Optimal Scheduling of Pipe Replacement Including Opportunity, Social and Environmental Costs
Abstract
During the last thirty years, different approaches have been published in the literature to evaluate the optimal scheduling of pipe¡¦s replacement. All consider two terms, C1 and C2, the capital and maintenance costs, this second currently evaluated throughout a break occurrence annual model and the average cost per repair. The paper outlines a new formulation of this problem. The model includes three additional costs currently despised in practice. They are:
âQ Opportunity cost, C3 that is negative when the pipe is replaced with occasion of a major work (for instance the urbanization of the area where the pipe is located). In that case postconstruction or handwork cots are shared between infrastructures, with a clear economic benefit scale.
âQ Social costs, C4, split into two terms. The first C41 is the negative impact generated by the pipe¡¦ installation. Between others, examples of these costs are vehicular traffic disruptions or business losses. But likewise, a social cost is the failure of a standard of service, C42. Pressures at peak hours under a minimum established, due to greater flows with passing time through the pipe, is a clear example.
âQ Last but not least, environmental costs C5 that can be split into three terms. The additional energy expenditure due to pipe aging and leaks, a cost typically considered as environmental indicator. The cost of water lost motivated by leakage too (its environmental value plus the cost of production). Last a term to account for the loss of water quality because of aged pipes and leaks. In some way, older pipes contributes (there is a greater potential risk of pathogen intrusion as well) to substitute water tap for mineral water for human consumption.
Some trends are clear. Two terms (C1 and C41) are very sensible to the used technology (trenchless or open cut). Others, C1, C2, C42 and C5, deeply depend on how long is the period of use of the pipeline. Last C3 and C41 are roughly constant in present value. That is not, indeed, the case of C42 that depends on the flow throughout the pipe and then on the demand temporal variation. And just for this reason, the C4 cost has been disaggregated.
The paper reviews or, alternatively, proposes expressions, referred to the current year, to evaluate all the terms and for the different technologies. From them, minimizing the total costs expected during the span time of the pipe, the optimal scheduling of pipe¡¦s replacement is determined. Additionally they help to find answers to these questions:
âQIn which way affects the new costs introduced to the optimum replacement time?
âQIn which way affects the technology (trenchless or not) to the optimum replacement time?
âQIn which way affects a negative opportunity cost to the optimum replacement time?
All in all, this contribution presents the first results of a wider research still in course.