Serial Replacement Under Evolving Productivity.

The infinite horizon, deterministic, serial replacement problem is studied under conditions of evolving productivity. Early models required some key simplifying assumptions about the evolving productivity of future assets to facilitate the solution. In this work, another model is presented that represents productivity improvement of future assets as a multiplicative function of cash flows of current assets. The effect of productivity improvement on the economic service life of current and future assets is studied for exponential and non-exponential functions. Data from industry is presented to illustrate the general trend exhibited by productivity change. The serial replacement problem is also studied under the conditions of no discounting. Optimality needs to be redefined for this possibility. Existing optimality criteria are reviewed and a new one, decision epoch optimality, is developed. Existence of a forecast horizon is proven when an unique decision epoch strategy exists and an algorithm is presented which finds the optimal first policy for the infinite horizon problem. Non-forecast horizon methods are also developed. Conditions are developed under which the existence of a turnpike asset is guaranteed. An upper bound for the time at which the turnpike asset is installed is obtained. This is done for the cases of profit maximization, cost minimization and a general model which includes costs and revenues. Finally, for the case where productivity improvement reaches its bound asymptotically, error-bounded turnpike times are defined and an upper bound for determining these times is obtained. An algorithm is also developed which obtains the entire strategy to the infinite horizon problem for the various cases when a turnpike asset exists.PhDIndustrial engineeringUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/161656/1/8801321.pd