A new framework for the selection of construction and maintenance for multi-unit deteriorating facilities.

Abstract

Some facilities deteriorate over time and use, and replacement or maintenance is necessary as they deteriorate. Selecting replacement and maintenance alternatives for these deteriorating facilities is challenging, because decisions are dynamic. Decisions become particularly complex for large deteriorating systems of thousands of deteriorating units, especially under limited budgets. Only integer programming provides truly optimal solutions, but it is expensive for even small problems, and it is practically impossible for systems of realistic size. This research explores the use of linear programming (LP) techniques together with aggregation to provide a new framework that can handle large deteriorating systems. The model collects similar units into aggregates. It also relaxes the integrality requirements of decision variables from an original IP at the cost of a small loss of optimality. The model also reduces the number of feasible alternatives efficiently by introducing threshold concepts, and it captures the interdependence of alternatives over time by using vector and matrix concepts. Finally, it uses LP techniques to select the best alternative for each aggregate, which is also the best alternative for aggregate's units. The model is implemented on a real multi-unit deteriorating system, the Ann Arbor City street system. In the case study, the performance of the aggregation is evaluated by measuring and comparing savings in effort (the solution times for an aggregated LP and for an unaggregated LP) and aggregation errors (objective function values from an aggregated LP and an unaggregated LP). A number of experiments investigate the sensitivity of aggregation to different factors. In these experiments, the computational savings range from 95% to 99%, and aggregation error is less than 0.1% in most cases and consistently less than 0.9%. The model is an effective tool especially for large deteriorating systems, because the number of aggregates can remain unchanged regardless of the number of units in a system. The model is also a very effective tool for a practical decision making process in which consistency of solutions is important and a variety of sensitivity analyses should be performed.