A linear programming formulation with integer solutions for solving an equipment replacement problem with multiple assets: The concave demand case

A linear programming formulation is presented for the deterministic equipment replacement problem in which multiple assets are required each period and a number of assets are available for replacement. Under common cost assumptions, the linear programming solutions are shown to be integer for certain demand constraints. This paper considers the case of concave demand over a finite horizon. The integer solutions allow for implementable decisions and the formulation allows for the solution of large replacement problems, such as vehicles in a fleet, without the computational effort of branch-and-bound procedures. Numerical solutions are provided for illustration of the formulation and its efficiency in solving large replacement problems.