Quality and Pricing for Outsourcing Service: Optimal Contract Design

Transcription

1 Qulity nd Pricing for Outsourcing Srvic: Optiml Contrct Dsign Smr K. Mukhopdhyy Univrsity of Wisconsin-Milwuk Co-uthor: Xiowi Zhu, Wst Chstr Univrsity of PA Third nnul confrnc, POMS Collg of Srvic Oprtions London usinss School July 1 & 13, 007 1

2 Introduction Why outsourc? Rduc oprtionl costs Us othr firm s comptncy Outsourcing mnufcturing : for dcds Srvic outsourcing: usinss procss outsourcing PO, Informtion tchnology outsourcing ITO cll cntr outsourcing Third nnul confrnc, POMS Collg of Srvic Oprtions London usinss School July 1 & 13, 007

3 Introduction Cll cntr onshor outsourcing Willow CS Mirmr, FL hndls clls for Offic Dpot. Alpin Accss Goldn, CO hndls clls for Flowrs.com. Cll cntr offshor outsourcing In 00, Dlt Air Lins outsourcd cll cntr srvic with n xpctd svings of $6 million in 003. Othrs, lik Amricn Exprss, Citibnk, Sprint, Hwltt Pckrd, Dll, nd IM. Third nnul confrnc, POMS Collg of Srvic Oprtions London usinss School July 1 & 13, 007 3

4 Introduction usinss procss outsourcing PO A.T. Krny Inc. prdicts tht 500,000 finncil-srvics jobs will go offshor by 008. Forrstr Rsrch prdicts tht som 79,000 lgl jobs, totling $5.8 billion in wgs, would b snt offshor by 015. Informtion tchnology outsourcing ITO McKinsy forcsts IT srvics nd bck-offic work in Indi will swll to $57 billion nnul xport industry mploying 4 million popl by 008. Third nnul confrnc, POMS Collg of Srvic Oprtions London usinss School July 1 & 13, 007 4

5 Introduction Outsourcing is not troubl fr solution. A mjor concrn is th ulity of outsourcing. Dll stoppd outsourcing th tchnicl support cll cntr, bcus of svr ulity problm Outsourcing dcision is composit of pric, ulity nd othr rltd fctors. W ddrss th issu of srvic outsourcing using cll-cntr s n xmpl. Third nnul confrnc, POMS Collg of Srvic Oprtions London usinss School July 1 & 13, 007 5

6 Litrtur Survy Mny of th pprs in th cll cntr modl th cll cntr s uu, s rviwd by Gn t.l. 00. Aksin, Vricourt nd Krsmn 004 study two typs of cll cntr outsourcing contrcts: volumbsd pr-cll pricing nd cpcity-bsd prgnt-pr-hour contrct. Extnsiv rsrch hv bn crrid out in th r of ulity, lik Kouvlis nd Mukhopdhyy Most rsrchs discuss th ulity undr full informtion. Third nnul confrnc, POMS Collg of Srvic Oprtions London usinss School July 1 & 13, 007 6

7 Modl Scnrio Supplir Q Profit functions For th supplir: π S p c Q or For th buyr: π p or π π S uyr Cll volum function p b + Q Dcision vribls For th buyr: untity of th cll nd cut-off point For th supplir: Q ulity of th clls Third nnul confrnc, POMS Collg of Srvic Oprtions London usinss School July 1 & 13, 007 7

8 Th contrcts Two scnrios studid Contrct- undr full informtion F th buyr knows. Contrct- undr symmtric informtion A th buyr dos not know, knows prior cumultiv distribution F with dnsity function f, dfind on [, ]. Third nnul confrnc, POMS Collg of Srvic Oprtions London usinss School July 1 & 13, 007 8

9 Th contrcts undr full informtion F Full informtion- buyr knows Following Stcklbrg mov: uyr - ldr, nnouncing first; Supplir -followr, nnouncing Q ftr tht. Third nnul confrnc, POMS Collg of Srvic Oprtions London usinss School July 1 & 13, 007 9

10 Third nnul confrnc, POMS Collg of Srvic Oprtions London usinss School July 1 & 13, Th contrcts undr full informtion F Rsult 1: Th uilibrium untity, ulity, nd pric undr F: whr binding Th corrsponding profits t uilibrium r givn s: whr nd b F b Q F p F + + F b π π 4 4 π π b F π 4 π F F F S c + b

11 Th contrcts undr full informtion F Rsult : F is incrsing in, b nd nd dcrsing in nd ; Q F is incrsing in, b nd nd dcrsing in ; p F is incrsing in nd ; F π is th incrsing convx function in. Rsult 3: Th optiml lvl of for th supplir * 3 + 4c b + 3 4c Third nnul confrnc, POMS Collg of Srvic Oprtions London usinss School July 1 & 13,

12 Th contrcts undr symmtric informtion A Asymmtric informtion- buyr dosn t knows Following Stcklbrg mov: uyr - ldr, nnouncing first; Supplir -followr, nnouncing Q ftr tht. Third nnul confrnc, POMS Collg of Srvic Oprtions London usinss School July 1 & 13, 007 1

13 Third nnul confrnc, POMS Collg of Srvic Oprtions London usinss School July 1 & 13, Th contrcts undr symmtric informtion A Rsult 4: Th buyr s optiml contrct undr A. All pirs of A, A stisfy th following utions: f b f b c d f F b π 0 + s c b π

14 Third nnul confrnc, POMS Collg of Srvic Oprtions London usinss School July 1 & 13, Rsult 4 continud If, th uilibrium untity, ulity, nd pric undr A: A b F d f A A A Q A A b f p +

15 Third nnul confrnc, POMS Collg of Srvic Oprtions London usinss School July 1 & 13, Th contrcts - Anlysis of F nd A Rsult 5: A < F if nd only if b Q F >Q A if nd only if < d f F 1 1 < F d f b E b.

16 umricl Exprimnts Th numricl vlus usd in th xprimnt r givn in th nxt tbl 1. b c π π S W ssum Uniform distribution for with f nd. F Third nnul confrnc, POMS Collg of Srvic Oprtions London usinss School July 1 & 13,

17 umricl Exprimnts Profit t A F Profit t SA SF Figur. vrsus th buyr s profit. Figur 3. vrsus th supplir s profit Third nnul confrnc, POMS Collg of Srvic Oprtions London usinss School July 1 & 13,

18 umricl Exprimnts Rng of t. Figur 7. th cut-off point vrsus widnss rng of Third nnul confrnc, POMS Collg of Srvic Oprtions London usinss School July 1 & 13,

19 umricl Exprimnts Profit SF F SA A Figur 8. Profit vrsus th bs dmnd Third nnul confrnc, POMS Collg of Srvic Oprtions London usinss School July 1 & 13,

20 Conclusion Our modl uss cll cntr s n xmpl to study outsourcing pric nd ulity issus. Th modl cn b pplid to othr outsourcing scnrio. Th modl cn b xtndd to mny diffrnt dirctions. W could includ bonus nd pnlty for. th high nd low ulity in th contrct, using nonlinr pricing schm. Third nnul confrnc, POMS Collg of Srvic Oprtions London usinss School July 1 & 13, 007 0