AUTHOR COPY. The co-production approach to service: a theoretical background

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1 Journal of the Operational Researh Soiety (213), Operational Researh Soiety td. All rights reserved /13 The o-prodution approah to servie: a theoretial bakground TH Trinh 1, V Kahitvihyanukul 1 and DB Khang 2 1 Shool of Engineering and Tehnology, Asian Institute of Tehnology, Pathumthani, Thailand; and 2 Shool of Management, Asian Institute of Tehnology, Pathumthani, Thailand The paper develops a theoretial bakground on the o-prodution approah as an extension of operations management priniples, in whih o-prodution funtion assumes well-defined funtional form with the input presene of both firm and ustomers. The o-prodution approah not only views a ustomer as a o-produer, but also onduts strategi trade-offs between a firm and ustomers in servie systems. Moreover, the value and the proess of value o-reation are also explored under the o-prodution approah. The experimental study with a hypothetial servie system indiates that the o-prodution funtion is feasible under eonomi and institutional onsiderations, and the oprodution approah generalizes both the firm approah and the ustomer approah. Furthermore, the o-prodution approah reates many rih opportunities for future researh on servie operations management. Journal of the Operational Researh Soiety advane online publiation, 27 February 213 doi:1.157/jors Keywords: o-prodution approah; o-prodution funtion; value o-reation; strategi trade-off; servie system Introdution Servie plays an important role in a nation s eonomy, with inreasing ontributions to Gross Domesti Produt (GDP). In developed ountries, about 7% of GDP omes from servie setors, whih employ about 8% of the total labour fore. In addition, an emerging trend towards the integration of goods and servie into a single ustomer offering implies that the prodution means the reation of a ombined produt of goods and servie (Johansson and Olhager, 26). Even many researhers have attempted to develop servie typologies, but theory and pratie still remain disonneted due to the lak of a theoretial bakground for servie operations management. Customers have always been the prime fous for marketing ativity, but the way that the servie firms view this relationship is hanging. Kotler (1991) notes that a shift of paradigm is emerging within marketing theory where the fous in the future will be on long-term relationships instead of on short-term exhange transations. The shift in attitude hanges from making a sale to gaining a lient, and to probably gaining a o-produer. Moreover, reent developments in marketing thought and pratie highlight the opportunities that servie o-prodution provides for value Correspondene: TH Trinh, Industrial and Manufaturing Engineering, Shool of Engineering and Tehnology, Asian Institute of Tehnology, P.O. Box 4, Klong uang, Pathumthani 1212, Thailand. s: Trinh.Hong.Truong@ait.a.th; hongtrinh@vnn.vn o-reation. The shift towards o-prodution as a means to enhane pereptions of value seems entirely reasonable, with ustomers reating value with the firm as opposed to the firm reating value for ustomers (Prahalad and Ramaswamy, 24; Vargo and ush, 24). In literature, the role of the ustomer as the o-produer has a long history in servie operations management. Whitaker (198) proposed o-prodution models used in the field of publi poliy management where itizen partiipation is ommonly viewed as attempts to influene the formulation of publi poliy. Globerson and Maggard (1991) reognized the importane of integrating the prodution role of ustomers into the design of servie delivery systems. Moreover, engnik-hall et al (2) argued that the ustomers, as important resoures for the firm, an atively partiipate in the firm s ativities as servie o-produers. Vargo and ush (24) stated that a ustomer is always a o-produer (Gro nroos, 1978; Parks et al, 1981; Wikstro m, 1996; Ojasalo, 23) who partiipates in value reation through o-prodution. ater, Vargo and ush (28) hanged this view to ustomers as value o-reators. Meanwhile, firms produe a provision of resoures labelled value failitation that an be regarded as a prerequisite or foundation for value reation (Gro nroos and Ravald, 211). The vagueness and the omplexity of value onept result in a limited understanding of the proess of value o-reation and a lak of analytial methods for value o-reation in servie systems.

2 2 Journal of the Operational Researh Soiety By ombining insights gained from prior literature with perspetive of o-prodution, the paper develops a theoretial bakground on the o-prodution approah that provides general priniples on behaviours of firm and ustomers in servie systems. The o-prodution approah views ustomers as o-produers and onduts strategi trade-offs between firm and ustomers in servie systems. The paper also provides strategi views for servie delivery system synthesizing the firm approah, the ustomer approah, and the o-produer approah. As a result, multi-objetive models are developed to identify strategi trade-offs between firm and ustomers. An experimental study is arried out to ompare the proposed o-prodution approah with the traditional ones, and to evaluate the o-prodution funtion under eonomi and institutional onsiderations. f( ) f * 1 f * f * 2 Feasible region Figure 1 F The traditional approah F f * 2 f * 1 The o-prodution approah Feasible region g * 2 g * g * F 2 g( ) U * 1 U * 2 U Eonomi onstraints under different approahes. inreasing returns to sale α + β + γ > 1 F α + β + γ > 1 Co-prodution funtion Co-prodution ours as a result of tehnologial, eonomi and institutional influenes (Parks et al, 1981). Tehnologial onsideration determines whether there are o-prodution funtions where both firm and ustomer ativities ontribute to the output. Meanwhile, eonomi and institutional onsiderations determine whether there exist effetive solutions under the o-prodution funtion. Co-prodution involves a mixing of the produtive efforts of firm and ustomers that may our diretly through oordinated efforts in the same prodution proess, or indiretly through related efforts of firm and ustomers (Parks et al, 1981). Aording to Parks et al (1981), two ideal types of relationships an be stipulated as o-prodution funtional form of both firm inputs and ustomer inputs. The first o-prodution funtion form of Q ¼ a f( )þ b g( ) indiates that firm inputs and ustomer inputs are substitutes. The seond o-prodution form of funtion Q ¼ f a ()þbg b ( ) indiates that firm and ustomer inputs are interdependent. The funtions f( ) and g( ) are portions of firm inputs and ustomer inputs, respetively. When the o-prodution relationship is substitution, firm inputs and ustomer inputs have independent influene on servie outome. The view of o-prodution approah adopts that both firm inputs and ustomer inputs have influene on servie outomes interdependently, and substitute relationship is used to relax strit interdependene in servie prodution. In addition, prodution is always subjeted to eonomi onstraints. For the traditional approah, eonomi onstraint is a ost funtion under the form of F ¼ w f f( )þ w g g( ), where w f isaunitostof firm inputs and w g is a unit ost of ustomer inputs. Sine the ost funtion is regarded as eonomi onstraint, the traditional approah identifies an optimal ombination of (f, g ). For the o-prodution approah, eonomi α + β + γ < 1 dereasing returns to sale Figure 2 Q α + β + γ < 1 Eonomies of sale and o-prodution funtion. onstraint is a trade-off between ost funtion and utility funtion, in whih the utility funtion is the total ustomer utility under the form of U ¼ w Q Q( ) w g g( ).The o-prodution approah identifies various effiient ombinations of (F, U ). Figure 1 illustrates eonomi onstraint under the traditional approah and the o-prodution approah. While the traditional approah onsiders eonomi onstraint through a trade-off between firm inputs and ustomer inputs, the o-prodution approah onsiders eonomi onstraint through an objetive trade-off between firm and ustomers. If there exists the orrelation between eonomy of sale and o-prodution funtion, as in Figure 2, o-prodution is then eonomially feasible. In addition to this, if the o-prodution funtion is onsidered under additional onstraints with market and non-market arrangements, and there exist non-dominated feasible solutions, o-prodution is institutionally feasible. There is no given mathematial funtional form for a prodution funtion. The best known of these funtional forms is the so-alled Cobb Douglas prodution funtion, whihhastheform: Q ¼ fðk; HÞ ¼ A K a H b ð1þ where K is firm apital and H is firm employee, and A, a, and b are predetermined parameters. The popularity of the Cobb Douglas prodution funtion stems from a number of mathematial advantages in onnetion with empirial analyses. Sine ustomer is treated as o-produer, in addition to firm apital (K ) and firm employee (H ), ustomer input () should be inluded in the following U

3 TH Trinh et al The o-prodution approah to servie 3 o-prodution funtion. Q ¼ fðk; H; Þ ¼ A K a H b g ð2þ where A is the average or mean produtivity; Q is the servie outome; K, H, and are firm apital, firm employee, and ustomer input, respetively; and a, b, andg are the output elastiities of input fators. The oprodution funtion yields onstant returns to sale with a þ b þ g ¼ 1; inreasing returns to sale with a þ b þ g41; and dereasing returns to sale with a þ b þ go1. The most stringent assumption in the Cobb Douglas prodution funtion is that inputs and outputs are homogeneous. Meanwhile, heterogeneity is one of the important harateristis of servie, in whih heterogeneity in proessing and outome is primarily aused by heterogeneity in proess inputs, espeially ustomer inputs (Sampson, 21). Sine prodution unit in servie is a proess with heterogeneity (instead of a produt with homogeneity as in manufaturing), proess inputs and outputs are defined by physial units with assigned pries. The heterogeneous proesses an be transformed into homogeneous prodution proesses that an expand to multiple inputs/outputs proess. Co-prodution approah The traditional approahes develop servie delivery strategy based upon either the firm behaviour or the ustomer behaviour. The o-prodution approah develops servie delivery strategy that simultaneously onsiders behaviours of firm and ustomers so as to maximize total utility and minimize total ost. Customer approah The ustomer approah assumes no hanges in poliies about firm apital (K ) and firm employee (H ). Customers intend to alloate resoure (ustomer input and servie output Q )soastomaximizetheirutility. Consider a ustomer that an use a multi-hannel servie delivery system onsisting of t different servie hannels, indexed by (¼1,..., t), to ondut servie transation. w is unit ost of ustomer inputs ( i )andw S is the unit value of servie outputs (Q i ). Thus, u i is utility of ustomer i in using servie at servie hannel. where Q is total outputs reeived by ustomers in using servie hannel, andq ¼ P n i ¼ 1Q i. is total inputs of ustomers in using servie hannel, and ¼ P n i ¼ 1 i. This problem yields a set of first-order onditions in whih the marginal produt of ustomer input equals the unit ost of ustomer input (w ): ¼ j qq ¼ w q w S ð5þ Substituting the form of the prodution funtion for Q and differentiating with respet to ustomer input yields the first-order ondition: ðqq =q Þ¼A g g 1 K a Hb, whih implies an optimal ustomer input hoie of : ¼ 1 1 g A g K a H b w S w ð6þ Substituting this bak into the original o-prodution funtion yields: Q ¼ A 1 1 g K a 1 g b 1 g H w 1 w 1 g S g g 1 ð7þ Thus, ustomers will utilize eah servie hannel to produe servie output (Q ) as a funtion of produtivity of input A at servie hannel, unit ost of ustomer input w, unit value of the servie w S, and the firm s inputs in the servie hannels, (K, H ). Firm approah The firm approah assumes that the hanges of firm apital (K ) and firm employee (H ) have influene on servie output (Q ), and the firm may vary both so as to minimize total ost. The o-prodution funtion with firm inputs and ustomer inputs an be expressed as follows: Q ¼ fðk ; H ; Þ ¼ A K a H b g ð8þ By using the least-ost ombination of prodution inputs, ost funtion F(Q ) of eah servie hannel an be determined as follows: FQ ð Þ ¼ w K K þ w H H þ w ð9þ u i ¼ w S Q i w i ; 8 ¼ 1;...; t ð3þ where w and w S are predetermined parameters. Total utility is the sum of the utility of all ustomers (i ¼ 1,...,n) obtained in all servie hannels. Therefore, total utility (U) is given by: U ¼ Xn X t i¼1 ¼1 u i ¼ Xt ¼1 ðw S Q w Þ ð4þ where denotes index of servie hannel ( ¼ 1,...,t). Unit pries of firm apital and firm employee are w K and w H, respetively. w is a unit ost of ustomer input. Find the values of K, H,,andl that minimize the agrangian: GQ ð ; K ; H ; Þ ¼ w K K þ w H H þ w þ l ½Q fðk ; H ; ÞŠ ð1þ G K ¼ w K l f K ¼ ð11þ

4 4 Journal of the Operational Researh Soiety G H ¼ w H l f H ¼ G ¼ w l f ¼ ð12þ ð13þ G l ¼ Q fðk ; H ; Þ ¼ ð14þ From Equations (11), (12), and (13), we have: Customer approah Total Utility U Max t U = Σ (w S Q w )?=1 K, H : Parameters : Variables Firm approah Total Cost F Min t F = Σ (w K K +w H H +w )?=1 : Parameters K, H : Variables w w K ¼ f f K ¼ g a K ) K ¼ a w g w K ð15þ Co-produer? approah w w H ¼ f f H ¼ g b H ) H ¼ b w g w H ð16þ Substituting K and H into the o-prodution funtion, we get: Q ¼ A a w a b w b g g w K g w H ð17þ Thus, the firm produes servie output (Q )asafuntion of produtivity of input (A ), ustomer inputs ( ), and unit osts of prodution inputs (w K,w H,w ). Co-produer approah The o-produer approah requires servie delivery strategy to ahieve a strategi trade-off between firm and ustomers. The o-produer approah assumes that all prodution inputs (K, H, ) will hange so as to maximize total utility and minimize total ost. Figure 3 presents approahes for servie delivery strategy. The following utility-ost model is used to determine non-dominated feasible solutions of (K, H, )thatsimultaneously maximize total utility and minimize total ost. The utility-ost model: Min Subjet to Max F ¼ Xt U ¼ Xt ¼1 Q ¼ A K a ¼1 8K ; H ; ; ðw S Q w Þ ðw K K þ w H H þ w Þ Hb g ; 8 ¼ 1;...; t 8 ¼ 1;...; t where is the index of servie hannel ( ¼ 1,...,t) and K, H, are deision variables. Sine all prodution inputs (K, H, ) are hanged in the utility-ost model, the o-prodution approah extends for both the ustomer approah and the firm approah. Moreover, the o-prodution approah provides a bakground for Figure 3 exploiting the proess of value o-reation in servie systems. The onept of value has a very long history in eonomi and philosophial thought that attempt to explain two key questions inluding why goods and servies are pried as they are, how the value of goods and servies omes about. Traditional models of value reation fous on the firm s output and prie. Firms reate value embedded in goods or servie and the value-added results from enhaning or inreasing attributes of goods and servies. However, the view of value reation shifts towards value o-reation. Customers are always value o-reators in whih firms an be viewed as reators of value foundation through a value failitation proess (Vargo and ush, 28). When ustomers use firm resoures and add their resoures and skills, the value potential of the resoures is developed into value-in-use. Total utility and total profit are alulated as follows: Total utility : U ¼ Xt Total profit : p ¼ Xt ¼1 ¼1 ððv p ÞQ w Þ ð18þ ðp Q ðw K K þ w H H ÞÞ ð19þ where v is value-in-use and p is value-in-exhange. Sine total value-added (VA) is sum of total utility (U ) and total profit (p), the formula of the total value-added an be expressed as: Total value added : VA ¼ Xt v Q Xt ¼1 Total Utility U Max t?=1 U = Σ (w S Q w ) Total Cost F Min t?=1 F = Σ (w K K +w H H +w ) K, H, : Variables Approahes for servie delivery strategy. ¼1 ðw K K þ w H H þ w Þ ð2þ

5 TH Trinh et al The o-prodution approah to servie 5 From the above formula, total value-added (VA) isthe differene between total value-in-use ( P t ¼ 1v Q )and total ost ( P t ¼ 1(w K K þ w H H þ w )). From the value o-reation perspetive, the proess of value o-reation is driven by value-in-use, but monitored by value-in-exhange. The utility-profit model is used to ondut behaviours of firm and ustomers under hanges in output, prie, and value in servie systems. The utility-profit model: Max Max U ¼ Xt p ¼ Xt ¼1 ¼1 ððv p ÞQ w Þ ðp Q ðw K K þ w H H ÞÞ osts of firm apital (w K ) and firm employee (w H ) are 1 and 3, respetively. The experiment uses MOPSO (Multi-Objetive Partile Swarm Optimization) algorithm from ET-ib: Objetive ibrary for Evolutionary Tehniques (Nguyen et al, 21) to identify strategi trade-offs (Pareto fronts) between firm and ustomers. Key parameters of MOPSO algorithm used in experiment are as follows: K Population size (number of partiles) is 5 partiles. K Personal/global/loal/neighbour aeleration onstants ( p / g / l / n ) are 1/1/1/1. K Number of iteration is 5. K The maximal/minimal inertia weights (w max /w min )are.9/.4. Subjet to Q ¼ A K a 8K ; H ; ; Hb g ; 8 ¼ 1;...; t 8 ¼ 1;...; t By better understanding of ustomers value reation, the firm may effetively provide resoures to support that value reation. Experimental study Experiment design The experiment is to ompare the o-prodution approah with the traditional approahes, and to evaluate the o-prodution funtion under eonomi and institutional onsiderations. The experiment is arried out via a hypothetial singlehannel servie system ( ¼ 1), in whih the o-prodution funtion is assumed to be a well-defined funtion with mean produtivity of 1 (A ¼ 1) and onstant returns to sale (a þ b þ g ¼ 1) with a ¼ b ¼ 2g. For a servie proess, prodution inputs and servie outome are defined by physial units with assigned pries. Unit ost of ustomer inputs (w ) and unit value of servie outome (w S ¼ v p ) are assigned by 2 and 5, respetively, in whih value-in-use (v ¼ 2) and value-in-exhange (p ¼ 15). In addition, unit Analysis and results Experiment 1 is to ompare the o-prodution approah with the traditional approahes. The experiment is performed for the ustomer approah, the firm approah, and the o-produer approah using the same hypothetial singlehannel servie system. The hypothetial servie system assumes urrent prodution status with (K, H,, Q ) ¼ (25, 25, 25, 25), in whih o-prodution funtion Q ¼ A K a H b g with assumptions of A ¼ 1 and a ¼ b ¼ 2g ¼.4, total utility (U )andtotalost(f) are 75 and 375, respetively. Table 1 shows prodution parameters and strategi approahes. The ustomer approah requires servie delivery strategy to maximize total utility (U ¼ 84.9) upon ustomer behaviour. This approah assumes no hanges in poliies about firm apital (K ¼ 25) and firm employee (H ¼ 25). Prodution apaity is set up as total ustomer inputs ( ¼ 1.5) and total servie outomes (Q ¼ 21.2). ikewise, the firm approah assumes no hanges in ustomer inputs ( ¼ 25). There are only hanges in firm apital (K ¼ 1.) and firm employee (H ¼ 33.3) that minimize total ost (F ¼ 25). Figure 4 illustrates different approahes for servie delivery strategy. The Pareto frontier is presented for non-dominated feasible solutions from the o-produer approah. Sine the o-produer model assumes that all Table 1 Current system and strategi approahes Channel strategy Unit ost/value Current system Customer approah Firm approah Firm apital (K ) w K = Firm employee (H ) w H = Customer input ( ) w = Servie outome (Q ) w S = Total utility (U) Total ost (F)

6 6 Journal of the Operational Researh Soiety prodution inputs (K, H, ) are allowed to be hanged within an objetive trade-off between total utility and total ost, the o-prodution approah provides better solutions in apaity planning than the traditional approahes sine it provides a wider range of non-dominated feasible solutions. Experiment 2 is to evaluate the o-prodution funtion under eonomi onsiderations. If the o-prodution funtion has eonomies of sale, it is eonomially feasible. The experiment is designed with respet to three ases of eonomies of sale inluding inreasing returns to sale (a þ b þ g41), onstant returns to sale (a þ b þ g ¼ 1), and dereasing returns to sale (a þ b þ go1). The experiment analysis will ondut with different values of these parameters (a, b, g). Figure 4 Traditional approahes and o-prodution approah. Average Cost (F) Figure 5 illustrates the relationship between average ost and total output under various eonomies of sale. The relationship represents the growth rates of total output and total ost. Inreasing returns to sale indiate that growth rate of total output is greater than the growth rate of total ost. Meanwhile, dereasing returns to sale indiate that growth rate of total output is smaller than that of total ost. As a result, average ost may tend to inrease in ase of dereasing returns to sale or derease in ase of inreasing returns to sale along with output inreasing. For onstant returns to sale, the growth of output and ost are almost at the same rate. Thus, average ost seems to be onstant with any levels of total output. The experimental result reveals that eonomies of sale of the o-prodution funtion depends on parameters (a, b, g) similar to that of the traditional prodution funtion. Figure 6 presents Pareto frontiers under eonomies of sale of o-prodution funtion. These Pareto frontiers represent trade-offs between total ost and total output/ total utility. Case 1 stands for dereasing returns to sale with a þ b þ g ¼.5, Case 2 stands for onstant returns to sale with a þ b þ g ¼ 1, and Case 3 stands for inreasing returns to sale a þ b þ g ¼ 1.5. The experimental result indiates that there is a orrelation between total ost with total output, as well as total utility under eonomies of sale. Moreover, the shape of the Pareto frontier is onave or onvex towards the origin depending on the eonomies of sale, as in Figure 7. For dereasing returns to sale, Case 11 is for a þ b þ g ¼.25, Case 12 for a þ b þ g ¼.5, and Case 13 Dereasing returns to sale Constant returns to sale Inreasing returns to sale α + β + γ =.5 Average Cost (F) Total Output (Q) Total Output (Q) Total Output (Q) Figure α + β + γ = 1 Average ost and eonomies of sale. Average Cost (F) α + β + γ = α + β + γ =.5 α + β + γ = 1 Eonomies of sale α + β + γ = 1.5 Eonomies of sale 2 Case1 Case2 Case3 2 Case1 Case2 Case Total Output (O) α + β + γ =.5 α + β + γ = 1 α + β + γ = 1.5 Figure 6 Pareto frontiers under eonomies of sale.

7 TH Trinh et al The o-prodution approah to servie α + β + γ =.25 α + β + γ =.5 Dereasing returns to sale Inreasing returns to sale α + β + γ = Case11 Case12 Case13 2 Case31 Case32 Case α + β + γ = 1.25 α + β + γ = 1.5 α + β + γ = 1.75 Figure 7 Pareto frontiers under dereasing/inreasing returns to sale. Total Profit (π) 16 2 Output=2 Output=25 Output= Figure 8 for a þ b þ g ¼.75. Sine the Pareto frontier is more onave with the lower value of parameters, total utility is less sensitive with hanges in total ost. ikewise, the higher value of parameters of inreasing returns to sale (Case 31 for a þ b þ g ¼ 1.25, Case 32 for a þ b þ g ¼ 1.5, and Case 33 for a þ b þ g ¼ 1.75), the Pareto frontier is more onvex and total utility is more sensitive with hanging in total ost. The aim of Experiment 3 is to evaluate the o-prodution funtion under institutional onsideration with institutional agreements. The following experiment is to ondut suh effets in output, prie, and value. Figure 8 presents the trade-offs with respet to three levels of output (Q ¼ 2, Q ¼ 25, Q ¼ 3). The trade-offs between total utility and total ost reveal that there are various effetive input ombinations to produe respetive Total Profit (π) Strategi trade-offs between firm and ustomers. 2 2 Prie=12 Prie=15 Prie=18 Value=18 Value=2 Value= Figure 9 Total Profit (π) Effets in prie and value on the strategi trade-off. levels of output. Meanwhile, the trade-off between total utility and total profit presents effetive input ombinations at a ertain level of output. An understanding of how the effets in the prie (valuein-exhange) and the value (value-in-use) an foster and inhibit o-prodution is important for the design of effiient servie systems. Figure 9 illustrates effets in prie to the trade-off between total utility and total profit. By inreasing the prie from p ¼ 15 to p ¼ 18, this auses an inrease in total profit and a derease in total utility. In ontrast, total profit will derease and total utility will inrease by dereasing the prie from p ¼ 15 to p ¼ 12. Meanwhile, effets in value often affet total utility rather than total profit. Figure 9 illustrates the trade-offs with different levels of value (v ¼ 18, v ¼ 2, v ¼ 22).

8 8 Journal of the Operational Researh Soiety The study result provides not only experimental evidene on the feasibility of the o-prodution funtion, but also insights on value and value o-reation under the oprodution approah that help managers make deisions on output and prie so as to maximize the value. approahes. ast, the o-prodution theory is still far from omplete, and requires various additional empirial studies to test the reality of the o-prodution approah and to suggest its shortomings to further researh and refinement. Conlusions The tradition of operations management is surely rooted in manufaturing, in whih most operations management is foused on manufaturing priniples that do not drive most servie systems. The development of the theoretial bakground on the o-prodution approah is an extension of operations management priniples, in whih the o-prodution funtion is expanded to heterogeneous and multiple inputs/outputs proesses. The o-prodution approah not only views ustomer as a o-produer with the presene of ustomer inputs, but also onduts strategi trade-offs between firm and ustomers. The strategi trade-off highlights opportunities for value o-reation and the shift towards o-prodution as a means to enhane pereptions of value seems entirely reasonable. The hypothetial servie system is proposed for the experimental study, in whih the o-prodution funtion assumes a well-defined funtional form. The experimental analysis reveals that the o-prodution approah generalizes for both the firm approah and the ustomer approah. In addition, the experiment indiates that eonomies of sale depend on parameters of the o-prodution funtion, and Pareto front is orrelated with eonomy of sale. The experimental result indiates that the o-prodution funtion is feasible under eonomi and institutional onsiderations, sine it is effiient to mix resoures from firm and ustomers to produe the servie. Even the paper ontributes a theoretial bakground on the o-prodution approah that provides general priniples in servie operations management. Some limitations remained and should be explored in future researhes. First, the o-prodution approah adopts that both firm inputs and ustomer inputs have influene on servie outome interdependently. Substitutable relationship between firm inputs and ustomer inputs should be onsidered in future researhes. Seond, measurement for ustomer input and servie outome remains a major hallenge. In fat, assessing servie outome often requires reasoning on ustomer s pereption of servie experiene, whih is far from preise, and different types of proess inputs are likely to require different measurement Aknowledgements We are grateful to anonymous referees for valuable omments, whih helped improve the overall ontents and presentation of the paper onsiderably. Referenes Globerson S and Maggard MJ (1991). A oneptual model of selfservie. International Journal of Operations and Prodution Management 11(4): Gro nroos C (1978). A servie-orientated approah to the marketing of servies. European Journal of Marketing 12(8): Gro nroos C and Ravald A (211). Servie as business logi: Impliations for value reation and marketing. Journal of Servie Management 22(1): Johansson P and Olhager J (26). inking produt proess matries for manufaturing and industrial servie operations. International Journal of Prodution Eonomis 14(2): Kotler P (1991). Philip Kotler explores the new marketing paradigm. Marketing Sienes Institute Review 1(4/5): 1 5. engnik-hall CA, Clayomb V and Inks W (2). From reipient to ontributor: Examining ustomer roles and experiened outomes. European Journal of Marketing 34(3/4): Nguyen S, Ai TJ and Kahitvihyanukul V (21). Objet ibrary for Evolutionary Tehniques ETib: User s Guide. HighPerformane Computing Group, Asian Institute of Tehnology: Thailand. Ojasalo K (23). Customer influene on servie produtivity. SAM Advaned Management Journal 68(3): Parks RB et al (1981). Customers as oproduers of publi servies: Some eonomi and institutional onsiderations. Poliy Studies Journal 9(7): Prahalad CK and Ramaswamy V (24). Co-reation experienes: The next pratie in value reation. Journal of Interative Marketing 18(3): Sampson SE (21). Understanding Servie Businesses: Applying Priniples of the Unified Servie Theory. John Wiley & Sons: New York. Vargo S and ush RF (24). Evolving to a new dominant logi for marketing. Journal of Marketing 68(1): Vargo S and ush RF (28). Servie-dominant logi: Continuing the evolution. Journal of the Aademy of Marketing Siene 36(1): 1 1. Whitaker GP (198). Coprodution: Citizen partiipation in servie delivery. Publi Administration Review 4(3): Wikstro m S (1996). The ustomer as o-produer. European Journal of Marketing 3(4): Reeived September 212; aepted Deember 212 after one revision