European Journal of Operational Research

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1 Euopean Jounal of Opeational Reseach 219 (2012) Contents lists available at SciVese ScienceDiect Euopean Jounal of Opeational Reseach jounal homepage Poduction, Manufactuing and Logistics Impact of soucing flexibility on the outsoucing of sevices unde demand uncetainty Michel Benaoch 1, Scott Webste, Buak Kazaz 2 Whitman School of Management, Syacuse Univesity, 721 Univesity Avenue, Syacuse, NY , United States aticle info abstact Aticle histoy Received 15 August 2011 Accepted 5 Decembe 2011 Available online 13 Decembe 2011 Keywods Sevices outsoucing Backsoucing Demand uncetainty Real options This pape investigates the elationship between maket conditions and the value and use of soucing flexibility fo sevice pocesses. We develop and analyze a seies of models, and we deive expessions fo the optimal switching decision, the value of the option to outsouce, the value of the option to backsouce, and the pobability and timing of switches between the altenative souces. One contibution is the models and associated deivations, which ae lagely new to the liteatue and may seve as a tool to suppot sevice soucing plans and decisions. The second contibution is a seies of esults with manageial implications (1) The pobability of outsoucing is geneally inceasing in volatility fo high-skill pocess and deceasing in volatility fo low-skill pocesses. Ealie wok has found that the hysteesis band is inceasing in volatility, which is intepeted as an indicato of inceasing oganizational inetia. We also find that the hysteesis band is inceasing in volatility, but inteestingly fo the case of high-skill pocesses, oganizational inetia tends to be deceasing in volatility. (2) The option to backsouce is geneally moe valuable fo high-skill pocesses than fo low-skill pocesses. This esult suggests that investments to make it easie to backsouce should have a highe pioity fo high-skill pocesses. (3) The value of the option to backsouce a high-skill sevice pocess can be deceasing in volatility. The esult suggests that a athe nuanced consideation of volatility is in ode when consideing investments in the flexibility to backsouce a high-skill pocess. Ó 2011 Elsevie B.V. All ights eseved. 1. Intoduction Much eseach has focused on manufactuing outsoucing, but today attention is shifting towads the outsoucing of sevice pocesses (Ellam et al., 2008; Hutzscheneute et al., 2011). The opeating implications of sevices outsoucing may be moe subtle than manufactuing outsoucing. Sevices ae chaacteized by intangibility, peishability (i.e., cannot be stoed), simultaneity and insepaability of poduction and consumption, and highe custome contact (Spohe and Maglio, 2008). Of paticula inteest to us is the outsoucing of tansactionbased, infomation-intensive sevice pocesses with volatile demand. Specifically, we conside a fim that is cuently insoucing such a sevice pocess and has the option to outsouce the pocess. The opeating cost stuctue compises a fixed cost pe peiod and vaiable cost pe tansaction. In insoucing, the fixed cost pe peiod is associated with ovehead fo salaies, pesonnel taining, and othe infastuctue esouces, such as office space, softwae Coesponding autho. Tel. +1 (315) addesses [email protected] (M. Benaoch), [email protected] (S. Webste), [email protected] (B. Kazaz). 1 Tel. +1 (315) Tel. +1 (315) licenses, hadwae leases, data centes, and softwae updates fo changing business and compliance equiements (SAP, 2006). In outsoucing, the fixed cost pe peiod is associated with monitoing vendo pefomance, sevice quality and egulatoy compliance, with using secued high-capacity telecom connections to tansaction exchanges, and with ongoing maintenance and updates of etained inte-dependent pocesses and intefaces in esponse to vendo-initiated changes to the outsouced pocess (SAP, 2006); it may also include a pe-peiod fee chaged to the fim by the vendo (Miiyala and Gubaxani, 2005). Fixed costs pe peiod ae not consideed in many ealie studies even though they ae a cucial element in the cost stuctue of eal-wold sevice pocesses (SAP, 2006; Aggawal et al., 2007). Capacity consideations, on the othe hand, ae of lesse concen due to the employment of usage-based picing and scalability of infomation technologies; this is clealy stated in Miiyala and Gubaxani (2005, p. 5) The client is able to buy capacity as and when needed without incuing high fixed costs. The vendo is able to spead its investment cost by scaling the delivey platfom to multiple clients that need the same kind of sevice. Like with manufactuing outsoucing, among the most cited eason fo outsoucing sevice pocesses is cost eduction (Miiyala and Gubaxani, 2005). Fo sevice pocesses that face volatile demand, the cost eduction is pimaily due to the ability to change /$ - see font matte Ó 2011 Elsevie B.V. All ights eseved. doi /j.ejo

2 M. Benaoch et al. / Euopean Jounal of Opeational Reseach 219 (2012) the cost stuctue by tuning fixed costs into vaiable costs combined with the ability to meet flexible capacity needs. Despite the benefits, though, cost eduction expectations ae not always met (Ren and Zhou, 2008; Wentwoth, 2008), and the popotion of fims that decide to backsouce is gowing despite contact temination penalties and the costs of binging a pocess back in-house (Wentwoth, 2008; Whitten and Leidne, 2006; Velti et al., 2008). Examples ae abundant, including a numbe we will elaboate on late, such as Dell and Lehman Bothes call cente opeations (Ren and Zhou, 2008) and a majo unnamed health insue s data enty opeations (Gingande, 2005). 3 A study of tens of cases found the easons fo backsoucing to cente aound high indiect costs and stategic consideations (Velti et al., 2008). Indiect costs ae due to eos, emedial wok on poblem tansactions that must be located and fixed in-house, unsatisfied customes, and eputational damage. Stategic consideations petain to the loss of expetise and tacit knowledge necessay to contol the outsouced sevices (Tiwana and Keil, 2007; Layne and Geen, 2011) and the loss of innovation in sevice opeations (Gay et al., 2009; Amaal et al., 2006; Takeishi, 2001). Concens ove indiect costs and stategic consideations motivate fims to eseve the flexibility to backsouce an outsouced pocess (Tan and Sia, 2007; Wentwoth, 2008). Reseving this flexibility, howeve, goes well-beyond adding a clause in the outsoucing contact. It equies etaining the management of the pocess along with the necessay expetise. The fim has to keep in-house a goup of expets and qualified pesonnel who can develop and maintain contol pocesses fo monitoing and benchmaking the vendo s wok and, moe impotantly, fo ensuing ongoing leaning fo continued pocess impovement and innovation (Ellam et al., 2008; neoit, 2004). Emphasizing stategic consideations in backsoucing, Chalene Begley, the chief infomation technology office of GE, states the following About 50% of the IT wok was done by non-ge employees. That stategy may have had its time, but thee was a lot of downside. We lost a lot of technical capabilities we have to own (Layne and Geen, 2011). How does the decision to eseve the flexibility to backsouce impact the decision to outsouce in the fist place is a question that has not been addessed in the liteatue. Ealie eseach offes valuable insights into the outsoucing decision pimaily in the manufactuing context; howeve, it is not clea how well these insights extend to the outsoucing of sevices. In manufactuing settings, capacity issues ae of pimay concen, howeve, these studies ignoe the influence of fixed costs pe-peiod in outsoucing decisions (Lu and Van Mieghem, 2009). Moe elevant is wok in eal options theoy (Dixit, 1989a,b; Dixit and Pindyk, 1994), and paticulaly Kogut and Kulatilaka (1994) and Kouvelis et al. (2001) who teat the flexibility to outsouce as a eal option and study the bounday demand condition at which it is optimal to switch to outsoucing. The pimay finding in these studies is that inceasing demand volatility inceases both the value of the option to outsouce and the hysteesis band defined by the optimal bounday conditions fo switching to outsoucing. This finding implies that the fim has a geate tendency to outsouce when demand volatility 3 Backsoucing is clealy evident among businesses that outsouce infomation technology (IT) sevices. Deloitte Consulting epoted that nealy two-thids of oganizations have bought some foms of outsouced sevice back in-house (Samuels, 2005). Gatne Goup epoted that 56% of small-sized business and 42% of mid-sized business contacts ae backsouced following contact discontinuance (Bown, 2004). SAP INFO Solutions epoted that 20 30% of all business pocess outsoucing contacts ae teminated within two yeas and 80% need to be enegotiated (Bloch and Spang, 2003; Mani et al., 2005). Diamond Cutte epoted that about half of all IT outsoucing contacts ae teminated o enegotiated within the fist yea (Weakland, 2006). These epots ae consistent with figues epoted by ealie academic studies (Fitzgeald and Willcocks, 1994; Lacity and Willcocks, 2000; Bathelemy, 2001). gows. Howeve, it is not clea whethe this finding extends to the outsoucing of sevices, especially when the fim eseves the flexibility to backsouce. This pape builds on the above eseach and extends eal option models fo finding the optimal demand thesholds fo making a switch to outsoucing modes in thee diections. We develop and analyze a seies of models that incopoate changing and uncetain tansaction volume ove time, insouce and outsouce fixed and vaiable costs, the cost to switch to outsoucing, and the cost to bing a sevice pocess back in-house. Fistly, we intoduce models of two dual situations, temed Regime 1 and Regime 2, in which the question of if and when to outsouce aises since no soucing mode offes an absolute cost advantage. Unde Regime 1 the outsouced vaiable cost (pe tansaction) is highe than the insouced vaiable cost, and the outsouced fixed cost (pe peiod) is lowe than the insouced fixed cost. Sample sevices that fit this egime ae high-skill sevices such as telemedicine and softwae development. We use late teleadiology to illustate what happens in Regime 1. Unde Regime 2 the outsouced vaiable cost is lowe than the insouced vaiable cost, and the outsouced fixed cost (pe peiod) is highe than the insouced fixed cost. Sample sevices that fit this egime ae low-skill sevices such as call centes, claims pocessing, and data enty. We use late data enty and call cente to illustate what happens in Regime 2. Secondly, we deive the optimal demand theshold fo switching to outsoucing, the value of the option to outsouce, the pobability of outsoucing, and the expected time to switch to outsoucing. Since it takes time to switch to outsoucing (vendo seach, contacting, tansition, etc.), a decision to outsouce ought to be eached befoe actual demand hits the optimal theshold. Hence, it is impotant to know the pobability that the theshold will be eached, conditional on the demand level obseved at the decision point; unless this pobability is easonably high, the expected time fo demand to hit the theshold is infinitely long. It is impotant to note that no ealie study has examined the pobability of hitting the optimal bounday demand values fo outsoucing. Alvaez and Stenbacka (2007), fo example, only chaacteize the sign of expected time of hitting the optimal demand theshold as a function of demand volatility. Thidly, we chaacteize how upfont consideation of the flexibility-seeking stategy of backsoucing impacts the pobability of making a decision to switch to outsoucing in the fist place, as a function of demand uncetainty and elative diffeences in soucing costs. In so doing, we seek to check whethe inceased soucing flexibility necessaily tanslates into inceased likelihood of outsoucing. We stat by developing and analyzing base models fo outsoucing the sevice pocess without the flexibility to backsouce in midsteam. The base model and all associated deivations fo Regime 1 ae new to the liteatue to ou knowledge. The base model of Regime 2 yields known esults on bounday conditions fo outsoucing and the expected time to outsoucing but includes a new esult that gives the pobability of outsoucing. In ode to tighten the focus of ou esults, we concentate ou intepetations on a setting whee long-un tansaction volumes ae expected to be flat o inceasing ove time a setting likely to have wide elevance due to population gowth in pactice, compaed to declining makets. We find fo both Regime 1 and Regime 2 that inceasing demand volatility inceases the value of the option to outsouce and the hysteesis band defined by the optimal bounday conditions fo switching to outsoucing, like in Kogut and Kulatilaka (1994) and Kouvelis et al. (2001). But, we also find that the pobability of making the switch depend citically on the cost stuctue of the egime. Unde Regime 1, inceased demand volatility geneally inceases the pobability of making a switch to outsoucing. By contast, unde Regime 2 the exact opposite is obseved inceased

3 274 M. Benaoch et al. / Euopean Jounal of Opeational Reseach 219 (2012) demand volatility geneally deceases the pobability of making a switch to outsoucing. The esult suggests that it is impotant fo manages to account fo the natue of the cost stuctue when consideing how the attactiveness of outsoucing changes unde scenaios of futue high o low volatility. We then expand the base models to examine the impact of incopoating backsoucing flexibility, that is, the flexibility to bing an outsouced pocess back in-house. The backsoucing models and associated deivations ae new to the liteatue. We find that the inclusion of backsoucing flexibility neve deceases the pobability of a switch to outsoucing. This is a obust esult as it holds unde both egimes, whee the outsoucing altenative has eithe a fixed-cost o a vaiable-cost advantage. Moe impotantly, we also find that the value of the option to backsouce is geneally highe in Regime 1 than in Regime 2, indicating that investments to make it easie to backsouce should be a highe pioity unde Regime 1. Finally, contay to conventional wisdom we show that the value of including backsoucing flexibility in the outsoucing aangement can be deceasing in demand volatility unde Regime 1. In essence, we find that as volatility inceases, the isks associated with sevice obsolescence in a high-skill pocess can dominate the value of the flexibility to bing a pocess back in-house. The esult implies that it is less impotant fo fims to build backsoucing flexibility fo outsouced pocesses with a highly volatile demand than it is fo pocesses with less volatile demand. These ae novel esults that aise questions about the common wisdom ove the value of additional flexibility in outsoucing. The pape contibutes to the gowing liteatue on outsoucing unde envionmental uncetainty (e.g., Alvaez and Stenbacka, 2007; Kogut and Kulatilaka, 1994; Kouvelis et al., 2001; Lu and Van Mieghem, 2009; Van Mieghem, 1999; Van Mieghem, 2003), by focusing on the impact of demand uncetainty and soucing flexibility on the decision to outsouce sevice pocesses and its likelihood of this decision to occu. To begin with, it pesents a simple, and yet unique, analytical famewok fo investigating pactical questions elated to backsoucing flexibility. Ealie studies typically focus on the value geneated fom the flexibility associated with the option to outsouce. We complement ealie liteatue by poviding an analytical investigation of the likelihood of execising the option to outsouce, and by examining how including a nested option to backsouce impacts the likelihood of execising the option to outsouce in the fist place. The emainde of the pape is oganized as follows. Section 2 eviews the elated liteatue. Section 3 pesents the base models fo full outsoucing in Regime 1 and Regime 2, along with numeic simulation esults. Section 4 expands the base models to conside the impact of added soucing flexibility in the fom of patial outsoucing and the option to backsouce, along with numeic simulation esults. Section 5 concludes with a summay and suggestions fo futue eseach. All deivations ae located in the Appendix. 2. Related liteatue Ou wok uses a eal options analysis to captue opeational flexibility to outsouce and backsouce a business pocess unde demand uncetainty. Fom a modeling pespective, Bige (2000) and Dixit and Pindyk (1994) povide good examples of how option picing can incopoate financial isk attitudes into opeational decision-making. Simila to ou outsoucing and backsoucing flexibilities, Dixit (1989a,b), fo example, demonstate how these models can be used to detemine whethe a fim should ente and exit a foeign maket. Alvaez and Stenbacka (2007) povide the closest match to ou modeling appoach, although thei emphasis is on the case of patial outsoucing. They investigate the effect of inceasing demand volatility on the expected time of a switch to outsoucing and on the faction of volume to outsouce. Thei model featues the case whee the outsouced cost pe tansaction is lowe than the insouced cost pe tansaction, howeve, ignoes an impotant component pesent in ou model fixed ovehead costs. In Alvaez and Stenbacka (2007), the cost to switch to outsoucing depends upon the faction of volume that is outsouced. In paticula, switching cost is inceasing convex in the outsouce faction, thus exhibiting diseconomies of scale. If switching cost is linea in the faction of volume outsouced, then the model of Alvaez and Stenbacka (2007) can be viewed as a special case of ou model with zeo fixed costs unde Regime 2. In anothe pape by Shy and Stenbacka (2005), split poduction is again justified though monitoing costs of outsouced poduction activities, but once again, missing the fixed ovehead costs. Unde the pesence of monitoing costs, the fim is less likely to incease its allocation to the outsouce altenative with maginal etuns in ode to avoid the inceasing monitoing costs. Ou wok is also elated with the liteatue on outsoucing in the pesence of vaious foms of economic uncetainty. Kogut and Kulatilaka (1994) is the fist study to descibe the flexibility to shift poduction between two manufactuing facilities with fluctuating exchange ates as equivalent to owning an option. They define maket pices and the associated demand as deteministic, but vaiables costs ae influenced by exchange ate fluctuations. When fixed switching costs ae incopoated, they find that the optimal policy stuctue featues a hysteesis band whee the fim does not shift poduction unde smalle vaiations in exchange ates. In a two plant scenaio, Dasu and Li (1997) extend this analysis using linea and step-function switching costs in a model whee exchange ate uncetainty is descibed with a discete-time Makov chain. They find that egadless of whethe the vaiable costs ae concave, piece-wise linea, o convex, the optimal policy stuctue featues a baie policy confiming the ealie desciption of a hysteesis band. Kouvelis et al. (2001) study the influence of exchange ate uncetainty in the type of the owneship in poduction facilities in intenational makets (e.g., expoting, joint ventues, and wholly-owned subsidiaies). In thei model, the fixed costs of switching incease as the fim s owneship in the foeign subsidiay inceases, i.e., the cost is highe fo switches fom expoting to wholly-owned subsidiay than to joint ventue. They conclude that inceasing switching costs extend the hysteesis band. Othe studies that emphasize capacity and/o poduction decisions unde exchange-ate and/o demand uncetainty in a multi-peiod setting includes Lowe et al. (2002), Kazaz et al. (2005), Ding et al. (2007), Li et al. (2009), Pendhaka (2010), and Li and Wang (2010). Ou pape diffes fom this steam of eseach in seveal ways. While the papes in the outsoucing steam of eseach conside exclusively vaiable costs and ignoe fixed costs, ou model incopoates economies of scale with the pesence of fixed and vaiable costs. Second, the amount of sevice demand is andom and exogenous in ou model as we focus on the influence of demand uncetainty on the expected time to switch to outsoucing and the pobability of making this switch. Ealie eseach, howeve, consides the amount of poduction/capacity volume as a decision vaiable. Ou study also diffes fom the liteatue that investigates the subcontacting decisions fom the pespective of a low vaiable cost outsoucing altenative in sevice opeations (e.g., Cachon and Hake, 2002; Osei-Byson and Ngwenyama, 2006; Aksßin et al., 2007, 2008; Ren and Zhou, 2008; Hasija et al., 2008; Milne and Olsen, 2008; Akan et al., 2011) Rathe than focusing on contacting decisions as in this steam of liteatue, ou wok emphasizes outsoucing and backsoucing decisions ove time. Moeove, with the inclusion of fixed costs, the outsouce facility is not always the less-costly altenative. While this steam of liteatue uti-

4 M. Benaoch et al. / Euopean Jounal of Opeational Reseach 219 (2012) lizes queuing systems in its modeling appoach, we employ a eal options analysis. 3. Base outsoucing case This section addesses the base case whee it is impactical to bing a pocess back in-house once it is outsouced; the impact of backsoucing flexibility is examined in Section 4. Section 3.1 fomalizes the poblem settings and two soucing egimes having diffeent opeating cost stuctues. Sections 3.2 and 3.3 poceed to illustate each egime and develop a espective base case model fo that egime. Section 3.4 compaes and contasts the two egimes though a seies of numeical expeiments Settings and two egimes A fim is cuently insoucing a tansaction-based business pocess and has the option to outsouce the pocess at any time in the futue. The pocess, if outsouced, must be completely outsouced (i.e., no patial outsoucing). We outline the notation and the modeling elements that ae common to both egimes below. Notation F I F O v I v O S IO D 0 D t fixed cost pe peiod fo opeating a business pocess when insouced fixed cost pe peiod fo opeating a business pocess when outsouced (vaiable) cost pe pocess tansaction when insouced (vaiable) cost pe pocess tansaction when outsouced one-time fixed cost to switch an existing insouced pocess to outsoucing cuent tansaction ate tansaction ate at time t fim s discount ate (net of inflation in fim and vendo opeating costs) Assumptions (A1) The business pocess is cuently insouced. (A2) Tansaction demand ove time is modeled as geometic Bownian motion dd t ¼ D t ldt þ D t dz; whee l is the gowth ate, is the volatility, and z(t) is a standad Weine pocess with z(0) = 0. (A3) > l. Assumption A2 is common in the liteatue and implies that the change in tansaction volume ove time confoms to a lognomal distibution. Assumption A3 is the standad absence of speculative bubbles condition. When the pocess is insouced, the cost ate is c I ðd t Þ¼v I D t þ F I ; when the pocess is outsouced, the cost ate is c O ðd t Þ¼v O D t þ F O ; and the expected total discounted cost of insoucing ove an infinite hoizon is Z 1 C I ðd 0 Þ¼E e t ðv I D t þ F I Þdt 0 As mentioned ealie, the question of if and when to outsouce aises only when no soucing mode offes an absolute cost advantage, as in the quadants labeled Regime 1 and Regime 2 in Fig. 1. We poceed to illustate and develop the base model fo each of these egimes Regime 1 outsouce at highe vaiable cost and lowe fixed cost Unde Regime 1, outsoucing has a fixed-cost advantage ove insoucing. The outsouced fixed cost (pe peiod) is lowe than the insouced fixed cost, but the outsouced vaiable cost (pe tansaction) is highe than the insouced vaiable cost. Sample sevices that fit this quadant ae high-skill sevices such as telemedicine and softwae development. These sevices involve low poductivity pocesses and high-salaied, high-skilled labo. In insoucing, these chaacteistics tanslate into high fixed costs pe peiod and low (o zeo) vaiable costs pe tansaction. Teleadiology, a subset of telemedicine, is a good example of Regime 1. Teleadiology is a pocess chaacteized by volume fluctuations, whethe due to a baage of incoming cases o a seasonal lull (Whitace et al., 2007; Wachte, 2006; Singh and Wachte, 2008). Outsoucing allows healthcae povides to align adiogam eading costs to actual volumes by shifting high fixed ovehead cost pe peiod (e.g., annual salay of $ K pe adiologist plus acceditation costs) into vaiable costs (e.g., $50 75 pe adiogam eading). Outsoucing vendos that focus only on poviding adiology eading sevices spead thei oveheads acoss a much lage volume of cases while optimizing and steamlining the pocess of physician ecuiting and cedentialing, adiology eading wokflows, and all ancillay activities. Hee, outsoucing could be favoable when the demand volume dops to a sufficiently low level. Hence, unde Regime 1 we have the following additional assumption. (A4) v I 6 v O and F I > F O. Due to A4, c O (D t ) 6 c I (D t ) if and only if D t 6 F IF O v O v I, i.e., low demand ates favo outsoucing and high demand ates favo insoucing. Suppose the fim elects to switch to outsoucing of the sevice pocess if and when the demand ate fo the sevice hits a theshold ate D < D 0. Such a switching policy is optimal due to the stationay behavio of dz. Let s 1 (D) denote the andom time of the switch to outsoucing, i.e., s 1 ðdþ ¼minftjD t 6 Dg The fim s expected discounted opeating cost of the pocess unde Regime 1 is " Z s1 ðdþ C 1 ðd 0 ; DÞ ¼E 0 Z 1 e t ðv I D t þ F I Þdt þ e t ðv O D t þ F O Þdt s 1 ðdþ þe s 1ðDÞ S IO # ¼ C I ðd 0 ÞV 1 ðdþ; ð1þ whee V 1 ðdþ ¼ D c F I F O S IO D 0 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðl 05 c 2 Þ 2 þ 2 2 þðl 05 2 Þ ¼ 2 v O v I l D The function V 1 (D) is the value of the option to outsouce the pocess given that the fim switches to outsoucing when the cuent demand ate passes below (o hits) theshold D. IfF I F O S IO 6 0, then it is appaent fom (2) that the fim will neve outsouce the pocess (i.e., if F I F O S IO 6 0, then V 1 (D) 6 0 fo all D > 0). Thus, fo the emainde of this section we limit consideation to cases whee F I F O S IO > 0. The optimal theshold ate D is D ¼ ag max DP0 ð2þ V 1 ðdþ ¼ cð lþðf I F O S IO Þ ð3þ ðc þ 1Þðv O v I Þ The value of the option to outsouce the pocess is obtained by substituting (3) into (2) while accounting fo the fact that it is optimal fo the fim to immediately switch to outsoucing if D 0 6 D

5 276 M. Benaoch et al. / Euopean Jounal of Opeational Reseach 219 (2012) FIFOSIO V 1 ¼ v O v >< I l D 0 if D 0 6 D ; c cþ1 > cðlþ FI F O S IO D 0 ðv O v I if D Þ ðcþ1þ 0 P D We let s 1 denote the optimal andom time that the fim switches to outsoucing (i.e., s 1 ¼ s 1ðD Þ). The pobability of a switch to outsoucing is 8 P s 1 < 1 < 2l D 21 ¼ D 0 if l 05 2 P 0 and D 0 P D ; ð5þ 1 if l oD 0 6 D ; and the expected time to making the switch is 8 1 if l 05 2 P 0 and D 0 P D ; >< E s 1 ¼ 1 l05 ln D 2 D 0 if l and D 0 P D ; > 0 if D 0 6 D We note that the expected time to making a switch to outsoucing is finite when the pobability of the switch is 100%, and is infinite othewise. Thus, both measues ae needed to povide a complete pictue of the effect of changing paamete values on outsoucing, as illustated in Section Regime 2 outsouce at lowe vaiable cost and highe fixed cost Unde Regime 2, outsoucing has a vaiable-cost advantage ove insoucing. The outsouced vaiable cost is lowe than the insouced vaiable cost, but the outsouced fixed cost (pe peiod) is highe than the insouced fixed cost. Sample sevices that fit this quadant include call centes, claims pocessing, and data enty. These sevices involve low-salaied and low-skill labo that includes houly and tempoay wokes. In insoucing, these chaacteistics tanslate into elatively low fixed costs pe peiod. When outsoucing, thee is a maginal advantage on vaiable costs, but this can be exploited only at the expense of inceased pe peiod monitoing and taining costs fo the management and quality contol of outsouced wok (Shy and Stenbacka, 2005; Fitsch et al., 2007). Examples can be widely seen in data enty and call centes. Data enty coves the captue, scanning and indexing fo late etieval of standad documents (e.g., tax etuns, medical claims) and unstuctued documents (e.g., invoices, explanations of benefits, shipping ecods) (Gingande, 2005). The vaiable cost pe tansaction is nomally lowe in outsoucing. Fo example, Fidesic, an e-payment sevices company, epots a $0.31 vaiable cost fo data enty of a typical non-scannable invoice, compaed with $2.42 in-house (Gingande, 2005). This cost diffeential is due to the fact that the vendo uses low-cost labo, makes a high investment in technologies fo automated ecognition of machine pint, hand pint, check boxes, and bacodes. Howeve, outsoucing usually also inceases the fixed costs pe peiod. In paticula, compaed to insoucing, pocess govenance equies building and maintaining administative pocess contols fo supevisos to tack and audit evey document fom the moment it is scanned until it is eleased to the epositoy, keeping tabs on who has access, when and what was done. Such tight and costly pocess govenance is cucial fo assuing high data accuacy and suppoting the Health Infomation Pivacy and Accessibility Act (HIPAA) and Sabanes Oxley govenment egulations on the handling of data. 4 This situation is also typical of call centes (neoit, 2004). Outsoucing yields majo savings on labo, but labo costs ae 4 SOX s stong focus on data secuity and who can access what infomation makes outsoucing and offshoing decisions a boad-level issue, paticulaly with invoice and emittance pocessing, and othe oganizational financial data. Fo example, in 2002, the fequency of non-compliance incidents, due to offshoe vendo caelessness, caused the Office of the Comptolle of the Cuency to issue isk-management compliance guidelines fo US banks that use offshoe sevice povides (Gingande, 2005). ð4þ ð6þ only ove 30% of the total cost of opeations. In paallel, outsoucing inceases the fixed costs pe peiod mostly fo communication systems, taining, and pocess govenance. 5 These components account fo 25% of the total cost of opeations. The balance is in favo of outsoucing when the demand volume is lage enough. Hence, unde Regime 2 we have the following assumption in place of A4. (A5) v I > v O and F I 6 F O. Due to A5, c O (D t ) 6 c I (D t ) if and only if D t P F OF I v I v O, i.e., high demand ates favo outsoucing and low demand ates favo insoucing. In the event of F I = F O, we have c O (D t )<c I (D t ), and the decision to switch to outsoucing involves a tade-off between the outsoucing vaiable cost savings and the switching cost. Suppose the fim elects to switch to outsoucing if and when the demand ate hits a theshold ate D > D 0. Such a switching policy is optimal due to the stationay behavio of dz. Let s 2 (D) denote the andom time of the switch to outsoucing, i.e., s 2 ðdþ ¼minftjD t P Dg The fim s expected discounted opeating cost of the pocess unde Regime 2 is " C 2 ðd 0 ; DÞ ¼E Z s2 ðdþ 0 Z 1 e t ðv I D t þ F I Þdt þ e t ðv O D t þ F O Þdt s 2 ðdþ þe s 2ðDÞ S IO # ¼ C I ðd 0 ÞV 2 ðdþ; ð7þ whee V 2 ðdþ ¼ D b 0 v I v O D F O F I þ S IO ; ð8þ D l qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðl 05 2 Þ 2 þ 2 2 ðl 05 2 Þ b ¼ 2 5 These fixed costs gow in call cente outsoucing fo seveal easons (neoit, 2004; Holman et al., 2007) Communication systems equie leased cicuits with enough dedicated bandwidth to cay simultaneous voice and data taffic ove long distances without latency, and edundancy of the links to ensue business continuity and avoid outages. IBM and Micosoft, which have outsouced thei call centes to developing counties, have actually invested in dedicated telecommunications lines instead of using the Intenet to field intenational custome calls, in ode to alleviate secuity isks and data pivacy concens of many consumes who hesitate to give pesonal infomation ove the phone (Rao, 2004). Taining costs incease due to the need to keep in-house highly qualified pesonnel to develop, maintain and coodinate with the vendo a pocess fo ongoing taining and development of esouces that cove both opeational business needs and cultual aspects that affect sevice delivey. This need is aggavated by the fact that, compaed to in-house call centes, vendos typically offe less taining to new employees (14 vs. 20 days), employ moe pat-time (20% vs. 15%) and tempoay wokes (15% vs. 10%), have lowe wokfoce tenue (e.g., in India, 60% of call cente wokes have less than one yea of tenue at wok), and expeience highe tunove (40% vs. 19%). Highe pocess govenance costs ae associated with having in-house enough qualified pesonnel fo two puposes. One is emedial wok on failed calls, call backs, follow-ups, etc. A moe impotant pupose is monitoing vendo pefomance. In in-house call centes, monitoing is less fequent as poximity allows supevisos to do side-by-side monitoing, wande among stations and listen in, o sit at monitoing stations. By contast, in outsoucing, emote monitoing is hade and must be moe fequent and thoough. It involves examination of call ecodings and some on site visits, by specialist supevisos and location expet esouces who ae highly tained in monitoing and coaching techniques. Moeove, since picing is often tied to sevice level ageements, moe igoous and fequent monitoing by the qualified specialists is needed to ensue that custome calls ae being handled as pomised by the vendo, on time and in a pofessional and quality manne.

6 M. Benaoch et al. / Euopean Jounal of Opeational Reseach 219 (2012) Fixed Pe-Peiod Cost Diffeential (Intenal Extenal) Always Outsouce Regime 1 Insouce o Outsouce Vaiable Cost Diffeential (Intenal Extenal) Regime 2 Insouce o Outsouce Always Insouce Fig. 1. Outsoucing egimes. The function V 2 (D) is the value of the option to outsouce the pocess given that the fim switches to outsoucing when the cuent demand ate passes above (o hits) theshold D. The optimal theshold D is D ¼ ag max V 2 ðdþ ¼ DP0 ( bðlþðf O F I þs IO Þ ðb1þðv I v O if b > 1; Þ 1 if b 6 1 If b 6 1, then it is appaent fom (9) that the fim will neve outsouce the pocess. Thus, fo the emainde of this section we limit consideation to cases whee b > 1. The value of the option to outsouce the pocess is obtained by substituting (9) into (8) while accounting fo the fact that it is optimal fo the fim to immediately switch to outsoucing if D 0 P D 8 D0ðv b b1 >< Iv OÞ ðb1þ V 2 ¼ bðlþ F O F I þs IO if D 0 6 D ; ð10þ > v I v O l D 0 F OF I þs IO if D 0 P D We let s 2 denote the optimal andom time that the fim switches to outsoucing (i.e., s 2 ¼ s 2ðD Þ). The pobability of a switch to outsoucing is 8 P s 2 < 1 < 2l D 21 ¼ D 0 if l and D 0 6 D ; ð11þ 1 if l 05 2 P 0oD 0 P D ; and the expected time to making the switch is 8 1 if l and D 0 6 D ; >< E s 2 ¼ 1 l05 ln D 2 D 0 if l 05 2 P 0 and D 0 6 D ; > 0 if D 0 P D ð9þ ð12þ Again, we note that the expected time to making a switch to outsoucing the pocess is finite when the pobability of outsoucing is 100%, and is infinite othewise. Thus, both measues ae needed to povide a complete pictue of the effect of changing paametes values on outsoucing, as illustated next Numeical analysis We next epot on how changing envionmental conditions affect the likelihood of outsoucing unde both egimes. Fig. 2 chaacteizes, within the space of possible fixed and vaiable cost diffeentials, the egions whee the pobability of making a switch to outsoucing is high, as a function of changing demand volatility. Assuming that a theshold pobability of 0.8 is sufficiently high to tigge a decision to outsouce (and the seach fo a vendo, tems negotiation, and contacting), we obseve the following as demand volatility gows, the outsoucing egion fo Regime 1 gows and the egion fo Regime 2 shinks. This patten is obust to changes in the values of all poblem paametes. To undestand the esults shown in Fig. 2, we summaize the effect of changing paamete values on the value of the option to outsouce, the optimal demand theshold, the pobability of a switch to outsoucing (i.e., of hitting the optimal demand theshold), and the expected time to making the switch to outsoucing (see Appendix B fo details). The base models yield esults simila to those of past studies in the eal options liteatue (e.g., Dixit and Pindyk, 1994), but also efine these esults and offe new insights. Pincipally, the value of the option to outsouce inceases in demand volatility, and the hysteesis band is inceasing in demand volatility. The optimal demand theshold fo a switch to outsoucing deceases in Regime 1 (D ) and inceases in Regime 2 (D )asa function of demand volatility, unde all conditions. Geneally, these conditions would suggest that a fim is less likely to outsouce as volatility inceases. Howeve, the new insights ou model offes efine these pediction. The pobability of a switch to outsoucing and the expected time to making the switch ae non-monotone in demand volatility in Regime 1 and monotone in Regime 2. Specifically, in Regime 1, the pobability of a switch can be 100% mostly fo elatively lage levels of demand volatility (i.e., the fim immediately switches to outsoucing). By contast, in Regime 2, fo low levels of demand volatility, the pobability of a switch can be 100% unde most situational conditions, but this pobability stats deceasing and continues to decease as demand volatility inceases. In sum, in Regime 1, significant demand volatility inceases the pobability of outsoucing despite the fact it also deceases the demand theshold, and, in Regime 2, significant demand volatility lowes the pobability of outsoucing as it also inceases the demand theshold. Thus, in Regime 2, highe demand volatility values imply that insoucing is a bette altenative fo the fim. These conclusions ae consistent with the expected time to making a switch to outsoucing, which deceases with inceasing demand volatility in Regime 1 and inceases in Regime 2. It is impotant to

7 278 M. Benaoch et al. / Euopean Jounal of Opeational Reseach 219 (2012) F I F O vo v I -$0.10 -$0.08 -$0.06 -$0.04 -$0.02 $0.02 $0.04 $0.06 $0.08 $0.10 -$0.10 -$ $0.06 -$0.04 -$0.02 $0.02 $0.04 $0.06 $0.08 $0.10 -$0.10 -$0.08 -$ $0.04 -$0.02 $0.02 $0.04 $0.06 $0.08 $0.10 $ $ $ $ $ $ $ $ $ $ $ $ Regime $ $ $ $ $ $ $ $ $ Outsoucing $ $ $ $ $ $ Region Insoucing $ $ $ $ $ $ Region -$ $ $ $ $ $ Regime $ $ $ $ $ $ $ $ $ σ =8% σ =16% σ =24% -$0.10 -$0.08 -$0.06 -$0.04 -$0.02 $0.02 $0.04 $0.06 $0.08 $0.10 -$0.10 -$0.08 -$0.06 -$0.04 -$0.02 $0.02 $0.04 $0.06 $0.08 $0.10 $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ σ =32% σ =40% Assumed paamete values D 0 = 900; = 10%; μ = 6% in Regime 1, μ = 2% in Regime 2; v O v I = ± $0.02 $0.1; F I F O = ± $20 $160; S IO =$15 Fig. 2. Outsoucing egions fo the base case (p > 0.8). note that all these esults ae obust ove a ange of values of poblem paametes (see Appendix B). The policy stuctue fo Regime 1 may seem suboptimal, o even counteintuitive, but it has a logical explanation that coesponds well with the ealities faced in the outsoucing of teleadiology by ual hospitals, fo example. If one holds a athe long-tem view on outsoucing decisions, and if demand has a positive dift, as is assumed in ou numeical analyses, a policy of outsoucing when the demand falls below a theshold could be suboptimal because demand is gowing in expectation and the hoizon is infinite. While thee is a positive pobability of hitting the low demand theshold fo the demand pocess with a positive dift and a switch to outsoucing would occu with a positive pobability, the total opeating cost would be lowe if the fim always adopts the insoucing option thoughout the hoizon given that the demand is gowing in expectation. Howeve, this agument makes little sense fo fims which do not, o cannot, hold a long-tem view on soucing decisions. Take the case of teleadiology in ual hospitals, fo instance, whee demand is volatile and has a positive dift (Whitace et al., 2007). 6 Hee, long-tem consideations take a backseat to an ongoing shotage of adiology specialists as well as to business cycle cost pessues, budgetay constaints, and competing pioities acoss diffeent specialty depatments. Thus, despite having positive dift in demand, ual hospitals would chose to outsouce when facing an unsustainable level of fixed costs pe peiod at times when demand fo sevices dops to a sufficiently low level. 4. Impact of backsoucing flexibility This section extends the base models to account fo the pesence of backsoucing flexibility. Section 4.1 discusses cicumstances unde which this fom of soucing flexibility could offe benefits. Sections 4.2 and 4.3 study the setting whee the fim 6 In teleadiology, and telemedicine in geneal, an aging population along with new technologies that continually expand the ange of diagnostic adiology have esulted in a steadily inceasing demand fo diagnostic intepetations (Stack et al., 2007). has the option to beak the outsoucing aangement in midsteam and bing the pocess back in-house. Section 4.4 contains numeical analyses of outsoucing with backsoucing flexibility unde the two egimes Beyond the base case As mentioned befoe, companies ae often unsatisfied with the esults of outsoucing fo a vaiety of easons. The main easons ae cited as high indiect costs and stategic consideations. Indiect costs in sevices outsoucing can come fom multiple souces. One souce is eos. In data enty outsoucing, fo example, delivey of inaccuate data may have expensive consequences, such as paying incoect invoices o health claims, o hindeing poductivity by emedial wok on poblems that must be located and fixed in-house (Gingande, 2005). Anothe souce is of indiect costs is poo sevice quality, which could educe the likelihood of futue custome puchases and esult in eputational damage. Fo instance, both Dell and Lehman Bothes moved call cente opeations fom India back to the US due to custome complaints about sevice quality (Ren and Zhou, 2008). Anothe souce is the need fo close monitoing of the vendo s wok, especially when it is impotant to ensue compliance with such govenment egulations as HIPAA and SOX. Fo instance, a majo health insuance fim has backsouced data enty opeations afte its sevice bueau in India displayed the names of company clients in a demonstation on thei Website, in clea violation of HIPAA ules (Gingande, 2005). Stategic consideations could be moe significant. They petain to loss of contol ove outsouced sevices and of the ability to innovate. Specifically, a key concen is ove the loss of expet undestanding of the outsouced pocess and of tacit knowledge that allows the fim to have beakthough thinking in sevice opeations (Tiwana and Keil, 2007; Amaal et al., 2006; Takeishi, 2001). NCR Cop., fo instance, backsouced the manufactuing of its most sophisticated automated telle machines (ATMs) fom China and India to the US, because outsoucing distanced its designes, enginees, IT expets and customes fom the manufactuing pocess.

8 M. Benaoch et al. / Euopean Jounal of Opeational Reseach 219 (2012) The backsoucing decision enabled the fim to tun out new models with new featues fast enough to satisfy its client banks (Holstein, 2010). Similaly, GE announced that it is in the pocess of inceasing its backsoucing capability due to stategic costs associated with the fim s technical capabilities (Layne and Geen, 2011). Fims use mainly two means to counte these concens and eseve the flexibility to backsouce in case the concens mateialize. One is to leave a goup of highly qualified pesonnel to handle poblem tansactions, callbacks fo incomplete tansactions and follow-ups, and to benchmak the vendo s pefomance moe accuately (Ellam et al., 2008; Whitace et al., 2007). Anothe is to etain the management of the pocess in-house. The latte involves keeping a lage intenal management goup to develop a poactive monitoing and management contol pocess fo intefacing with the vendo on sevice pefomance evaluation issues and, moe impotantly, fo ensuing ongoing leaning fo continued pocess impovement and innovation (Ellam et al., 2008; neoit, 2004; Layne and Geen, 2011). Oftentimes, unless patially etained, these capabilities would be lost ove the outsouced sevice pocess, and the cost to switch back to insoucing would become pohibitively lage. We next seek to examine the impact of having the flexibility to backsouce on the initial decision to outsouce. Conside a fim that is cuently insoucing a business pocess and has the option to outsouce at any time in the futue. In addition, once the fim decides to outsouce, it has the option to backsouce at any time in the futue. The cost to execise this flexibility is denoted S OI. The value of S OI can be intepeted as the cost of beaking the outsoucing contact and switching back to insoucing. The implicit assumption is that S OI is pohibitively lage when the fim fails to eseve the flexibility to backsouce Outsoucing with backsoucing flexibility unde Regime 1 Unde Regime 1, we have v I 6 v O and F I > F O, and thus low demand ates favo outsoucing and high demand ates favo insoucing (see A4). Suppose the fim elects to switch to outsoucing if and when the demand ate hits a theshold ate D < D 0.Asin Section 3.2, we let s 1 (D) denote the andom time of the switch to outsoucing, i.e., s 1 ðdþ ¼minftjD t 6 Dg At the moment of the switch to outsoucing, the fim has the option to switch back to insoucing at any time in the futue. The optimal theshold fo switching back to insoucing once a fim has switched to outsoucing is ( D þþ ¼ bðlþðf I F O þs OI Þ ðb1þðv O v I Þ if b > 1; 1 if b 6 1; whee qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðl 05 2 Þ 2 þ 2 2 ðl 05 2 Þ b ¼ 2 ð13þ Note that b > 1 fo any finite 2 (due to A3). The value of the option to backsouce at the moment the fim switches to outsoucing (i.e., the moment in time when the demand ate hits theshold D) is 8 Dðv b b1 >< Ov IÞ ðb1þ if D 6 D þþ ; bðlþ V 2 ðdþ ¼ > v O v I l F I F O þs OI D F IF O þs OI if D P D þþ ð14þ The fim s expected discounted opeating cost is the same as in Section 3.1 except that the cost to switch fom insoucing to outsoucing (S IO ) is educed by the value of the backsoucing option V 2 ðdþ that is activated at the moment the fim switches to outsoucing, i.e., " C 1 ðd 0 ; DÞ ¼E Z s1 ðdþ 0 þe s 1ðDÞ Z 1 e t ðv I D t þ F I Þdt þ e t ðv O D t þ F O Þdt s 1 ðdþ S IO V 2 ðdþ # ¼ C I ðd 0 ÞV 3 ðdþ; whee V 3 ðdþ ¼ D c F I F O S IO V 2 ðdþ D 0 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðl 05 c 2 Þ 2 þ 2 2 þðl 05 2 Þ ¼ 2 v O v I l D ; The optimal theshold fo making a switch to outsoucing is D o ¼ ag max V 3 ðdþ; DP0;D6D 0 ;D<D þþ whee, due to the constaints, Dðv V 2 ðdþ ¼ O v b I Þ ðb 1Þ bð lþ F I F O þ S OI b1 ð15þ thee is no closed fom expession fo D o (i.e., D o is the oot of a high-ode polynomial). But, D o can be obtained numeically using eadily available softwae such as Nonlinea Solve in Micosoft Excel. The pobability that the fim will switch to outsoucing and the expected time to making the switch can be obtained fom expessions (5) and (6). Given that the fim switches to outsoucing, the pobability that the fim will switch back to insoucing (i.e., backsouce) and the expected time to making the switch to insoucing can be obtained fom expessions (11) and (12), whee D ++ is used in place of D and D o is used in place of D Outsoucing with backsoucing flexibility unde Regime 2 Unde Regime 2, we have v I > v O and F I 6 F O (see A5), and thus high demand ates favo outsoucing and low demand ates favo insoucing. Suppose the fim elects to switch to outsoucing if and when the demand ate hits a theshold ate D > D 0. As in Section 3.3, we let s 2 (D) denote the andom time of the switch to outsoucing, i.e., s 2 ðdþ ¼minftjD t P Dg At the moment of the switch to outsoucing, the fim has the option to switch back to insoucing at any time in the futue. A fim that has switched to outsoucing will neve choose to backsouce if F O F I S OI 6 0 (see (2)). Thus, fo the emainde of this section we limit consideation to cases whee F I F O S IO > 0. The optimal theshold fo switching back insoucing once a fim has switched to outsoucing is D þ ¼ cð lþðf O F I S OI Þ ; ð16þ ðc þ 1Þðv I v O Þ whee qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðl 05 c 2 Þ 2 þ 2 2 þðl 05 2 Þ ¼ 2 The value of the option to backsouce at the moment the fim switches to outsoucing (i.e., the moment in time when the demand ate hits theshold D) is

9 280 M. Benaoch et al. / Euopean Jounal of Opeational Reseach 219 (2012) FOFISOI V 1 ðdþ ¼ v I v >< O l D if D 6 D þ ; c cþ1 > cðlþ FO F I S OI Dðv I v O if D P D þ Þ ðcþ1þ ð17þ The fim s expected discounted opeating cost is the same as in Section 3.2 except that the cost to switch fom insoucing to outsoucing (S IO ) is educed by the value of the backsoucing option V 1 ðdþ that is activated at the moment the fim switches to outsoucing, i.e., " Z s2 ðdþ C 2 ðd 0 ; DÞ ¼E 0 þe s 2ðDÞ Z 1 e t ðv I D t þ F I Þdt þ e t ðv O D t þ F O Þdt s 2 ðdþ S IO V 1 ðdþ # ¼ C I ðd 0 ÞV 4 ðdþ; whee V 4 ðdþ ¼ D b 0 v I v O D F O F I þ S IO V 1 ðdþ ; D l qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðl 05 2 Þ 2 þ 2 2 ðl 05 2 Þ b ¼ 2 The optimal theshold is D oo ¼ ag max DPD 0 ;D>D þ V 4 ðdþ; whee, due to the constaints, c V 1 ðdþ ¼ cð lþ F O F I S OI Dðv I v O Þ ðc þ 1Þ cþ1 ð18þ thee is no closed fom expession fo D oo (i.e., D oo is the oot of a high-ode polynomial). Howeve, D oo can be obtained numeically using eadily available softwae such as Nonlinea Solve in MS- Excel. The pobability that the fim will switch to outsoucing and the expected time to making the switch can be obtained fom expessions (11) and (12). Given that the fim switches to outsoucing, the pobability that the fim will switch back to insoucing (i.e., backsouce) and the expected time to making the switch to insoucing can be obtained fom expessions (5) and (6) in Section 3.2, D + is used in place of D and D oo is used in place of D Numeical analysis We next illustate the influence of the option to backsouce fo vaious poblem paametes unde both egimes. Fig. 3 chaacteizes the changes in the egions whee the pobability of making a switch to outsoucing is high, as a function of changing demand volatility. Assuming that a theshold pobability of 0.8 is sufficiently high to tigge a decision to outsouce (and the seach fo a vendo, tems negotiation, and contacting), we obseve the following as demand volatility gows, the pesence of backsoucing flexibility expands the outsoucing egion, but mostly fo Regime 1; the pats of the egion showing pobabilities in White font ae due to backsoucing flexibility. Specifically, backsoucing flexibility expands the ousoucing egion fo Regime 1 athe notably unde low- and medium-level demand volatilities, and only maginally fo Regime 2 unde all levels of demand volatility. This patten is obust to changes in the values of all poblem paametes. To undestand the esults shown in Fig. 3, we summaize the effect of changing paamete values on the value contibution of the option to backsouce, the optimal switching demand theshold, the pobability of a switch to outsoucing, and the expected time to making the switch to outsoucing (see Appendix C fo details). Stating with the net added value of having the flexibility to backsouce, in both egimes this net added value is significant only when the value of the plain option to outsouce (with no backsoucing flexibility) is high (see Appendix C, Figs. C1 and C2). A low value of the plain option means a negligible pobability that a switch to outsoucing will occu, in which case thee is a negligible value to having the flexibility to backsouce. Howeve, what is moe impotant is how this net added value would impact the initial decision to switch to outsoucing in the fist place. In Regime 2, while this net added value is stictly inceasing in demand volatility, and the optimal demand theshold is geneally loweed by the pesence of backsoucing flexibility, the pobability of a switch to outsoucing gows only maginally fo intemediate and high values of the demand volatility, and no beneficial impact can be obseved fo the expected time to making a switch to outsoucing. By contast, in Regime 1, the net added value of backsoucing flexibility has a significant beneficial effect on the initial decision to outsouce. While the optimal demand theshold is consistently highe than that of the plain option to outsouce (Fig. 2), it continues to decease monotonically unde all poblem paametes until a point whee the decease tapes off significantly with inceasing values of the demand volatility. As a esult, the pobability of a switch to outsoucing inceases unde all poblem paametes, and the expected time to making the switch goes to zeo when the pobability is close enough to 100%. In summay, intoducing backsoucing flexibility into the option to outsouce adds value in both egimes, but its contibution is significantly moe beneficial unde Regime 1. A fim opeating unde the cost stuctue of Regime 2 will have less to gain fom the inclusion of the backsoucing flexibility. This is due to the long-tem positive gowth unde both egimes, wheeby expected demand is inceasing in time. Thus, in the case of a sevice pocess opeating in gowth makets, the flexibility to educe cost unde Regime 2 by binging tansaction pocessing back in-house adds elatively little value. By contast, unde Regime 1, in the long tem (i.e., unde high sevice demand volumes), the fim is bette off pocessing tansactions in-house. As such, backsoucing flexibility pevents the fim fom having to wait to make a switch to outsoucing until demand levels dop significantly to a point whee the possibility of keeping the pocess in house may no longe be viable. It is woth expanding a bit on the net added value of the flexibility to backsouce in Regime 1. Unde Regime 1, this value geneally inceases in demand volatility but in fact has a evesed bowlshape fo some poblem paametes (see Appendix C, Fig. C1). It inceases fo elatively low values of the demand volatility, but deceases o just conveges to a elatively stable value fo highe demand volatilities. This evesed-bowl shape can be explained using popeties of the model. As demand volatility inceases, the stochastic demand pocess descibed by the geometic Bownian motion can hit the absobent state (zeo) with a highe pobability. As the pobability of expeiencing zeo demand inceases, implying that the sevice pocess is no longe viable, the option to backsouce, which is attactive when volume is high, becomes less valuable, and its net value contibution stats deceasing with inceasing volatility. In essence, as volatility inceases, the isks associated with sevice obsolescence can dominate the value of binging a pocess back in-house when volume is high. This eading of the situation coesponds well with the outsoucing of teleadiology sevices in ual hospitals descibed in Section 3.1 (Whitace et al., 2007). Outsoucing when demand levels dop sufficiently low (even if only fo a tempoay duation that is sufficiently long) exposes ual hospitals to the isk of having to shut down thei adiology specialties and tansfe all patients to lage egional hospitals, because no effective economies of scale would be sufficient to allow fo any on-site adiology specialists (Whitace et al., 2007). When this is a viable possibility, the net added value of backsoucing flexibility diminishes.

10 M. Benaoch et al. / Euopean Jounal of Opeational Reseach 219 (2012) Fig. 3. Outsoucing egions fo the case with backsoucing (p > 0.8). Impotantly, the last two esults fo Regime 1 efine the findings of ealie liteatue poviding examples of how inceasing maket volatility ceates a highe value fo vaious foms of flexibility (Alvaez and Stenbacka, 2007; Van Mieghem, 1999; Van Mieghem, 2003; Van Mieghem and Rudi, 2002). Consistent with the findings in the eal options liteatue, the common peception is that the value of flexibility inceases with highe volatility. Yet, ou esults show that the incemental value of additional flexibility, in ou case it is the ability to backsouce an outsouced pocess, depats fom this common undestanding. 5. Summay and Conclusions We define and analyze models fo soucing a tansaction-based sevices pocess unde two opposing cost stuctues. The cost stuctues coespond to the two egimes wheein the decision of whethe to outsouce is nontivial. Unde Regime 1 the outsouced vaiable cost is highe than the insouced vaiable cost and the outsouced fixed cost is lowe than the insouced fixed cost. Examples include high-skill pocesses such as telemedicine and softwae development. Unde Regime 2 the outsouced vaiable cost is lowe than the insouced vaiable cost and the outsouced fixed cost is highe than (o the same as) the insouced fixed cost. Examples ae low-skill pocesses such as data enty and call cente opeations. The esults of ou study lead to thee main conclusions that apply in settings whee volume ove the long-tem is expected to be flat o gowing. The esults suggest that a caeful consideation should be given to the decision to outsouce sevice pocesses, especially in light of potentially high indiect costs and stategic consideations. Fist, the impact of demand volatility on the likelihood and timing of a switch to outsoucing depends citically on the egime. Unde Regime 1, as demand volatility inceases, the pobability of a switch to outsoucing geneally inceases and the expected time to making the switch geneally deceases. Unde Regime 2 we find the opposite behavio; as demand volatility inceases the pobability of a switch to outsoucing geneally deceases and the expected time to making the switch geneally inceases. Thus, as economic conditions become moe volatile, ou models pedict geate levels of outsoucing of sevice pocesses having the cost stuctue of Regime 1, and lowe levels of outsoucing of sevice pocesses having the cost stuctue of Regime 2. We find that these pedictions continue to hold when the fim has the flexibility to backsouce an outsouced pocess. This conclusion efines and adds new insights into an ealie esult on the elationship between volatility and the hysteesis band in a diffeent setting. Kogut and Kulatilaka (1994) and Kouvelis et al. (2001), fo example, examine the impact of exchange ate volatility on owneship stuctues and find that the hysteesis band is inceasing in exchange ate volatility. In these studies, the inceasing hysteesis band is associated with inceasing pesistence of the cuent soucing stategy, o in othe wods, inceasing oganizational inetia. We, too, find that the hysteesis band is inceasing in volatility unde both egimes; the optimal demand theshold tiggeing a switch to outsoucing deceases in demand volatility unde Regime 1 and inceases in demand volatility unde Regime 2. Howeve, what we also find that is new is that unde Regime 1 the pobability of hitting the optimal theshold defining the hysteesis band is inceasing in volatility, indicating that oganizational inetial is actually deceasing in demand volatility. The esult suggests that it is impotant fo manages to account fo the natue of the cost stuctue when consideing how the attactiveness of outsoucing changes unde scenaios of futue high o low volatility. A second conclusion is that the value of backsoucing flexibility is moe significant unde Regime 1 than Regime 2. In this light, the inclusion of backsoucing flexibility should be a highe pioity fo sevice pocesses with the cost stuctue of Regime 1. This holds paticulaly tue in high gowth makets, whee the flexibility to educe cost unde Regime 2 by binging back the sevice pocess in-house adds elatively little value. The last conclusion is that thee is a elationship between volatility and the value of flexibility which diffes fom conventional

11 282 M. Benaoch et al. / Euopean Jounal of Opeational Reseach 219 (2012) wisdom and ealie esults. Ealie eseach points out that the highe the demand volatility the highe the value of flexibility (Alvaez and Stenbacka, 2007; Lu and Van Mieghem, 2009; Van Mieghem, 1999; Van Mieghem, 2003; Van Mieghem and Rudi, 2002). We show that the incemental value fom incopoating additional flexibility that allows backsoucing an outsouced pocess can be deceasing with highe demand volatility. This esult occus unde Regime 1 whee highe demand volatility inceases the likelihood of a switch to outsoucing and, at the same time, inceases the pobability that the outsouced pocess will not emain viable in-house if demand dops to a sufficiently low level. This inceasing pobability of sevice obsolescence mitigates the benefit of backsoucing flexibility, even to the point whee the net value added fom the backsoucing flexibility begins to decease. A manage must be caeful not to assume that inceasing volatility necessaily inceases the attactiveness of investments to incease flexibility. With all this said, ou models ae stylized epesentations of eality that ely on a key assumption that may limit the applicability of ou conclusions. The assumption elates to the infinite time hoizon and the fact that the poblem paametes ae stable ove the time hoizon. Unde a shot poblem hoizon o non-stable paametes ove time, the conclusions may change. Investigating the influence of changes in both these assumptions and an empiical evaluation of ou pedictions ae wothy topics fo futue eseach. Moeove, ou models do not conside the outsoucing vendo s pespective. Based on ou esults, the patten of client fim outsoucing behavio can clealy lowe the vendo s pospect of getting the client s business, the pofit it can geneate even if the client decides to outsouce, and the benefit fom beaing the costs of making contact flexibility options available to the client. It is woth examining what stategies could help the vendo modulate the client s outsoucing behavio. Would chaging a lowe subsciption fees pe sevice unit outsouced induce the client to outsouce ealie and incease the vendo s pofit? Would both the vendo and client benefit moe fom the flexibility to switch to flat-fee picing o to tieed-picing, fo example, instead of the flexibility to backsouce? Examining such questions could suggest stategies that the vendo could use to induce clients to outsouce ealie and stay outsoucing longe, while at the same time inceasing the vendo and client benefits. Appendix. 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