Characterization of optimal policy for capital replacement models

Abstract

In this paper we describe the behaviour of a number of replacement models that are used in practice to model replacement decision problems. For clarity of outcome in our analysis, we focus on the following problem: an existing equipment of a certain age and performance performs a necessary function; should we replace this equipment with a new equipment (which performs the same function), and, if so, when? The reasons for replacement of the existing equipment may be numerous, but we focus solely on the economic aspect. In practice, the outcome of an economic replacement modelling exercise, for which the models we describe would be useful, would be expected to influence the actual replacement decision and not necessarily drive it. The decision-maker would bring other technological, social and political factors to bear on the decision. The replacement problem above may be generalized as the consideration of the release of a capital project at some time in the future. The purpose of our analysis is to consider whether the models behave sensibly in general, and are therefore useful in practice, and also to compare and contrast alternative model choices. We essentially look at two replacement decision models: a fixed planning horizon model with a variable number of replacement cycles; and a variable planning horizon model with a fixed number of replacement cycles. These models are also related to the classic ‘economic life’ model. We use R to denote the capital cost of the new equipment, and τ to denote the age of the existing equipment at the start of the planning horizon. The planning horizon is that interval over which we consider the economic consequences of operation and replacement. The current and new equipment perform identical functions. We model age-related costs (operating costs, revenue, resale values) using a function f (t) that models the rate of change of age-related costs with respect to the age of the plant. We call f the cost rate for