|
| Set and indices | |
| Set of activities topologically ordered and indexed by |
| Set of resource types indexed by |
| Set of time slots indexed by |
| Set of time scales indexed by |
| Set of time intervals of scale indexed by |
|
| Parameters |
| Adjacency matrix: if activity is activity ’s immediate predecessor, ; otherwise, |
| Duration of completing activity |
| Quantity of resource required when executing activity |
| Capacity of resource |
| If time slot be in period of scale , ; otherwise, |
| The cost of input one unit of resource for a period of time scale |
| Vector of possible values taken by , |
| The number of total independent samples of |
| is observed with occurrences |
| An arbitrary big scalar |
|
| Variables | |
| Objective vector of the two objectives |
| Project completion time |
| Resource cost |
| If activity is completed at the end of time slot , ; otherwise, 0 |
| is the amount of resource allocated in interval of time scale |
| is the probability of being , |
| is the start time of activity |
| The total amount of resource allocated in time slot |
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