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

Abstract

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.