A capital equipment replacement model for a fleet with variable size Available to Purchase

A replacement model over two cycles, with decision variables based on age at replacement of the current fleet and size of the new fleet is considered. In order to consider both age at replacement and fleet size, the concept of penalty cost for unmet demand is introduced and modelled using results from birth‐and‐death processes. Optimal values for decision variables may be found through minimization of the total discounted cost per unit time or the equivalent rent value. The role of the penalty cost and its influence on decision variables is emphasized. A numerical solution is proposed and illustrated using data on a particular fleet of medical equipment.