Landfill construction and capacity expansion

We study the optimal capacity and lifetime of landfills taking into account their sequential nature. Such an optimal capacity is characterized by the so-called Optimal Capacity Condition. Particular versions of this condition are obtained for two alternative settings: first, if all the landfills are to have the same capacity, and second, if each of them is allowed to have a different capacity. In the second case we obtain an optimal control problem, with mixed elements of both continuous and discrete time. The resulting optimization problems involve dividing a time horizon of planning into several subintervals of endogenously decided length. The results obtained may be useful to address other economic problems such as private and public investments, consumption decisions on durable goods, etc.