Quantifying the Uncertainty Associated with Long Term Maintenance Contracts
Kostuk, Kent Joseph
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Long term maintenance contracts are emerging as an alternative for state agencies to man age their infrastructure assets. For the owner, long term maintenance contracts establish a deterministic schedule for maintenance costs over a fixed time horizon. It has been documented that contractors are willing to accept the risks associated with long term maintenance contracts when provided with the information necessary to assess the potential risk and the freedom to provide innovative solutions to address these risks. The objective of this research was to develop a generic framework to quantify the financial risk faced by a contractor in bidding a long term maintenance contract for public sector infrastructure. To accomplish this goal, a methodology was developed to take generic infrastructure asset performance curves, maintenance treatment costs, and mini mum performance criteria as inputs to calculate the present value of the expected maintenance costs for a long term maintenance contract. The probability distribution associated with these predicted costs can then be applied by a contractor (in conjunction with their risk tolerance) to establish the appropriate tender price. By adjusting the input parameters, the contractor can determine the sensitivity of the optimal maintenance strategy to model inputs. The sensitivity analysis allows the contractor to determine the inputs that must be controlled to ensure success as well as to identify the areas which could potentially provide the greatest opportunity for savings. The framework developed in this research is a generic mathematical methodology, applicable to all forms of public sector infrastructure. To illustrate its application, a roadway pavement management problem was selected. The methodology to accomplish the research objective was quite straight forward. The first step in the process was to generate transition probabilities from infrastructure asset performance curves. These transition probabilities provided a mathematical representation of asset deterioration and the effects of maintenance and rehabilitation activities throughout the term of the contract. From the transition probabilities, an optimal maintenance strategy was determined. The optimal maintenance strategy was modelled over a ten year time horizon (the typical length of a long term maintenance contract). From the ten year model, expected costs, variance, and in tum the risk associated with a project (individual maintenance segments in a contract) were determined. The sum of the expected project costs is equal to the expected total cost of the long term maintenance contract. The variance of expected costs of a long term maintenance contract can be determined in a similar manner. Thus, if the risk associated with individual maintenance segments can be determined, the risk associated with a long term maintenance contract can be deter mined. A series of sensitivity studies were also included to determine the sensitivity of the optimal maintenance strategy to changes in asset performance, maintenance costs, or performance constraints. In general, the methodology performed well. It was observed, as would be expected, that reducing the rate of asset deterioration reduced maintenance costs. Similarly, in creasing treatment effectiveness resulted in a decrease in overall maintenance costs. The maintenance strategies for each scenario were quite similar. The only real change between scenarios was the frequency with which the treatments were applied. A limitation to this study was the use of a Markov process to create numeric representations of asset deterioration. The Markov process overestimated early deterioration and underestimated deterioration late in the lifecycle of the asset. It is suggested that a semi markov model would be better suited to model performance curves with the geometric characteristics of the performance curves included in this research; curves with little or no slope for the first few years of the asset's design life.