Managing Learning and Turnover in Employee Staffing*

Transcription

1 Maagig Learig ad Turover i Employee Saffig* Yog-Pi Zhou Uiversiy of Washigo Busiess School Coauhor: Noah Gas, Wharo School, UPe * Suppored by Wharo Fiacial Isiuios Ceer ad he Sloa Foudaio

2 Call Ceer Operaios cusomer populaio call rouig ad CSR schedulig algorihms CTI resources CSR populaio Call Cere Workshop, Cere de Recherches Mahemaiques, Uiversie de Moreal, 07/25/2004

3 CSR Plas Are Made a 3 Levels Mome-by-mome o-he-fly adjusmes of call rouig, overime, luch, breaks Week-by-week assigme of CSRs o schedules Mohly, quarerly arge saffig levels se ad hirig plas made Call Cere Workshop, Cere de Recherches Mahemaiques, Uiversie de Moreal, 07/25/2004

4 Our Hierarchical Approach Focus o high level saffig problem formulae as discree-ime dyamic program Embed lower level schedulig ad call rouig problems schedulig sofware Call Cere Workshop, Cere de Recherches Mahemaiques, Uiversie de Moreal, 07/25/2004

5 Relaed Lieraure Aggregae Plaig HMMS Model (1960) Orrbeck, Schuee, ad Thompso (1968) Griold ad Saford (1974) Eber (1976) Khoshevis ad Wolfe (1986) Gerchak, Parlar, ad Segupa (1990) Huma Resources Barholomew, Forbes, ad McClea (1991) Call Cere Workshop, Cere de Recherches Mahemaiques, Uiversie de Moreal, 07/25/2004

6 Relaed Lieraure Iveory Theory Arrow, Karli ad Scarf (1958) Veio (1965) Iglehar ad Jacque (1969) Karli (1960) ad Zipki (1989) Gerchak ad Wag (1994) Call Ceer Call Cere Workshop, Cere de Recherches Mahemaiques, Uiversie de Moreal, 07/25/2004

7 Saffig Problem Descripio Sochasic o-saioary service requireme Ucerai service capaciy: people's service capaciies chage Radom learig Radom urover Log hirig/raiig leadime Call Cere Workshop, Cere de Recherches Mahemaiques, Uiversie de Moreal, 07/25/2004

8 Service Requireme Varies by Time of day Day of week / moh Moh of year Promoio Special eves umber of calls per day day umber Call Cere Workshop, Cere de Recherches Mahemaiques, Uiversie de Moreal, 07/25/2004

9 Learig Source: Gusafso, 1982 Call Cere Workshop, Cere de Recherches Mahemaiques, Uiversie de Moreal, 07/25/2004

10 Turover Call ceers have high urover raes Turover decreases wih job eure Empirical evidece Naioal Logiudial surveys (Ligh ad Ureda 1990) AT&T service represeaives (Gusafso 1982) Theoreical explaaios loger eure implies beer ``fi" (Jovaovic 1979) repeaed searches for a beer job (Parsos 1973) Call Cere Workshop, Cere de Recherches Mahemaiques, Uiversie de Moreal, 07/25/2004

11 Oulie Model Srucural Properies of The Opimal Policy Model Deails Numerical Aalysis Call Cere Workshop, Cere de Recherches Mahemaiques, Uiversie de Moreal, 07/25/2004

12 Model: Dyamics Idices i = 1, 2,, m : employee ype = 0, 1,, T : discree ime periods Sae variables i, : ype i employee, ime period (before hirig) x : ype 1 employee hired, ime period (decisio variable) y : ype1 employee, ime period (afer hirig) y = 1, + x Call Cere Workshop, Cere de Recherches Mahemaiques, Uiversie de Moreal, 07/25/2004

13 Model: Dyamics (cod) Trasiio variables q i, ( i, ) : ype-i employees who ur over, ou of radom variable i, l i, ( i, ) : ype-i employees who lear, ou of radom variable i, q i, ( i, ) = i, qi, l i, ( i, ) = i, (1 qi, ) li, Call Cere Workshop, Cere de Recherches Mahemaiques, Uiversie de Moreal, 07/25/2004

14 Model: Coss α : discou facor h : ui hirig cos W i : per sage wage cos, ype i employee O ( y,,,...,, ; D : operaig cos 2 m icludig overime ad ousourcig coss joily covex i ) ( y,,..., ) 2, m, Call Cere Workshop, Cere de Recherches Mahemaiques, Uiversie de Moreal, 07/25/2004

15 Call Cere Workshop, Cere de Recherches Mahemaiques, Uiversie de Moreal, 07/25/2004 Dyamic Programmig Model { } = = ),..., ( ),...,, ( ) ( mi ),..., ( 1, 1 1, 1 },...,,,..., {, 2, 1, 2, 1, 1 0, 1, 1, 1,, 1, m l l q q m m i i i x m V E x O W x W hx V m m α

16 Call Cere Workshop, Cere de Recherches Mahemaiques, Uiversie de Moreal, 07/25/2004 Cosrais Subjec o he sysem dyamics: ) ( ) ( ) ( ) ( ) ( 1, 1,,,,,, 1, 1, 1, 1 1, 1, i i i i i i i i l l q y l y q y x y = = + = 1 m. < i

17 Sysem Dyamics Illusraed ype i i, demad ad coss realize q ( ) l ( ) + l ( i, i, i, i, i, i 1, i 1, ) x learig ad hirig urover hirig ime period ype 1 y y q ( y ) l ( y 1, 1, ) Call Cere Workshop, Cere de Recherches Mahemaiques, Uiversie de Moreal, 07/25/2004

18 Opimaliy of Base-Level Policy Base-Level Policy: here exis saedepede base-levels y ( 2, *,..., m, ) such ha he opimal umber o hire is x = * * y ( 2,,..., m, ) 1, if 1, < y ( 2,,..., m, 0 oherwise * ) Call Cere Workshop, Cere de Recherches Mahemaiques, Uiversie de Moreal, 07/25/2004

19 Proof Idea Covexiy of oe-period cos fucio propagaes V (,..., ) where 1, m, ( h+ W1 ) y + O( y,..., m, ) = mi h + y { } 1, + α E V+ 1( 1, + 1,..., m, + 1) 1, + 1 i, + 1 m, + 1 = (1... = (1... = (1 q q q 1, i, m, )(1 )(1 ) m, l 1, l i, ) y ) + l i, m 1, + l i 1, m 1, i 1, m W 1, i i, i= 2 Call Cere Workshop, Cere de Recherches Mahemaiques, Uiversie de Moreal, 07/25/2004

20 Proof Idea Call Cere Workshop, Cere de Recherches Mahemaiques, Uiversie de Moreal, 07/25/2004

21 Model Deails (I): Operaig Cos Fucio O (y m, ; D ) Sub-ierval: s , S D = D1 D 2 D3 Ds DS w = work schedule 1 I(w,s)=0 I(w,s)=1 Type-1 (42) Type-2 (26). work schedule w Type-3 (15) Type-4 (9). work schedule WS Call Cere Workshop, Cere de Recherches Mahemaiques, Uiversie de Moreal, 07/25/2004

22 Operaig Cos Fucio O() s = 1,, S : sub-iervals i ay hirig period w = 1,, WS : work schedules (I(w,s) = 1 if w requires workig i sub-ierval s, 0 oherwise). x i,w = he umber of ype-i employees assiged o work schedule w z s : he amou of work o be ousourced i sub-ierval s Call Cere Workshop, Cere de Recherches Mahemaiques, Uiversie de Moreal, 07/25/2004

23 Operaig Cos Fucio O() Call Cere Workshop, Cere de Recherches Mahemaiques, Uiversie de Moreal, 07/25/2004

24 More Geeral O() Call Cere Workshop, Cere de Recherches Mahemaiques, Uiversie de Moreal, 07/25/2004

25 Model Deails (II): Hirig/Traiig Lead Time Hirig/raiig lead ime λ > 0 modeled by addig employee ypes m > λ i = 1,, λ idicae hirig/raiig sages Hirig lead ime µ i = 0 W i may be 0 Traiig lead ime µ i may be 0 W i > 0 Call Cere Workshop, Cere de Recherches Mahemaiques, Uiversie de Moreal, 07/25/2004

26 Numerical Aalysis Modelig of differe CSR classes Modelig of he sochasic elemes Compare Opimal policy: sae-depede recogize differe employees have differe capaciies ake io accou he sochasic elemes Heurisic: headcou policy check oly he oal umber of employees assume everyoe has he same (average) capaciy ake io accou he sochasic elemes Heurisic: LP-based recogize differe employees have differe capaciies use average learig ad urover raes Call Cere Workshop, Cere de Recherches Mahemaiques, Uiversie de Moreal, 07/25/2004

27 Example Problem: Slow ad Fas CSRs CSR urover slow CSRs: 48% yearly (15% per quarer) fas CSRs: 34% yearly (10% per quarer) CSR learig: slow ad fas CSRs CSR becomes fas afer oe quarer of experiece % speedup wih learig: 20%, 40%, 60%, 80% Call volume Demad: 250,000 per quarer CSR capaciy: 10,000 per quarer o average Overime as % of regular ime: 10%, 20%, 30% Call Cere Workshop, Cere de Recherches Mahemaiques, Uiversie de Moreal, 07/25/2004

28 Coss Used for Examples Wage is capaciy eural, for a avg. capaciy of 10,000 per quarer: Base wage: $4,500, beefis: $1,000 (22.2%) Overime: 1.5 imes base wage rae Ousource cos: 1.8, 18, 36, 91, 182 imes base wage rae Call Cere Workshop, Cere de Recherches Mahemaiques, Uiversie de Moreal, 07/25/2004

29 Opimal v.s. Headcou: Ample Overime % 0.6% 0.4% 0.3% % cos icrease Average Aual Cos ($ 000's) OT+OS Hirig Wage 400 HC 20% OPT 20% HC 40% OPT 40% HC 60% OPT 60% HC 80% OPT 80% policy, % learig Call Cere Workshop, Cere de Recherches Mahemaiques, Uiversie de Moreal, 07/25/2004

30 Opimal vs Headcou: Limied Overime % 2.6% 6.6% 9.9% % cos icrease Average Aual Cos ($ 000's) OT+OS Hirig Wage 400 HC 20% OPT 20% HC 40% OPT 40% HC 60% OPT 60% HC 80% OPT 80% policy, % learig Call Cere Workshop, Cere de Recherches Mahemaiques, Uiversie de Moreal, 07/25/2004

31 Cos Variabiliy Average Cos +/- 1 Sadard Deviaio HC 20% OPT 20% HC 40% OPT 40% HC 60% OPT 60% HC 80% OPT 80% $ (000's) Ample Overime HC 20% OPT 20% HC 40% OPT 40% HC 60% OPT 60% HC 80% OPT 80% Limied Overime Call Cere Workshop, Cere de Recherches Mahemaiques, Uiversie de Moreal, 07/25/2004

32 probabiliy Opimal vs. Headcou Disribuio of Regular Time Capaciy 30% overime 0.3 capaciy below which 0.3 ousourcig required service requireme head- 0.2 cou policy opimal policy % overime service requireme capaciy below which ousourcig required headcou policy opimal policy capaciy (1,000 calls / quarer) Call Cere Workshop, Cere de Recherches Mahemaiques, Uiversie de Moreal, 07/25/2004

33 Our Fidigs Whe spare capaciy is cheap simpler hirig schemes do well less eed o rack employees carefully heurisics ha igore learig Whe spare capaciy is igh simpler hirig schemes ca do poorly value o rackig employees carefully more complex approaches: DP, IPA Call Cere Workshop, Cere de Recherches Mahemaiques, Uiversie de Moreal, 07/25/2004

34 Opimal vs. LP Heurisic W/O raiig LT: LP does very well Whe here is a oe-period leadime: LP capaciy ofe falls shor 80% 60% 40% 20% 0% os=$1 $10 $20 $50 $100 10% 20% 30% learig Call Cere Workshop, Cere de Recherches Mahemaiques, Uiversie de Moreal, 07/25/2004

35 Our Fidigs LP heurisic performs well, whe raiig is fas -- LP ca wai o observe he umber of employees available ad hire accordigly raiig akes ime, bu overime is ample, or OS (or service failure) is cheap -- OT ad OS ca cover capaciy shorfall whe urover is higher ha average The opimal base level srucure simplifies calculaio LP performs poorly, whe overime is limied ad OS (or service failure) is expesive If MDP is oo complicaed o use, he a leas add some buffer capaciy i cojucio wih LP Call Cere Workshop, Cere de Recherches Mahemaiques, Uiversie de Moreal, 07/25/2004

36 Summary A ew framework o sudy employee saffig problems DP approach, allows radomess i he sysem Naural icorporaio of he schedulig ad rouig problem Opimal policy ad srucural properies Numerical resuls show whe i is worhwhile o more carefully moior sysem capaciy Call Cere Workshop, Cere de Recherches Mahemaiques, Uiversie de Moreal, 07/25/2004