Optimization of schedules with precedence logical conditions

The problem of constructing a time-optimal schedule for jobs execution with precedence logical conditions is considered. Every job is associated with a list of its direct predecessors, execution time and the number of the completed direct predecessors necessary to start execution of the job. It is shown that the problem can be solved by the methods of the cyclical games theory [1, 2]. We propose a pseudopolynomial algorithm for construction of the optimal schedule; i.e. the presented algorithm is efficient for the problems with small data arrays. The paper extends the results from [3], where AND/OR schedules are considered. A job can be started, when all its direct predecessor have been executed or when at least one of its direct predecessors has been completed.