General Motors Company · NYSE:GM

General Motors — Technical Presentation (December 2005)

29 slides from General Motors's technical presentation, Dec 9, 2005

  1. Slide 1: Impact of Stair-Step Incentives and Dealer Structures on a Manufacturer's Sales Variance

    Impact of Stair-Step Incentives and Dealer Structures on a Manufacturer’s Sales Variance Milind Sohoni, ISB Sunil Chopra, Kellogg Usha Mohan, ISB M. Nuri Sendil, NWU GM ISL WORKSHOP ON FRONTIERS OF E-BUSINESS Bangalore 8-9 December 2005

  2. Slide 2: Introduction

    Introduction Motivation and problem description Modeling assumptions Exclusive dealer’s problem ¾ The manufacturer’s problem The non-exclusive dealer’s problem ¾ Comparison with the exclusive dealer scenario Conclusions, work in progress, and future research 2 Milind Sohoni, ISB – Presentation for G

  3. Slide 3: Motivation

    Motivation The basic idea is to study the effect of stair-step dealer incentives on a manufacturer’s sales variance Chrysler’s story ¾ In May 2001 Chrysler’s sales dipped by 18 to 20% when the industry average was between 8 to 12% ¾ What could have caused such a dip? ¾ Could it be related to stair-s

  4. Slide 4: Exclusive Dealer: Model Assumptions

    Exclusive Dealer: Model Assumptions Timeline of events ¾ Manufacturer offers stair-step incentive (p, D, ∆, K) ¾ Dealer observes the input market signal (x) ¾ Dealer decides on the effort to be exerted (e) at cost c(e) to maximize profits ¾ The resulting sales are x+g(e) The dealer’s cost (c) is con

  5. Slide 5: Exclusive Dealer: Scenarios

    Exclusive Dealer: Scenarios Dealer sells for only one manufacturer ¾ Scenario 1: when D = 0 ¾ Scenario 2: when D > 0 5 Milind Sohoni, ISB – Presentation for GM ISL Workshop on Frontiers of E-Business India Science Lab

  6. Slide 6: Exclusive Dealer: Scenario 1

    Exclusive Dealer: Scenario 1 D=0 Dealer makes a profit of ‘p’ for every unit sold below the threshold ‘K’ and (p+∆) for every unit above K The dealer’s problem ¾ To find an optimal effort level for every market signal x  1 x, e  p x  ge  ce if x  ge  K,  2 x, e  p   x  ge 

  7. Slide 7: Exclusive Dealer: Scenario 1 Effort level

    Exclusive Dealer: Scenario 1 Notice that both the profit functions are concave in ‘e’ ( Π2 x,b*2 ) Effort level Πi ( x, e) b*2 ( Π1 x,b*1 ) b *1 x=0 x x co1 x=0 co1 2 optimal effort levels when D=0 The optimal profit function when D=0 7 Milind Sohoni, ISB – Presentation for GM ISL Workshop on Fronti

  8. Slide 8: Manufacturer's expected sales and variance as K increases

    Exclusive Dealer: Scenario 1 What happens to the expected sales and variance as ‘K’ increases? ( ) g b*2 Manufacturer’s E(s) − E( x) Expected sales x + g (b2 *) ( ) g b*2 − ε K sales D=0 V (s) − V ( x) ( ) x + g b*1 Varianceof sales ( ) g b*2 − ε K x   1 pgb 1   cb 1   pgb 2   cb

  9. Slide 9: Exclusive Dealer: Scenario 2

    Exclusive Dealer: Scenario 2 D>0 Dealer makes a profit ‘p’ for every unit sold below the threshold ‘K’ and (p+∆) for every unit above K in addition to the bonus ‘D’ The dealer’s problem ¾ To find an optimal effort level for every market signal x  1 x, e  p x  ge   ce if x  ge   K,  2

  10. Slide 10: Exclusive Dealer: Scenario 2 Effort level

    Exclusive Dealer: Scenario 2 ( Π 2 x, b * 2 ) Effort level bK ( Π 2 x, b K ) * b2 Π i (x, e ) ( Π 1 x, b *1 ) * b1 x =0 x x=0 co1 co2 x co1 co2 More than 2 optimal effort The optimal profit function when D>0 levels when D>0 10 Milind Sohoni, ISB – Presentation for GM ISL Workshop on Frontiers of E-B

  11. Slide 11: Manufacturer's expected sales and variance as K increases

    Exclusive Dealer: Scenario 2 What happens to the expected sales and variance as ‘K’ increases? Manufacturer’s ( ) g b*2 E (s) − E ( x) x + g (b2 *) D>0 Expected sales sales ( ) g b*2 cc1 K K ( ) x + g b*1 Variance of sales V ( s) − V ( x) ( ) g b* 2 cc1 K ( )x K − g b* 2 p cc 1  cg 1 cc 1   D

  12. Slide 12: Exclusive Dealer: Manufacturer's Problem

    Exclusive Dealer: Manufacturer’s Problem Notice that when D > 0 the variance reduces below the input signal variance for certain values of K Manufacturer has to choose p, D and K ¾ We assume that p is given and manufacturer chooses D and K to maximize profits ¾ Manufacturer’s cost of variance is ‘cv

  13. Slide 13: Exclusive Dealer: Manufacturer's Problem

    Exclusive Dealer: Manufacturer’s Problem When designing a stair-step incentive, with D=0, the manufacturer maximizes profits either by setting the threshold K = g(b**22)-ε (or sets K to an extremely large value) ( ) g b*2 E ( s) − E ( x) Expected sales ( ) g b*2 − ε K V (s) − V ( x) Variance of sale

  14. Slide 14: Exclusive Dealer: Manufacturer's Problem

    Exclusive Dealer: Manufacturer’s Problem When designing stair-step incentives with D>0, the manufacturer maximizes profits by either setting K = cc11 or by setting K to a very large value (impossible to reach) ( ) g b*2 E (s) − E ( x) Expected sales ( ) g b*2 cc 1 K Variance of sales V (s) − V ( x)

  15. Slide 15: Exclusive Dealer: Manufacturer's Problem

    Exclusive Dealer: Manufacturer’s Problem For high enough value of cv, the manufacturer can increase profits by setting a positive bonus (i.e. when D > 0) 15 Milind Sohoni, ISB – Presentation for GM ISL Workshop on Frontiers of E-Business India Science Lab

  16. Slide 16: Non-Exclusive Dealer

    Non-Exclusive Dealer There is plenty of evidence that dealers tend to sell products for multiple manufacturers How does this impact a manufacturer’s sales; especially sales variability 16 Milind Sohoni, ISB – Presentation for GM ISL Workshop on Frontiers of E-Business India Science Lab

  17. Slide 17: Non-Exclusive Dealer: Model Assumptions

    Non-Exclusive Dealer: Model Assumptions We consider a simple model with 2 manufacturers selling through a single dealer Timeline of events ¾ Manufacturers offers stair-step incentive (p, K) ¾ Dealer observes the input market signal (x11 and x22) ¾ Dealer decides on the effort to be exerted, e11 and

  18. Slide 18: Non-Exclusive Dealer: Dealer's Problem

    Non-Exclusive Dealer: Dealer’s Problem D=0 Dealer makes a profit of p for every unit sold below the threshold K; and (p+∆) for every unit above K The Dealer’s problem ¾ To find an optimal allocation of effort levels across manufacturers for every pair of market signals x11 and x22 18 Milind Sohoni,

  19. Slide 19: Non-Exclusive Dealer: Profit Functions

    Non-Exclusive Dealer: Profit Functions Profit 1 px 1  ge11   px 2  ge12 : x 1  ge11   K, and 2 c e11e 2 12  x 2  ge12   K 2 px 1  ge21   p  x 2  ge22  : x 1  ge21   K, and K  2 c e21e 2 22  x 2  ge22   K 3 p  x 1  ge31   px 2  ge32

  20. Slide 20: Non-Exclusive Dealer: Dealer's Effort Levels

    Non-Exclusive Dealer: Dealer’s Effort Levels x2 c    e11 e12 2 * * ge11   ge12   ; e , e 41 42 e  21e 22 p e  21e 22 c c co3 e*21, e*22  g e21   p 2  , g e22   2 ; p e  31e 32 e  31e 32 c c co1  g e31   2  , g e32   2 ; * * p p e , e 31 32   e4

  21. Slide 21: Non-Exclusive Dealer: Link to Chrysler's Story

    Non-Exclusive Dealer: Link to Chrysler’s Story       e 31  e 41  b 2  e 11  b 1  e 21 The effort levels are nested One possible explanation for Chrysler’s sales dip ¾ Unfortunately, Chrysler’s market signal was not high enough to induce the dealer to exert high effort levels to meet the t

  22. Slide 22: Non-Exclusive Dealer

    Non-Exclusive Dealer A non-exclusive dealer strictly makes more profit than an exclusive dealer ¾ It is always possible for the non-exclusive dealer to act as an exclusive dealer and make at least as much profit ¾ There are input market signals such that the non-exclusive dealer can reallocate effor

  23. Slide 23: Non-Exclusive Dealer: Sales Variability

    Non-Exclusive Dealer: Sales Variability –The effect of increasing ∆2 x2 –By increasing ∆2 manufacturer 2 can increase the range for which e*41, e*42 manufacturer 1 experiences sales co3 e*21, e*22 variation –Even when x1 is larger than x2 co1 dealer favors x2 because of a higher e*31, e*32 ∆2; since

  24. Slide 24: Non-Exclusive Dealer: Sales Variability

    Non-Exclusive Dealer: Sales Variability For the same input signal a manufacturer experiences different effort levels; this results in sales fluctuations What happens to the gap co4 – co2 when we increase ∆ ¾ Under some mild conditions the gap increases ¾ Since this is the region when the fluctuation

  25. Slide 25: Non-Exclusive Dealer: Comparing Dealer Structures

    Non-Exclusive Dealer: Comparing Dealer Structures If the effort function g and the pay-off ∆ are such that b 31 b 11 b 11  b 21  2 and p  1 and K*ED ED , and K*NED NED denote the optimal threshold levels for an exclusive dealer and a non-exclusive dealer, then 1. K*NED NED < K*ED ED 2. For

  26. Slide 26: Non-Exclusive Dealer: When D > 0

    Non-Exclusive Dealer: When D > 0 Offering a bonus does not change the structure of the effort levels of the non-exclusive dealer. The only effect a positive bonus has is to lower cut off co22; i.e. the non-exclusive dealer exerts a higher effort level earlier. Thus, unlike the case of an exclusive d

  27. Slide 27: Numerical Experiments – Exclusive Dealer

    Numerical Experiments – 1 Exclusive Dealer 76.5 150 cv=0.433 cv=0.5 76.3 100 cv=0.6 76.1 cv=0.7 50 V(s)-V(x) E(s)-E(x) 75.9 K 0 cv=0.433 75.7 70 80 90 100 110 cv=0.5 -50 75.5 cv=0.6 cv=0.7 -100 75.3 K 75.1 -150 70 80 90 100 110 The effect of input signal coeffecient of variance on sales 27 Milind So

  28. Slide 28: Numerical Experiments – Comparing Dealer Structures

    Numerical Experiments – 2 Comparing Dealer Structures 158.4 2260 NED withD = 10000 2230 2200 Expected Sales E(s) Variance of Sales V(s) 2170 158.35 ED 2140 NED with D = 0 2110 2080 158.3 2050 NED 2020 1990 ED with D=0 158.25 1960 1930 K 1900 158.2 K 60 65 70 75 80 85 90 95 100 105 110 115 120 125 13

  29. Slide 29: Conclusions

    Conclusions For an exclusive dealer, the manufacturer makes more profit by offering a positive bonus if the cost of sales variance is high When dealers become non-exclusive they exert different effort levels for a single input market signal resulting in more fluctuations in total sales for the manuf

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