The use of dynamic optimization in building System Dynamics models for forecasting criminal activities

The aim of the paper is to show how dynamic optimization techniques could be used in creating System Dynamics models. There are two possible applications of optimization in the context of System Dynamics methodology. The first application concerns the calibration of System Dynamics models - one can introduce computational technique which is the extension of the Gauss-Newton for the calibration of models described by algebraic equations. The second application is related to the problem of creating proper decision rules which usually are present in System Dynamics models. In that case we substitute original decision rules by control variables and then define an optimal control problem whose performance index is used to verify the effectiveness of a particular decision rule. Having the solution of the optimal control problem we use it to modify the decision rule or its parameters. We show the application of the proposed approach to System Dynamics models describing criminal activities: one model is related to drugs prevalence, the other one is based on relations known from epidemics models and can be treated as a generic model which can be used to describe various criminal activities.