Do governments involve Operations Research (Techniques) for Decision making?

I cannot give you a complete answer. As we can guess, governments SHOULD involve OR techniques for decision making, but we cannot be sure that they actually do.The problem with the governments is that they have "increased power" to relax the constraints. Thus, while an OR scientist has a specific problem under specific constraints and seeks for an optimal solution, the government usually has the problem, the "preferred political solution" and the ability (by using laws) to manipulate the constraints in order to make the "preferred political solution" a feasible one.Let me give you an example. Suppose we have a government seeks for a solution on public pension system. We know the problem (to have a viable pension system over time), we have the constraints (incomes to the system, number of employees, working years to get a pension, etc.) and we seek for an optimal solution. But if the optimal solution, as comes from OR, is far away from "preferred political solution", then the politicians will say: "No, I want a new problem, where 'preferred political solution' will be a feasible solution". So, by law they change the constraints and the "preferred political solution" becomes a feasible solution. Is it the optimal solution? Who cares, since it is legal...

This a good idea for a startup for those who have understood the power of multivariate analysis (as well as the power of optimization techniques) techniques in the decision making. In other statutory institutions like the courts, OR techniques could be used and have a considerable impact on the quality of the verdicts. I expect that the landscape would change in the future but for the time being these techniques are not widely used. Nevertheless, OR analysts are among the citizens that understand the government irresponsibility at most (e.g. mistakes in terms of resource allocation etc.).

Well... if they don't, they should, assuming goverments should exist (which they shouldn't :P). Operations Research is key in nearly every aspect of managing optimally any kind of endeavour where money is involved. Without such techniques, Government (or any organization) is operating as if nothing could be done to improve and will likely lose to the competition (unless everyone in the market is just ignorant of the techniques, but if you aren't, then take advantage of the fact that most people don't!). The problem with governments is that they have no incentive to optimize, since they get paid anyway... "by law".