A Resource-Constrained Optimal Control Model for Crackdown on Illicit Drug Markets

In this paper we present a budget-constrained optimal control model aimed at finding the optimal enforcement profile for a street-level, illicit drug crackdown operation. The objective is defined as minimizing the number of dealers dealing at the end of the crackdown operation, using this as a surrogate measure of residual criminal activity. Analytical results show that optimal enforcement policy will invariably use the budget resources completely. Numerical analysis using realistic estimates of parameters shows that crackdowns normally lead to significant results within a matter of a week, and if they do not, it is likely that they will be offering very limited success even if pursued for a much longer duration. We also show that a ramp-up enforcement policy will be most effective in collapsing a drug market if the drug dealers are risk-seeking, and the policy of using maximum enforcement as early as possible is usually optimal in the case when the dealers are risk averse or risk neutral. The work then goes on to argue that the underlying model has some general characteristics that are both reasonable and intuitive, allowing possible applications in focussed, local enforcement operations on other similar illegal activities.crackdown enforcement;illicit drug markets;optimal control

Optimal Enforcement Policies (Crackdowns) on a Drug Market

In this paper an optimal control model is presented to design enforcement programs minimizing the social costs from both the market and crackdown.By using the maximum principle we show that performing an enforcement policy that leads to a collapse of the drug market is more likely to be optimal when the sales volume depends on the number of dealers.In case of a buyer's market the optimal enforcement policy leads to a saddle point equilibrium where the enforcement rate is fixed such that the number of dealers is kept constant at a positive level.