The dynamics of asset lifetime under technological change

The variable lifetime of assets is analyzed in a serial replacement problem. Technological change impacts the maintenance cost and new asset cost. The optimal asset lifetime appears to be constant only when both costs decrease with the same rate. We identify cases when the technological change decreases or increases the optimal lifetime.     

Hybrid approach to the rational management of machine replacement

The paper analyzes a nonlinear integer-valued optimization problem that describes the optimal machine replacement under improving technology. The problem is extended into the classes of real-valued discrete-time optimization problems and continuous-time optimal control. The results include some qualitative properties of optimal management policies and the construction of an efficient numeric algorithm.     

A paradox in equipment replacement under technological improvement

It is commonly assumed that an acceleration in technological improvement should result in a more rapid introduction of new technology. Under a simple technological change model of a constant factor improvement in equipment costs per period, we show that, paradoxically, the effect is to optimally delay the introduction of new technology.     

Network economics and optimal replacement of age-structured IT capital

The constructed hierarchical optimization model of vintage capital replacement takes into account network effects and the age-dependent technological structure of capital equipment. It involves the control of a network coalition choice, endogenous investments, capital structure, and capital lifetime. The qualitative analysis of the model shows how the lifetime and financial structure of the IT capital depends on technological change. These results are relevant for strategic management on a firm level. Provided numeric examples simulate the optimal lifetime of personal computers. This research is partially supported by the NATO grant CLG 982209.     

Integral equation of optimal replacement: Analysis and algorithms

The paper is devoted to theoretic and numeric investigation of a nonlinear integral equation with an unknown function in the upper limit of integration. This equation appears in optimal replacement problems of engineering and production economics. Its solution is essential for finding the optimal policy of equipment replacement under technological advances. Solvability and qualitative dynamics of the solution are analyzed. Computational algorithm for solving the equation is constructed. A numeric example illustrates the obtained results.     

Equipment replacement under continuous and discontinuous technological change

Technological change is a major motivator for replacing equipment.Models in the literature generally assume that technology evolvescontinuously according to some known function or that thereare breakthroughs in technology in a given (or uncertain) futuretime period. We model the situation where breakthroughs occurperiodically, providing a new vintage of challenger and eachchallenger within a vintage evolves according to a known function.We examine the economic life of an asset with respect to modelsthat only assume continuous or discontinuous technological change.For the case of exponential technological change, we illustratethat the economic life tends to be shorter in our models andthat significantly different solutions can occur when breakthroughsare ignored. We believe this work leads to new questions inreplacement analysis which examine the combined effect of continuousand discontinuous technological change.     

Optimal replacement policies for two-unit machines with running costs: II

In a previous paper [1] we have proved the optimality of a control limit policy for certain two-unit systems with running costs. Under such a policy when either of theunits fails we also replace the other unit if its age exceeds a predetermined control limit.In this work we develop a procedure for computing various important characteristics for any control limit policy including, of course, the optimal one. Some of the resulting characteristics can then be used for a restricted optimization within the class of control limit policies. The fact that this restricted optimization leads to the global optimal is implied by the previous paper. In this sense the two approaches are complementary.