC:PCOTU/(percent change inCMC)

CMC/totalcost(PCMC)

Percent changein CMC(PC-PCMC)

Elasticity of time w.r.t.CMC/total cost: PCOTU/PC-PCMC

14,379 3.578 0.000 Indeterminate 0.046 0.000 Indeterminate28,955 3.613 0.996 0.010 0.088 92.450 0.01143,733 3.650 1.006 0.020 0.127 44.543 0.02358,716 3.687 1.016 0.030 0.164 28.653 0.03573,909 3.725 1.027 0.040 0.198 20.760 0.04989,315 3.763 1.037 0.050 0.229 16.063 0.065104,939 3.803 1.047 0.060 0.259 12.960 0.081⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮256,004 4.195 1.136 0.152 0.460 4.022 0.282274,020 4.243 1.145 0.163 0.477 3.678 0.311292,295 4.292 1.154 0.173 0.493 3.378 0.342310,833 4.342 1.162 0.183 0.509 3.115 0.373⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮511,207 4.894 1.233 0.284 0.630 1.607 0.767532,784 4.955 1.238 0.293 0.640 1.520 0.814554,645 5.016 1.242 0.303 0.649 1.440 0.863576,790 5.079 1.247 0.312 0.658 1.366 0.913599,219 5.142 1.250 0.322 0.666 1.297 0.964⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮813,641 5.755 1.262 0.399 0.731 0.851 1.482838,823 5.828 1.260 0.407 0.737 0.815 1.546864,266 5.901 1.259 0.415 0.742 0.782 1.611889,965 5.975 1.257 0.423 0.748 0.750 1.676915,917 6.050 1.254 0.430 0.753 0.719 1.743942,118 6.126 1.251 0.437 0.758 0.691 1.811

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cost from about $238,000 to $443,600 causes a changein the optimal time to upgrade from 4.4 to 1.5years. Thisis strongly echoed by Nordstrom.com's Ornen's com-ment “Forget cost; think opportunity” with regards tothe upgrade investment in Windows 2000 [15]. Hefurther adds that the total cost of ownership may nothold as much weight as it did in the past as compared tothe opportunity.

Fig. 3a shows that a 1% increase in opportunitycost decreases optimal time by more than 1%throughout the range of costs considered. This is incontrast to the investment and change-managementcosts for which time was inelastic to changes in both.Thus, it might suggest that opportunity cost may exertmore influence on time to adopt than the other twodirect upgrade-related costs. However, as one looks atFig. 3b, the percentage change in time as a fraction ofthe percentage change in opportunity cost as a shareof upgrade cost, the sensitivity of time declines quitesharply. When opportunity cost is about 40% of thetotal upgrade related cost, a 1% increase in it dropsadoption time by 1.15%, but when that ratio rises toabout 99%, the percentage change in time drops to0.86% for a 1% increase in opportunity cost's share.This is partly because the percentage change in

upgrade cost for a 1% change in opportunity costdeclines from 0.84 to 0.36.

5. Conclusions and areas for future research

The phenomenal rate at which new technology isavailable and the competitive business environment areputting increasing pressure on firms to make difficultupgrade decisions. Theoretically, upgrading technologyevery time a new version is released should keep firms atthe cutting edge constantly. Practically, in an environ-ment of continuous technological change, this is fraughtwith difficulties of managing change. Analysis suggeststhat even if continuous upgrading is feasible, it is not anoptimal strategy if the adoption costs are significant.Specifically, this study's findings support the idea thatinvestments in upgrades are best made when the gapbetween the new technology and the one currently in usereaches a “critical” threshold. Among other factors, thisthreshold is influenced by technology cost, changemanagement cost and opportunity cost.

One of the important implications of this study forpracticing managers is that if organizations can set up along-term plan to leapfrog (optimal/near optimal) it willresult in better management of their resources and

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0 200000 400000 600000 800000 1000000

Change Management Cost

Ela

sticity o

f O

ptim

al T

ime t

o

Upgra

de w

.r.t. C

hange M

anagem

ent

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Change Management Cost / Total Cost

Ela

sticity o

f O

ptim

al T

ime t

o

Upgra

de w

.r.t. C

hange M

anagem

ent

a

b

Fig. 2. Impact of change management cost on optimal time to upgrade.

1693N. Mukherji et al. / Decision Support Systems 42 (2006) 1684–1696

substantial cost savings. From a vendor's perspective—an understanding of the patterns of leapfrogging canhelp them time the release of new products and servicesto increase sales.

Like every research project, some of the assumptionsmade limit the generalizability of the results to allupgrade scenarios. In studying the impact of different

Table 3Simulation results for impact of opportunity cost

Opportunitycost (OC)

Optimal time toupgrade (OUT)

Percent change in optimaltime to upgrade (PCOTU)

Elasticity of timPCOTU/(percenOC)

215,822 5.76 0.00 Indeterminate237,793 4.37 �24.10 �2.37264,976 3.41 �21.97 �1.92297,261 2.74 �19.67 �1.61333,481 2.27 �17.33 �1.42371,626 1.93 �14.96 �1.31409,172 1.69 �12.55 �1.24443,604 1.51 �10.17 �1.21472,958 1.39 �7.90 �1.19496,119 1.31 �5.83 �1.19512,742 1.26 �4.00 �1.19

costs, the model does not account for any uncertaintyassociated with new technologies (growth rate isassumed to be known and constant). In general, this isnot a major concern as long as it is applied to upgradesituations with relatively low uncertainty. Also, it doesnot allow for prices of the same technology to fall overtime. However, a quick look at the historical price

e w.r.t. OC:t change in

OC/totalcost(POC)

Percent changein OC(PC-POC)

Elasticity of time w.r.t.OC/total cost: PCOTU/PC-POC

0.31 0.00 Indeterminate0.38 20.52 �1.170.46 21.15 �1.040.55 20.75 �0.950.66 19.39 �0.890.77 17.25 �0.870.89 14.62 �0.860.99 11.80 �0.861.08 9.06 �0.871.15 6.59 �0.881.21 4.46 �0.90

1

1.2

1.4

1.6

1.8

2

2.2

250000 300000 350000 400000 450000 500000 550000 600000

Opportunity Cost

Ela

sticity o

f O

ptim

al T

ime to U

pgra

de w

.r.t.

Opport

unity C

ost

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Opportunity Cost /Total cost

Ela

sticity o

f O

ptim

al T

ime to U

pgra

de w

.r.t

Op

po

rtu

nity C

ost

a

b

Fig. 3. Impact of opportunity cost on optimal time to upgrade.

1694 N. Mukherji et al. / Decision Support Systems 42 (2006) 1684–1696

information of software products indicates that there islittle variation in price of upgrades even after the releaseof a newer version. Hardware costs on the other hand aremore likely to go down and hence, the model in thecurrent form is more suitable for software upgrades thanhardware.

Furthermore, upgrade decisions are sometimesdriven by some external factors like lack of vendorsupport of old technologies, application or platformupgrades made by clients. Although the study does notdeal with such factors explicitly, in most cases theseaffect one of the costs discussed in the article. Consider,for example, the case of vendor driven upgrades thatinclude SAP and EDI, among others. In the context ofthis model, this becomes part of the opportunity cost. Ifthe loss of support involves a very high cost for the firmand outweighs its adoption costs, the optimal strategywill be to upgrade. Otherwise, the firm may choose towait. Sometimes whether a firm would automaticallyupgrade when the vendor removes support or continuewith an unsupported technology may well depend on the

type of technology. Application software are upgradedmore frequently than platforms and the duration ofsupports are also different. Removing support ofplatforms may adversely affect a very large number ofusers. Thus, for example, Microsoft would remove itssupport of older OS many years after its release. Duringthat interval a number of upgraded OS may be availableand a firm will face the problem of whether or not toupgrade and a model like the one proposed here will beuseful to make that decision. On the other hand, someapplication software may become unsupported within2years of its release. If the costs of adoption are notsignificant but the costs of loss of support are high, afirm may well adopt when the support is removed.

Another example of an external factor influencing theupgrade decision would be the firm's clients. Forexample, in a customer facing system, whether a firmhas the most upgraded technology or not becomesevident to its clients using the system. Not upgrading insuch instances may involve a very high opportunity costand leapfrogging may not be the optimal strategy.

1695N. Mukherji et al. / Decision Support Systems 42 (2006) 1684–1696

Again, if the adoption costs are not insignificant, thefirm has to weigh these costs against the opportunitycosts.

In addition, upgrading a particular application maybe triggered by upgrade decisions of other softwareor hardware used. For example, if a firm that runsWindows 95 is compelled to upgrade some of itsapplication software that require at least Windows 98,then the firm is forced to upgrade its operatingsystem as it upgrades its application software. In thiscase, the decision to upgrade the application softwareshould include the cost of upgrading the operatingsystem as part of its adoption and change-manage-ment costs.

Thus, whether a firm is forced by a vendor to upgradeor by upgrades of other applications or platforms or byits customers, these seemingly external factors can bemodelled in the opportunity or adoption costs consid-ered in the study. In many cases, one of these costs mayso overwhelmingly outweigh the other costs that there isno need to use a model to decide whether to upgrade ornot. If that is not the case there remains the need to do amore systematic analysis and a model like the oneproposed here can be useful.

Although the proposed model does not capture allfactors that drive upgrade decisions, it does provide aframework to analyze how cost–benefit factors impactthe frequency with which firms must invest in ITupgrades. It provides a normative basis to supportupgrade decisions and is valuable in assessing thedifferential impact of the various cost factors on thedecision to invest in upgrades.

Acknowledgement

The authors thank the reviewers of the paper formany useful suggestions. The authors are responsiblefor any remaining errors.

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