WIN WIN SITUATIONS IN SUPPLY CHAIN MANAGEMENT Logistics Systems 2005 Spring Jaekyung Yang, Ph.D....

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.