Helsinki University of Technology Systems Analysis Laboratory EURO 2009, Bonn Supporting Infrastructure Maintenance Project Selection with Robust Portfolio Modelling (RPM) Juuso Liesiö, Pekka Mild and Ahti Salo Systems Analysis Laboratory Helsinki University of Technology P.O. Box 1100, TKK, Finland

Helsinki University of Technology Systems Analysis Laboratory 2EURO 2009, Bonn Road Asset Management in Finland n Central authority Finnish Road Administration (Finnra) –Annual funding on maintenance and repair some 600 Mє –Central administration and 9 road districts –Need for multiple criteria optimization tools to support asset management –Collaboration with Systems Analysis Laboratory since 2004 n This presentation: RPM to support district level bridge repair programming –Which of candidate repair projects to select under limited resources and multiple value criteria? –Hundreds of repair projects → need for approximate optimization algorithms

Helsinki University of Technology Systems Analysis Laboratory 3EURO 2009, Bonn RPM-Model for Bridge Repair Programming n Annually some m= candidate projects –Repair program (= portfolio of projects) for three years »Not scheduled year by year –Repair budget of 9,000,000€ –Maximum of 90 bridges »Limited availability of equipment and personnel etc. –Must repair at least 15,000 ‘damage units’ n Additive-linear value 6 repair urgency criteria »E.g. Sum of damages, Average daily traffic, Road salt usage, Outward appearance → Integer linear programming (ILP) problem

Helsinki University of Technology Systems Analysis Laboratory 4EURO 2009, Bonn Incomplete Preference Information in RPM n Set of feasible criterion weights instead in point estimates –Criteria 1 and 2 most important –Criteria 5 and 6 least important n Interval scores instead in point estimates »e.g. daily traffic is between 3000 and 4000 vehicles n Non-Dominated portfolios –No other feasible portfolio has a greater overall value for all feasible weights and scores Value w2≥w1w2≥w1 ND-portfolios: z 1, z 2, z 3 z1z1 z3z3 z2z2 z4z4

Helsinki University of Technology Systems Analysis Laboratory 5EURO 2009, Bonn Approximate Computation of ND-portfolios (1/3) n What does not work: –Exact dynamic programming algorithm (Liesiö et al. 2008) due to curse of dimensionality –Maximizing value (ILP) with random w,v »e.g. z 2 does not maximize value for any w n New approach: –Measure the value difference in each extreme point w i to a ”utopian portfolio” V* i –Distance: maximum of weighted differences max i λ i (V* i -V(z,w i )) (max-norm) Value utopian portfolio z1z1 z2z2 z3z3 z4z4 λ 1 =λ 2 z1z1 z2z2 z3z3 z4z4

Helsinki University of Technology Systems Analysis Laboratory 6EURO 2009, Bonn Approximate Computation of ND-portfolios (2/3) n Theorem 1.Any ND-portfolio minimizes distance for some v and λ 2.For any v and λ there exists at least one ND-portfolio among the portfolios that minimize the distance n With given v and λ, minimizing distance to utopian portfolio over feasible portfolios is a MILP-problem »t is the number of extreme points in S w

Helsinki University of Technology Systems Analysis Laboratory 7EURO 2009, Bonn Approximate Computation of ND-portfolios (3/3) n Algorithm: 1) Sample λ from a simplex and scores v from the intervals 2) Find portfolios that minimize distance to the utopian portfolios by solving the MILP 3) Store the non-dominated ones to a list (remove duplicate portfolios) 4) Go to 1 until sufficient number of ND-portfolios have been found

Helsinki University of Technology Systems Analysis Laboratory 8EURO 2009, Bonn Bridge Repair Programming Results (1/2) n In each case 10,000 ND-portfolios computed –Some 25,000 MILPs solved in ~1 hour n Core Index: The share of ND-portfolios that include the project »Core projects, CI=1, included in all ND-portfolios »Borderline projects, 0<CI<1 included in some »Exterior projects, CI=0, included in none n Average case with some –15% core, 35% borderline, 50% exterior

Helsinki University of Technology Systems Analysis Laboratory 9EURO 2009, Bonn Bridge Repair Programming Results (2/2) n Projects listed in decreasing order of Core Indexes –Scores, costs and other characteristics displayed –Tentative priority list –Found practical and transparent by the programming managers

Helsinki University of Technology Systems Analysis Laboratory 10EURO 2009, Bonn Conclusions n RPM-model for bridge repair programming –Flexible (=usable) multicriteria prioritization of bridge repair project –Academic research created new business –14 cases carried out in »4 by Systems Analysis Laboratory, 10 by Pöyry ltd consulting company n Approximate algorithm extends applicability RPM of in other contexts –Commercial MILP-solvers can tackle problems with hundreds of projects –Any non-dominated portfolio possible to find –Easy to implement –Compared to ILP, only t additional constraints, one continuous variable

Helsinki University of Technology Systems Analysis Laboratory 11EURO 2009, Bonn References Liesiö, Mild, Salo (2008): Robust Portfolio Modeling with Incomplete Cost and Budget Information, European Journal of Operational Research, Vol. 190, pp Liesiö, Mild, Salo (2007): Preference Programming for Robust Portfolio Modeling and Project Selection, European Journal of Operational Research, Vol. 181, pp