WIN WIN SITUATIONS IN SUPPLY CHAIN MANAGEMENT

Logistics Systems 2005 SpringJaekyung Yang, Ph.D.

Dept. of Industrial and Information Systems Eng.

Chonbuk National University

Introduction

Manufacturer Retailer

CONSUMER

A fashion type of product

• A simple quantitative model• The manufacturer and retailer are free to set the price• Two scenario

• Solitaire: do not collaborate• Partnership: collaborate

• If they set the price jointly, total supply chain profit improves

MODEL AND ANALYSIS

ASSUMPTIONS The supply chain assumed here has a single manufacturer

and a single retailer. The product has a short life cycle ,one time orders only

i.e no reordering possible, no on hand inventory. SOLITAIRE :No collaboration.each one sets his own price.

PARTNERSHIP:Price decided jointly. Demand D(P) is linearly dependent on the price P.

PPD )( 0 ,

MODEL AND ANALYSIS The retailer sets the price P and

determines demand D(P) and accordingly places an order size

Q = D(P).

Manufacturers profit equation M = (W – C ) Q Retailers profit equation R = (P – W ) Q Supply Chain Profit T = M+R = (P – C ) Q

;/0 PC .PWC

Solitaire: W is first set, then P Manuf. Knows only C, Retailer does , W only

Partnership: P first then W Both know all

,

THE SOLITAIRE SCENARIO

Assuming that the manufacturers price W has been set.

The Retailer wants to maximize profit

The profits based on optimal P and Q values are

WPWPPWPR )())(( 2

0P

R

2:1

WP

)(

2

1:1 WQ

4

)(:)(

2

1

WWR

))((2/1:)( 21 WWCCWM

SOLITAIRE

All profits depend on W thus optimal W is given by

The profits using this W are

2

)( 0,

)(1 CW

W

WMM

SC

WR M

16

)(:)(

2

1

SC

WM M 28

)(:)(

2

1

SWT 3)(1

Assumption: Manuf knows all info.

SOLITAIRE

If Manufacturer sets his price W=C ,the profits now are

For we have

:)(1 TWR SC

44

)( 2

0))((2

1:)(1 CCCWM T

.4)( 1 SWT T

:RWW

0)( and ,0)(,0)( 111 RRR WTWMWR

PROFIT GRAPH UNDER VARIOUS W

THE PARTNERSHIP SCENARIO

The Manufacturer and Retailerjointly determine P first and then W..

And the order size is given by

We see that and ie. if total supply chain is optimised

then P – lower and Q – higher and the consumers benefit from this collaboration

0

P

T

2

)(2

CP

12 PP 12 QQ

SCC

CC

QCPT 44

)(

2

)(

2

)()(

2

222

)(2

12 CQ

PARTNERSHIP

It is independent of W or in case of ,

W1 – manufacturer’s price in solitaireRetailer’s profit=

Manufacturer’s profit = M2(W)

R2(W)=0 if and only if

12 TT CW 12 TT 2

112 )(4

: CWTT

4

))(()(

2

1)(:)( 222

CCWCQWPWR

CCWCQCW )(2

1)(

2

1)( 2

MWPC

W

22

WM – max profit of manufacturer

R2(W) = M2(W) if and only if W= WE defined by

From R2(W) = M2(W),

,4

3:

C

WE

EWC

W

4

3

PARTNERSHIP

Figure 3: Profits for Manufacturer (M), Retailer (R) and total supply

chain (T) for various prices W under the Partnership-scenario

Profit

0

S

2S

3S

4S

C WE WM

R2

T2

M2

W

PARTNERSHIP

When W = WE , R2(WE)= M2(WE)=2S

If W1 stays the price in the partnership scenario , the retailer will lose while the manufacturer gains.

Therefore W < W1. W is acceptable as long as , )()( 112 WRWR

)(4

))(()(

2

1

4

)()( 2

21

1 WRCC

WCW

WR

)(2

2 211

2

C

WWCWW

)(

)( 211

2

C

WWCCWW

)(2

)( 21

C

CWWW

PARTNERSHIP

The result ,

Shows that W exists so that the manufacturer and retailer have a higher profit in partnership than in solitaire.

This happens when W- < W < W +.

W = W+ implies all additional profit for manufacturer

W = W- implies all additional profit for retailer

For equal profit =

CWWWWW 1 ifonly and if and

2

WW

W 21

PARTNERSHIP

EXAMPLE

Let D(P) =100-2P and C = 30.

P2 =40. T2=200(=4S), R2(W)= 800 – 20W,and M2(W)=20W-600

If W=WE=35, then retailer and manufacturer have a profit of 100

Let W1=WM=40, ie. R1=50 and M1=100. The increase in profit due to the collaboration is 50(33%). W+=37.5 ,W-=35

W=(35+37.5)/2 =36.25, profit(retailer)=75(inc of 25)

Profit(manufacturer)=125(inc of 25)

W=(50W-+100W+)/150=36.67, profit(retailer)=66.67(inc of 33.33%), profit(manufacturer)=133.33(inc of 33.33%)

EXTENSIONS

Customer demand X for the product is uncertain and depends on the price p set by the retailer and is given by

The residual values can be positive if (Q-x) units can be sold at discounted sale prices (r>0) ,or they can be negative if (Q-x) units must be disposed .

If at the end of period ,demand x is more than the order quantity Q ,then additional demand (x-Q) is lost.

We assume that Q is linearly dependent on p:

,0 where,0 1

)(

xxf /0 pv

pQ /0 pv

production cost

Assumptions

·        Customer demand:

X

,0 where,0 1

)(

xxf /0 pv

·        ~ Uniform Distribution

,pQ ·        Order Quantity:

: unit purchase cost (manufacturer’s unit sales price)

: production cost

: retailer’s unit sales price

: discounted sales price

c

v

p

r

BASIC MODEL

/0 pv

· BASIC MODEL

• Retailer’s profit function, For profit = sum of revenue + residual values of unsold items – purchasing costsFor profit = sum of revenue – purchasing costs

• Retailer’s expected profit

,Qx ,Qx

pQp

prpcp

dxxfQcpdxxfxQrcQpxQpRQ

Q

where,)())((

)(])[()()(),(0

• Total Supply Chain

QvccM )()(

)()( cMpRT

• Manufacturer’s Profit = Unit Profit Margin Order Quantity

SOLITAIRE SCENARIO

,0)(

From dp

pdR

2

)1(* cp

2

1**

cpQ

2

1

2

1)2()2()(

2*

ccrc

pR

2

)1)(()(

cvccM

Retailer’s Profit

Manufac.’s Profit

Graphical ResultsProfits under the Solitaire Scenario

-400

-200

0

200

400

600

800

1000

1200

1400

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32

Manufacturer's Cost

Pro

fit Retailer's Profit

Manufacturer's Profit

Total Supply Chain Profit

PARTNERSHIP SCENARIO

,0 From dp

dT

2

)1(( 2*

2

rvp

2

)1(2*

2

rvQ

2

))1((

2

))1()22(()(

2

2

23*

2

rvrrvcvpR

2

)1()()(

2 rvvccM

Retailer’s Profit

Manufac.’s Profit

Graphical ResultsProfits under the Partnership Scenario

-400

-200

0

200

400

600

800

1000

1200

1400

1600

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32

Manufacturer's Cost

Pro

fit Retailer's Profit

Manufacturer's Profit

Total Supply Chain Profit

2 100, ,1 ,5 ,10 rvc

8.29* p 5.40* Q

2.788)( * pR 5.202)( cM

7.9905.2022.788 T

NUMERICAL EXAMPLE

Let

Solitaire Scenario

Partnership Scenario

3.27*2 p 51.45*

2 Q

9.772)( *2 pR 6.227)( cM

5.10006.2279.772 T

CONTRIBUTION AND CONCLUSION

Contribution • Considered the uncertain demand and backorder cost• Made the conservative assumptions lax• Proved that the partnership scenario is still higher than solitaire scenario

Conclusion Despite a few parameters like Random Demand, Backorder Cost, etc. are changed,

the partnership scenario is better than the solitaire scenario.