WIN WIN SITUATIONS IN SUPPLY CHAIN MANAGEMENT Logistics Systems 2005 Spring Jaekyung Yang, Ph.D. Dept. of Industrial and Information Systems Eng. Chonbuk National University

Introduction ManufacturerRetailer CONSUMERCONSUMER 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. 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 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

SOLITAIRE All profits depend on W thus optimal W is given by The profits using this W are Assumption: Manuf knows all info.

SOLITAIRE If Manufacturer sets his price W=C,the profits now are For we have

PROFIT GRAPH UNDER VARIOUS W

THE PARTNERSHIP SCENARIO The Manufacturer and Retailer jointly 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

PARTNERSHIP It is independent of W or in case of, W 1 – manufacturer’s price in solitaire Retailer’s profit= Manufacturer’s profit = M 2 (W) R 2 (W)=0 if and only if

W M – max profit of manufacturer R 2 (W) = M 2 (W) if and only if W= W E defined by From R 2 (W) = M 2 (W), PARTNERSHIP

Figure 3: Profits for Manufacturer (M), Retailer (R) and total supply chain (T) for various prices W under the Partnership-scenario PARTNERSHIP

When W = W E, R 2 (W E )= M 2 (W E )=2S If W 1 stays the price in the partnership scenario, the retailer will lose while the manufacturer gains. Therefore W < W 1. W is acceptable as long as, 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 = PARTNERSHIP

EXAMPLE Let D(P) =100-2P and C = 30. P 2 =40. T 2 =200(=4S), R 2 (W)= 800 – 20W,and M 2 (W)=20W-600 If W=W E =35, then retailer and manufacturer have a profit of 100 Let W 1 =W M =40, ie. R 1 =50 and M 1 =100. The increase in profit due to the collaboration is 50(33%). W + =37.5,W - =35 W=( )/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: production cost Assumptions

· Customer demand:· ~ Uniform Distribution · Order Quantity: : unit purchase cost (manufacturer’s unit sales price) : production cost : retailer’s unit sales price : discounted sales price BASIC MODEL

· BASIC MODEL Retailer’s profit function, For profit = sum of revenue + residual values of unsold items – purchasing costs For profit = sum of revenue – purchasing costs Retailer’s expected profit Total Supply Chain Manufacturer’s Profit = Unit Profit Margin  Order Quantity

SOLITAIRE SCENARIO Retailer’s Profit Manufac.’s Profit

Graphical Results

PARTNERSHIP SCENARIO Retailer’s Profit Manufac.’s Profit

Graphical Results

NUMERICAL EXAMPLE Let Solitaire Scenario Partnership Scenario

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.