The Efficiency-Quality Trade-Off of Cross-Trained WorkersMotivationAgendaOverviewModel FormulationThe Service Process ModelThe Service Process Model StatisticsTenure ProcessTenure Process StatisticsService Quality and the Value to the Firm of Worker ExperienceService Quality and the Value to the Firm of Worker ExperienceService Quality and the Value to the Firm of Worker ExperienceObjective FunctionApproximating the Average QualityApproximation ErrorSimulation ResultsWhen is the Optimal Staff Mix Important?Which Extreme System is Best?Optimal Staffing ConfigurationsSystem Performance - ProfitSystem Performance - QualityConclusionsShortcomings / Future WorkCritiqueDiscussionThe Efficiency-Quality Trade-Off of Cross-Trained WorkersEdieal J. Pinker • Robert A. ShumskyWilliam E. Simon Graduate School of Business AdministrationUniversity of RochesterRochester, New YorkManufacturing & Service Operations ManagementWinter 2000Presented by: Dan McCarthyThis summary presentation is based on: Pinker, Edieal J., and Robert A. Shumsky. "The Efficiency-Quality Trade-Off of Cross-Trained Workers." Manufacturing and Service Operations Management 2, no. 1 (2000).Motivation2Generalists vs. Specialists in MedicineLabor and Delivery Story• Why wasn’t there an obstetrician on duty?• Staffing flexible servers (i.e. generalists) is more efficientgiven heterogeneous customers, all else being equal• What about cost?• What about speed of service?• What about quality of service?Call CentersOther fields?Agenda3• Overview• Model Formulation– Service Process Model– Tenure Process– Service Quality and the Value to the Firm of Worker Experience• Service Process Approximation Method• Numerical Experiments– General Model Testing and Insights– Case Study• Conclusions• Critique• Questions / DiscussionOverview4Goal: Study the trade-off between the cost efficiency provided by cross-trained (or generalist) workers and the experience based quality provided by specialistsDevelop a general model that integrates:– Queuing system model that includes multiple server types– Model of an individual worker’s career path (tenure)– Model of experience-based learning• Output of system = Revenue (varies with the quality of service)• System Performance = Gross Profits (varies with both revenue andcosts)Links managerial decisions about staffing policies and worker specialization with worker learning curves, system costs and service qualityModel Formulation5• The Service Process Model– Who gets served?– By whom?• Employee Tenure Model (Tenure Process)– Experience of Servers• Experience-Based Learning Model of Service Quality– Experience Æ Service Quality– Service Quality Æ Value to the Firm (Revenue)• Objective Function– Expected Profit of the FirmThe Service Process Model6(See Figure 1 on page 34 of the Pinker and Shumsky paper)• Focuses on quality of service [ f(server experience) ]– Traditional focus is on waiting time or time in system• Assumes that service standards (e.g. % customers served) are set exogenously– Treated as constraints in the model• Models the SP structure as a “loss system” (i.e. queuing not allowed)– Above routing scheme achieves the highest server utilization7The Service Process Model StatisticsThroughput:R = RAA+ RBB+ RAF+ RBF(Erlang’s Loss Formula , Approximation Method)Server Utilization:)/(,,,FFAFAFBFAFBBAANRµρρρρρ=(Little’s Law)Tenure Process8• Tenure defined• Model tenure as a random variable drawn from a mixed exponential probability distribution(See Figure 2 on page 35 of the Pinker and Shumsky paper))/(211λλλ+=p32λλ>• Career path model – can be modeled as states of a continuous time Markov chain• Time a worker stays in a given stage is exponentially distributed• What is the expected length of tenure?Tenure Process Statistics9• x = worker tenure of a worker{}ttxeetGtx3213211)(32132)(Prλλλλλλλλλλλλ−+−−++−+−==>⎟⎟⎠⎞⎜⎜⎝⎛++=312111)(λλλλxE• y = time worked][)()(xEtGtgxy=10Service Quality and the Value to the Firm of Worker ExperienceHow does worker experience translate into monetary value to the firm?Worker Experience Service Quality Firm Revenue1)(nLbbQ =Experience-based Service Quality11Service Quality and the Value to the Firm of Worker ExperienceHow does worker experience translate into monetary value to the firm?Worker Experience Service Quality Firm Revenue2)(nMqqV =Value of Increased Quality12Service Quality and the Value to the Firm of Worker ExperienceHow does worker experience translate into monetary value to the firm?Worker Experience Service Quality Firm Revenue1)(nLbbQ =Experience-based Service Quality2)(nMqqV =Value of Increased QualityRevenue generated by a worker with b time units of experience in a particular tasknKbbW =)(21,2nnnMLKn==Objective Function13Maximization of Expected Gross Profits[])(RevenueijijijbWER∑∑=Where: i = A or Bj = A, B or FCost = cANA+ cBNB+ cFNFExpected Profit of the firm: Z = Revenue - CostLabor OnlyApproximating the Average Quality14[][][]ybEEK)W(bEnijyijij=conditioning the probability distribution of bijon yLink the models for tenure, learning and serviceWhen the expected time it takes to provide service (1/µj) is significantly shorter than the time on the job (y), then:where ρijis the long-run fraction of time that a j worker spends on a type i job.[]nijnijypybE )(by edapproximatclosely is ASTA Property (Melamed and Whitt, 1990):Intensity of the arrival process is independent of the tenure of servers Æarrivals to the process see time averages Æ the distribution of y is gy(t)[]⎭⎬⎫⎩⎨⎧++−•++−+Γ+=≈++∞∫131121322113322130)()()()()1()()()(nnnijijynijijijnKdttgtK)W(bEλλλλλλλλλλλλρλλλρApproximation Error15[][]1)()()( −⎥⎥⎦⎤⎢⎢⎣⎡Υ⎟⎟⎠⎞⎜⎜⎝⎛Υ=ΥΥ−Υ=ΥnijijnijnijnijbEbEρρρεLemma 1:1lim=⎥⎥⎦⎤⎢⎢⎣⎡Υ⎟⎟⎠⎞⎜⎜⎝⎛Υ∞→nΥbEρImplies:0)(lim=Υ∞→εΥHow long does it take for the true expectation and the approximation to converge?(i.e. How long does a server have to be on the job for the approximation to be close enough?)Simulation Results16(See Figure 3 on page 39 of the Pinker and Shumsky paper)Impact of Staff Mix on Cost17Cost / Customer:BAFFBBAANcNcNcλλ+++(See Figure 4 on page 41 of the Pinker and Shumsky paper)Impact of Staff Mix on Quality18[]BAijijijbWERλλ+∑∑)(Quality / Customer:(See