Maintaining a network of roads and paths

How do you manage conflicting objectives?

When I went to Lancaster University to study for my Master's degree in O.R., there was  a cohort of 28 students.  Some of them have made their career in O.R., others used the subject as a stepping stone into management.  Early in the course, we sat a "Jumbo" exam for the first time.  This was a Lancaster speciality; a fabricated case-study, prepared by the staff, and for which we were in the exam room for seven hours with food and drink supplied during the day.  There wasn't much risk of collaboration - partly because we were all striving to tackle the problem as individuals, but also because by the time we broke for lunch together, we had all started to analyse the data and problem and it would be too late to change our planned analysis.  Later on, the exam was extended to eight hours, with the first hour devoted to reading, and not writing or calculating - this was to help those who had come from a non-UK culture, and staff could be asked to clarify any cultural questions.

We were, I believe, the first cohort to sit a "Jumbo" during our first month on the course.  We were part of an experiment to see how we progressed during the year on the course, so our marks did not count, but were used to demonstrate the benefit of the degree programme.  What I remember of that first case-study was that most of us made an incorrect assumption about presenting the results.  Most of us reached the end of the case-study, which concerned water treatment, and tried either to find the best water quality (measured by pollution level) irrespective of cost, or find the least cost treatment which barely satisfied the water quality requirements.  What we should have done, we discovered later, was to help the decision-makers by tabulating several options, of quality versus cost, and then leaving the choice to management.   So we ended up with something like this:

During the following twelve months, we became familiar with such a set of results, either as a table or in a graph, one of the classic forms of showing the Pareto frontier. There is a conflict of objectives - reduce the pollution, and increase the cost.  The Pareto frontier allows one to eliminate dominated solutions.

A few years later, when we needed a mortgage for a house, the advisor asked me to describe what I did in O.R., and I talked about conflicting objectives with such enthusiasm that he complemented me and happily granted us the maximum mortgage that we needed.  (I wish all my hearers had been so enthusiastic!)

There is a research paper in September's issue of the Journal of the Operational Research Society (the UK's leading O.R. journal!) which describes a project with conflicting objectives.  In their paper, "A decision support tool for Public Rights of Way officers based on the Analytic Hierarchy Process", the authors (David John Parsons, Andrew Angus, Martyn Brawn and Joe Morris) describe a widespread problem for local government in the United Kingdom.  How should one look after the network of roads, tracks and paths which are "Rights of Way" - i.e., available for anyone to use.   Some tracks and paths are well used, by riders, dog-walkers, hikers, or simply because they go where people want to go.  Others are very seldom used, possibly because there have been changes in the road layout or because their original purpose no longer exists.  But, legally, the local government has to ensure that Public Rights of Way (PROWs) are maintained, within the budget.

The whole paper makes good reading, especially as I often use Devon's PROWs, and not always the well-used ones.  So I will single out one table as it is concerned with the conflicts involved.

Conceptual framework for the PROW decision tool: attributes influence user preferences, and use generates social and economic outcomes
AttributesUser groupsSocial and economic outcomes
physical characteristicswalkers (travel)community cohesion
structurescyclists (travel)community safety
signagecasual walkersculture and leisure
facilitiesserious walkersenvironmental quality
marketing and promotionsleisure cyclistshealth and social well-being
local relevancehorse riderstransport and access
strategic relevanceusers with impaired mobilityeconomic well-being
social priority groups

The table sums up the range of conflicts involved with maintaining the roads and paths.  As the rest of the paper demonstrates, the simple process of developing a framework is an important first step in helping make decisions.  An old description of O.R. is that it provides "Tools for thinking with" and a summary that started with the table above gave Officers in the local authority some extremely useful tools to think with.

The many outcomes and objectives conflict - if more money is spent on signs for a track used by leisure cyclists, less is available for marketing tracks for serious walkers.   And how do you measure some things on a common scale?  But the tools are there! 

I wish that the decision support tools could be used in other parts of the U.K.!

A decision support tool for Public Rights of Way officers based on the Analytic Hierarchy Process

David John Parsons, Andrew Angus, Martyn Brawn & Joe Morris

Journal of the Operational Research Society (2014) 65, 1387–1395 doi:10.1057/jors.2013.94

Local Government Authorities (LGA) in England and Wales have statutory responsibility for the maintenance of Public Rights of Way (PROW), such as pathways and byways open to non-motorised traffic. The departments responsible have to compete for budgets and justify their expenditure in terms of councils’ priorities, such as well-being and environment. A need was identified for a simple decision support tool to provide a consistent and transparent framework for assessing the range of possible social and economic benefits from expenditure on PROW. The tool uses the Analytic Hierarchy Process to elicit weights forming the links from path attributes to users and usage to benefits, with a final stage to combine the benefits according to LGA priorities. It was successfully tested through case studies, where improving signage was generally found to be the most cost effective option, giving moderate benefits at low cost, whereas improving the physical conditions of the surface gave greater benefits at relatively high cost.


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