Table 2. Denotation of the parameters and variables.
| Indexes | Description |
|---|---|
| Sub operation number, | |
| Transportation service number, | |
| Operation number, | |
| service point number, | |
| Parameters | Description |
| transportation service ’s cost between service point and , ($) |
|
| the performance cost of subtask in service point , ($) |
|
| Distance between service points and (mile) | |
| Operation performing time in service point (hour) | |
| Service quality of service point (%) | |
| The operation performing cost in service point ($ per hour) | |
| The cost of transportation service ($ per mile) | |
| sub-operation of the operation | |
| operation | |
| a binary parameter, 1, if operation needs sub-operation, otherwise 0. | |
| Variables | Description |
| a binary variable, 1, if sub-operation for operation in service point is to be fulfilled, otherwise 0. | |
| a binary variable, 1, if transportation service between two service points and ′ for proceeding from sub-operation to +1 for operation is needed, otherwise 0. |