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This serial schedule generation scheme operating on an activity list (lambda) only generates active schedules (mathcal {AS}) which are a subset of the quasi-stable schedules, i.e., (mathcal {AS} subseteq mathcal {QSS}), when enumerating over all possible activity lists (lambda) as input data.
It is hence not sufficient or advisable to limit the search to the set of active schedules.
As a consequence, it is sufficient to consider "only" all active schedules to find the optimal solution.
For scheduling problems with regular objective functions, e.g., makespan minimization, this is the set of so-called active schedules (mathcal {AS}).
Like the RCPSP, the problem is (mathcal {NP} -hard, but unlike the RCPSP, it turns out that an optimal schedule does not have to be among the set of so-called active schedules.
The parameter alpha is the non-delay factor (in [0, 1]) to control the look-ahead ability of the algorithm by restricting operations included in P' (the algorithm generates non-delay schedules if alpha = 0 and active schedules if alpha=1).
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