Courses

The "Transportation" Problem. Definition, Balanced and Unbalanced Problems, Linear Programming Model, Related Problems. Existence of Solution, Finding an Initial Basic Feasible Solution, Method of Redistribution of Assignments (MODI), Multiple Optimal Solutions, Degenerate Solutions. Sensitivity Analysis, Duality. The "Assignment" Problem. Definition. Known Applications that can be Solved as Assignment Problems. Mathematical Models for the Assignment Problem. The Hungarian Algorithm. Lattice Analysis. Models for the Shortest Path, Spanning Tree and Maximum Flow Problems. Project Time Scheduling (the PERT/CPM method, the variation of the duration of a project's completion, project cost optimization, project activity control). Decision Theory. Decisions under Risk Conditions, Decision Trees. Decisions under Uncertainty Conditions. Game Theory. Perfect Information Games (Nash Equilibrium, Mixed Strategies). Game Solving through the Linear Programming Problem Model. Principles of Dynamic Programming. Basic Concepts, Deterministic and Stochastic Models of Route and Tool Replacement - Maintenance. The Optimal Load Problem. The Traveling Salesman Problem. Production and Storage Problems.