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Decision variables | | | |
Notation | Description | Notation | Description |
| Transportation capacity | | Manufacturer’s order forecast |
| Order point | | |
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Parameters | | | |
Notation | Description | Notation | Description |
| Period | | Supply chain’s total cost |
| Retailer’s total cost | | Manufacturer’s total cost |
MH | Retailer’s in-transit inventory | | Retailer’s remaining inventory |
MR | Order received by the retailer | | Total delayed penalty cost of the carrier |
ML | Retailer’s in-transit 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 | | |
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