Infinite-Horizon Optimality in an Equipment Replacement and Capacity Expansion Model - Hopkins, David S. P. (Management Science, 1971)
The problem faced by a single-product firm that must choose among alternative investments in capital equipment to meet a known demand for capacity in each discrete time period is formulated as a linear program. The formulation explicitly includes a transient set of investment opportunities which are available in early periods, as well as a stationary set which will become available in the near future. Also, no finite time horizon is placed upon the planning process. The approach taken to obtain the optimal solution to the infinite-horizon problem is to solve first a finite-horizon problem that includes a valuation of terminal capital stocks. The optimal solution to this problem is then used to construct a solution to the infinite-horizon problem that is identical to the finite-horizon solution in early periods. This construction is shown to be optimal for the infinite-horizon problem.