Table 1: The decision variables and parameters in the model.

Decision variables
NotationDescriptionNotationDescription
Transportation capacityManufacturer’s order forecast
Order point

Parameters
NotationDescriptionNotationDescription
PeriodSupply chain’s total cost
Retailer’s total costManufacturer’s total cost
MHRetailer’s in-transit inventoryRetailer’s remaining inventory
MROrder received by the retailerTotal delayed penalty cost of the carrier
MLRetailer’s in-transit inventoryYield risk factor
IRetailer’s initial inventoryManufacturer’s back order
IERetailer’s ending inventoryHManufacturer’s unit inventory holding cost
IPRetailer’s current inventoryBManufacturer’s unit short cost
Retailer’s back orderManufacturer’s ending inventory
Order process timeManufacturer’s initial inventory
SThe maximum inventory levelsaleDelivered order quantity of the manufacturer
The safety factor on inventoryTotal penalty cost of the manufacturer
QRetailer’s order quantityThe cost of maintaining the transportation capacity
hRetailer’s unit inventory holding costRetailer’s unit short cost
Carrier’s total costThe actual market demand
Transportation time, System parameters
Unit transportation costMean of uncertain market demand
Unit penalty cost due to transportation delayStandard deviation of uncertain market demand
Mean of order process timeStandard deviation of uncertain yield
Standard deviation of order process timeStandard deviation of transportation time
Mean of transportation timeFixed order cost of the manufacturer
Fixed order cost of the retailer