An Algorithm to Search for a Solution to a Production Scheduling Problem

A mathematical model of raw materials processing is proposed. The production consists ofunits processing raw materials, storage tanks, and mixing units. The processing units are assumedto operate in one of two known modes. Switching from one mode to another can be carried out nomore than once. The problem of finding the optimal capacity of production at each of units, aswell as the time of switching units from one operating mode to another is formulated in a form ofdiscrete optimization problem. The solution of this problem should ensure an achievement of thespecified production plan. A method for its solution is proposed, including a transition toa convex statement, as well as an algorithm for discretizing the obtained control.