Integer Optimization of Package Compositions and Schedules in Flow Shop Systems with Varying Frequency of Instrument Maintenance

The implementation of job package execution processes in Flow Shop systems is affected by instrument failures and downtime during recovery. Maintaining a given level of reliability of the systems is ensured by periodic maintenance of their devices related to troubleshooting, which are the causes of failures. During the maintenance time intervals, the devices are unavailable for the implementation of their assigned functions. Device maintenance planning allows you to determine the time intervals between their implementations. However, the position of the instrument maintenance implementations may not be fixed, but may fall within time intervals of a given duration (time "windows"). In this case, the position of instrument maintenance implementations is optimized taking into account the nature of the processes of completing task packages in the systems. At the same time, tasks performed in systems that are included in packages may be part of orders for which specific deadlines have been set. As a result, the task of optimizing the composition of task packages, including packages in the availability intervals of devices of non-fixed duration, and the order of execution of packages in these intervals when tasks enter orders, with specific deadlines for them, is urgent. With small problem sizes, their solutions can be obtained by using mixed integer linear programming.

The purpose of the work is to form a new mathematical model of integer programming for optimizing solutions of this type. Methods of constructing mathematical programming models were used to achieve this goal. At the first stage, the formation of a nonlinear mathematical model was implemented. Expressions are obtained that are used to construct constraints corresponding to the distribution of all tasks into packages. In order to reduce the time spent on obtaining solutions, the model was linearized. To verify it, an application has been developed in the IBM ILOG CPLEX environment. In the course of the research, results were obtained that showed the effectiveness of the model for solving the tasks of planning the execution of task packages in Flow Shop systems with varying service frequency and the condition that tasks are included in orders with specific deadlines for their execution. The results are of practical importance in solving small-dimensional problems of constructing scenarios for completing task packages in production systems.

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