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The work considers the work performance scheduling with minimization of overall advance in schedule date and maximization of the moment of the beginning of the work performing by parallel devices. Over the past years, many methods have emerged for solving this problem, which seek to simplify the process of compiling optimal scheduling plans for the performance of work for specific schedule date and execution time. The developed method allows you to draw up a work schedule for a case where there is a certain number of devices working in parallel. In the work, the most famous methods for solving this class of problems are considered and their comparative characteristic is performed. The goals and objectives of the work are defined. The statement of the problem is formulated. Investigations of the properties of the problem are presented. The application of the task for both a single device and parallel devices is considered. An algorithm for solving the problem is developed. Experimental studies of the work of the developed algorithm were carried out, where classes of tasks were distinguished, which in turn were divided into subclasses, each of which determines the average execution time, variance of the duration of the work, and variance of its schedule date. Taking into account the adopted approach to the classification of tasks, a total of 27 subclasses were identified. In the work, 200 experiments were conducted for each subclass with a different number of jobs for several parallel devices, the results of which are a comparison of the developed algorithm and the exhaustive search method. For the experiments, an algorithm for generating tasks was developed with a value of the duration and the deadline corresponding to each subclass. Experimental studies have confirmed the effectiveness of the developed algorithm in the framework of the above task. [ABSTRACT FROM AUTHOR]

The process of optimization work schedule is important for meeting the needs for staff and requirements of work time standards and also for accounting staff availability and preferences. The paper considers shifts scheduling problems for staff with a flexible work schedule. It was formulated three problems of determining the number of staff, who start to work in a given interval of the day. The problems deal with a given duration of the shift and lunchtime, which can be planned in the given bounds and the given staff number. The objective of the problems is to minimize the total deviation of staff count from needs for them in each time interval during the day. There have been proposed two methods for determining the staff number in each interval, which envisages the solve of the two optimization problems. The problem, in which it is needed to define the number of staff without the count of lunchtime is solving in the first stage of the first method and with the count of lunchtime in given intervals in the first stage of the second method. After the solution of the first stage problem, in both methods, it is needed to assign lunchtime in allowed bounds in the solution got in the previous problem to minimize the total deviation of staff numbers from needs for them. It was got nonlinear problems, which were transformed into the integer linear and binary integer programming problems. There have been developed heuristic algorithms for solving the problem with unfixed lunchtime. There were two series of experiments with the purpose of research their efficiency. The input dataset for experiments was generated randomly in given bounds of interval time. The number of intervals and bounds of flexible lunchtime are variated parameters. The results of experiments prove the efficiency of the first method and the needs of additional research on the second one. [ABSTRACT FROM AUTHOR]