A systems approach to replacement

Abstract

The object of this study is a new approach to the problem of replacement of assets which deteriorate and become obsolete with time. The investigator views replacement theory as a subset of capital budgeting. Capital budgeting has received much more attention, has benefited from many advances in mathematical programming techniques, and in general has been advanced to a much more sophisticated state of the art than has replacement theory.

The approach taken in this work is to point out this divergence in advances in these areas by surveying the literature in each. Next a new approach to the replacement problem is presented. This approach is new in that it attacks the replacement problem as a system of interacting components rather than take the normal replacement approach to a single machine. The production process is modeled as a network in which each machine is represented by an arc. A single machine or two or more machines in parallel compose a stage of the process. Several stages are combined to complete the network.

The general model is formulated as a mixed zero-one programming problem for a finite planning horizon. This model can be further modified by adding specialized constraints to make it fit more specific cases. The general model has provisions for equivalence relationships to carry funds forward or backward through time. It also takes into account such items as process requirements and machine capacities.

Difficulties are encountered in that a normal problem is too large to solve. Further study reveals that by making a conservative assumption of using a single interest rate the problem can be reduced to a much smaller zero-one programming problem. This formulation for a reasonably sized production process is small enough to be solved by zero-one algorithms available in the literature.

An example problem is formulated for illustrative purposes.