Solution of a project scheduling problem by using methods of tropical optimization

The paper deals with the application of methods of tropical optimization to the solution of project scheduling problems. A problem is considered to find an optimal schedule for a project, which consists of a set of activities to be performed under various constraints on the initiation and completion times of the activities. The optimal scheduling objective takes the form of the minimum of maximum deviation between completion times of the activities. In the paper, the scheduling problem is first formulated in the form of an ordinary constrained optimization problem. Next, certain basic definitions and results of tropical mathematics are presented, required for the subsequent analysis and solution of tropical optimization problems. A new tropical optimization problem with constraints is formulated, and its solution is derived. Finally, the scheduling problem under study is solved by reduction to the tropical optimization problem, which was previously investigated. To conclude, a numerical example is given. Refs 18.