
Decision variables    
Notation  Description  Notation  Description 
 Transportation capacity   Manufacturer’s order forecast 
 Order point   

Parameters    
Notation  Description  Notation  Description 
 Period   Supply chain’s total cost 
 Retailer’s total cost   Manufacturer’s total cost 
MH  Retailer’s intransit inventory   Retailer’s remaining inventory 
MR  Order received by the retailer   Total delayed penalty cost of the carrier 
ML  Retailer’s intransit inventory   Yield risk factor 
I  Retailer’s initial inventory   Manufacturer’s back order 
IE  Retailer’s ending inventory  H  Manufacturer’s unit inventory holding cost 
IP  Retailer’s current inventory  B  Manufacturer’s unit short cost 
 Retailer’s back order   Manufacturer’s ending inventory 
 Order process time   Manufacturer’s initial inventory 
S  The maximum inventory level  sale  Delivered order quantity of the manufacturer 
 The safety factor on inventory   Total penalty cost of the manufacturer 
Q  Retailer’s order quantity   The cost of maintaining the transportation capacity 
h  Retailer’s unit inventory holding cost   Retailer’s unit short cost 
 Carrier’s total cost   The actual market demand 
 Transportation time  ,  System parameters 
 Unit transportation cost   Mean of uncertain market demand 
 Unit penalty cost due to transportation delay   Standard deviation of uncertain market demand 
 Mean of order process time   Standard deviation of uncertain yield 
 Standard deviation of order process time   Standard deviation of transportation time 
 Mean of transportation time   Fixed order cost of the manufacturer 
 Fixed order cost of the retailer   
