Capacity expansion for a loss system with exponential demand growth
We study a loss system to forecast the demand for capacity based on the forecast demand for service and a specified service level. A little-used property of the Erlang loss formula allows the linear transformation of demand for service into demand for capacity. Next, given the forecast demand for capacity, we approximate a long-run optimal capacity expansion policy by optimizing over successively longer finite time horizons. Analytical formulas together with regression analysis show the significance of the number of potential customers, frequency and duration of their requests for service, and the specified service level on the demand for capacity. Numerical sensitivity analysis exposes the effects of cost parameters, the demand growth rate and the required rate of return on the optimal time intervals between expansions.