Inventory is the bloodline of supply chains. Yet, most challenges to executing a profitable operations comes from the inability to optimize inventories as they start to propagate across their supply chain. 

Buyback contract is a supply chain contract in which a retailer is allowed to return unsold “inventory” up to a specified amount at an agreed upon price to the supplier. This lowers the loss to the retailer and makes it optimal for the retailer to order more quantity resulting in higher product availability, thereby increasing profits for both retailer and supplier. 

Buyback contracts are very common in the publishing industry wherein publishers accept unsold books from retailers. To minimize the cost associated with return, retailers do not have to return the book but only the cover. This provides publishers with the proof that book did not sell while reducing the cost of returns. Buyback are common in videocassette, newspaper and apparel industries also. 

Suppose the manufacturer has a production cost vand charges the retailer a price c.Manufacturer buys back at a price b and can sell the returned quantity at a salvage price Sm. Retailer sells each unit at a price p. Let O be the optimal order quantity ordered by the retailer and actual demand is D. 



Expected manufacturer's profit = Margin per unit * No. of units sold to retailer  buyback price * returned quantity + returned quantity * salvage value per unit. 




Expected retailer's profit = Revenue generated through sales + Buyback price * overstock  cost of optimal
ordered Quantity 




Expected Supply Chain Profit = Expected manufacturer's profit + Expected retailer's profit. 



Example: 

Suppose a manufacturer sells a product to the retailer and the demand for this product is distributed as follows: 

Quantity 
Probability 
100 
0.15 
110 
0.22 
120 
0.30 
130 
0.20 
140 
0.90 
150 
0.04 



Assume that v = 3300, c = 4000, p = 4500 and Sm=2600 

Without Buyback Contract: 

Under this scenario, a stochastic constrained optimization model that maximizes the retailer’s profit yields the following: 

Optimal order size 
110 
Manufacturer's Profit 
77000 
Retailer's Profit 
522900 
Supply Chain Profit 
129900 



With Buyback Contract: 

Both the manufacturer and retailer will enter into a buyback contract only if their profits after the contract are more than their respective profits without buyback contract. To increase their profits, they will now decide optimal order size (O), buyback price (b) and the price (c) such that it will earn maximum profit for both the parties which will ultimately lead to maximization of supply chain profit. 

Under this scenario, a stochastic constrained optimization model that maximizes the supply chain profit (Not Retailer’s or Manufacturer’s profit separately) yields the following: 

Cost for retailer 
3969 
Buy back price 
3101 
Order size 
120 
Manufacturer's Profit 
77675 
Retailer's Profit 
56445 
Supply Chain Profit 
134120 


We can now easily compare the retailer’s profit, manufacturer’s profit and supply chain profit with those obtained without buyback contract: 



Without Buyback Contract 

With Buyback Contract 

% increase 

Manufacturer's Profit 

77000 

77675 

0.88 

Retailer's Profit 

52900 

56445 

6.70 

Supply Chain Profit 

129900 

134120 

3.25 


