The maintenance backlog on national roads in Norway has been estimated to NOK 11 billion. In addition, there is a backlog of similar size on regional roads. To alleviate this problem, funds will probably be shifted from infrastructure investment to maintenance and rehabilitation in the next National Transport Plan. How much is needed? The obvious answer seems to be “NOK 11 billion”. A closer look at the method used to compute the backlog reveals that this is far from certain. From the point of view of maximizing social welfare, it might be more or it might be less. One of the reasons for this is that the backlog is computed as the cost of bringing all roads to predefined states, but the benefits of doing so have not been assessed. Nor is the question of timing sufficiently addressed.
This is not a criticism of these reports. What they do, they do correctly. It is rather the tools to do something more comprehensive that are lacking. The problem we would like to solve is the following: Consider a set of infrastructure objects that will have to share the same annual maintenance budgets. Their rates of deterioration may differ. Their initial states may be anything between the best possible and the worst possible. The worse the state, the higher the user costs. The agency in charge has at its disposal a number of rehabilitation activities of different intensity and cost. A rehabilitation strategy is the allocation of rehabilitation activities to the different objects for a number of future years, subject to annual budgets. The problem is to find a rehabilitation strategy which minimizes the sum of user costs and agency costs subject to the budget constraints and constraints on end states.
If this problem – applied to road pavements
– could be solved efficiently, a limited number of experiments with the annual budgets could establish the benefit-cost ratio of allocating more money to maintenance, the best time profile for the budgets as well as the long-run average states to be aimed at for the different classes of road.
All practical strategic road maintenance systems at present fail to solve this problem. The Finnish HIPS is probably the best, as it solves correctly the problem of finding welfare optimal pavement rehabilitation strategies for a set of roads when there are no annual budget constraints. Unfortunately, annual budget constraints do exist and are |
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known to make the problem extremely complex. Therefore, simple but incorrect methods are often offered instead, in the hope of not getting too far off the mark. A few articles in the academic literature solve versions of the rehabilitation strategy problem, but we do not know if they have been put to practical use.
In an article about to be published in the journal Computers & Operations Research, we study the rehabilitation strategy problem and model it as an integer programming problem with underlying dynamic programming structure. A heuristic algorithm with upper and lower bounds for the solution is proposed. The algorithm has been programmed for the road pavement application and applied to what we thought were realistic cases with respect to deterioration rates and costs. The results are promising and indicate that the model might indeed be applied to find optimal pavement rehabilitation strategies and do cost-benefit analysis of maintenance budget changes.
For practical applications we still need to validate our functions and parameters. Suggestions from other researchers and practitioners are welcomed. We also need to test the software on a wider range of cases. A wider choice of functional forms and applications to other types of infrastructure will require some reprogramming, which we hope to be able to do in the future.
Geir Dahl, University of Oslo, Norway
Harald Minken, TŘI, Norway
Contact:
Geir Dahl
Harald Minken |
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