Developing feasible and optimal schedules of jobs on one machine

The paper considers the properties of feasible and optimal scheduling of jobs on one machine under constraints on the terms of the beginning and completion of jobs and on partial sequences of job performance. The established properties and the lower-bound estimates of the length of the optimal schedule are used to develop methods for the exact and approximate solutions of the formulated problem by sequential optimization algorithms. The proposed algorithms are illustrated by numerical examples and can be successfully applied to solve these problems in the absence of constraints.