On the Optimality of an Equal Life Policy for Equipment Subject to Technological Improvement

The equipment replacement model with equal replacement intervals has been studied by a number of authors. When new equipment is identical to old equipment, it has been proved that an optimum policy involves replacement at equal intervals (the equal life assumption). However, when equipment is subject to technological change, no such proof exists.Since almost all equipment is subject to technological improvement over time, and since the assumption of equal lives vastly simplifies the analysis, such a proof is highly desirable. In the absence of a proof, authors have attempted to justify the equal life assumption as a good approximation to a correct solution. For example, Smith argues that the process of discounting makes future replacements less important and with gradual technological improvement an equal life policy is close to optimum. This paper shows that under the definition of technological change employed by most authors working on equipment replacement problems, it is unnecessary to assume that an equal life policy is optimum, rather the optimality of such a policy can be proven.