An Optimal Control Approach to National Settlement System Planning

In this paper, an optimal control approach to a problem in national settlement system planning is presented. The problem description is the same as considered by MacKinnon [6] and by Evtushenko and MacKinnon [4]. It is shown how the special structure of the model and the singular nature of the control can be used to reduce the solution of a nonlinear programming problem to the solution of sets of linear equations. A branch and bound integer programming algorithm is used to handle inequality constraints on the control variables. The organization of the paper is as follows. Section I considers problem formulation and an optimal control solution is discussed in Section II. A branch and bound technique for determining active constraints is presented in Section III. A more general problem is considered in Section IV and conclusions are stated in Section V