# multi objective decision making goal programming

NEED HELP WITH THIS QUESTION:

a)      This is a follow-up to the road network problem (assignment 2). Assume the city has set some road performance measures that can be used to assess the overall performance of the road network according to some Level of Service indicators.

 Performance Indicator Calculation Notes Average Network Condition Index (ANCI) 20X1 + 40X2 + 60X3 + 80X4 + 100 X5 X1: % roads in failing condition state X2: % roads in poor condition state X3: % roads in fair condition state X4: % roads in good condition state X5: % roads in excellent condition state International Roughness Index (IRI) 1.5X5 + 3X4 + 6X3 + 10X2 + 12X1 Fuel Consumption Factor (FCF)* 0.0397 * IRI + 0.9524

*Indication for the level of extra fuel consumed during vehicle travel due to pavement unevenness.

The City has set performance targets as follows:

ANCI ≥ 75

IRI ≤ 4

FCF ≤ 1.1

The available total road budget in 2013 is \$10,000,000 and increases by 5% annually. It is required to find the most optimal static rehabilitation policy to be implemented from 2013-2018 that will meet these targets as closely as possible.

Formulate the goal programming optimization problem that considers these objectives simultaneously and solve them using excel solver. Clearly develop and show the equations for the objective function, constraints and deviation variables. Make any necessary assumptions.

*will provide solution from previous assignment

Previous Assignment (HAVE SOLUTION FOR THIS) – Not attaching for privacy reasons

You have developed a Markov Chain for a 800 km road network for a new town. The road network was constructed in 2000 and it is assumed that 90% of all pavement segments had a condition of “Excellent” at that time. Due to poor workmanship 10% of the network was classified as “Good”. Based on your experience managing similar road networks, the transition probabilities for a one year time-step of condition states are shown below.

 P Excellent Good Fair Poor Failing Excellent 0.85 0.15 0 0 0 Good 0 0.9 0.1 0 0 Fair 0 0 0.75 0.25 0 Poor 0 0 0 0.6 0.4 Failing 0 0 0 0 1

a)      Based on this information calculate the condition states of the road network in 2010, 2015, and 2020 assuming deterioration without rehabilitation:

 Length of Road (km) 2010 2015 2020 Excellent Good Fair Poor Failing

b)      In 2013, the road network has experienced some deterioration. As the asset manager of the road network you are evaluating rehabilitation policies for the road network. You have developed the following three policies:

i.      Policy A: Rehabilitate 20% of all road segments that are in a condition state of ‘Fair’, 5% of all segments that are in a condition state of ‘Poor’ and 2% of all segment that are in a condition state of ‘Failing’.

ii.      Policy B: Rehabilitate 10% of all road segments that are in a condition state of ‘Fair’, 10% of all segments that are in a condition state of ‘Poor’, and 10% of all segments that are in a condition state of ‘Failing’.

iii.      Policy C: Rehabilitate 2% of all road segments that are in a condition state of ‘Fair’ and 5% of all segments that are in a condition state of ‘Poor’, and 20% of all segments that are in a condition state of ‘Failing’.

Develop the 1-year and 5-year transition probability matrices for each policy considering both deterioration and rehabilitation.

c)      Based on your previous experience in maintaining the road network you know that the costs for annual reactive maintenance are 2 \$/m for ‘Fair’ pavements, 8 \$/m for ‘Poor’ pavements and 50 \$/m for ‘Failing’ pavement. No maintenance is needed for ‘Good’ or ‘Excellent’ pavements. This amount has to be spent to maintain minimum safety standards of the road.

In addition, the estimated costs to rehabilitate a ‘Fair’ road is 500\$/m, a ‘Poor’ road is 1000 \$/m and a ‘Failing’ road is 3000\$/m.

Since the road was constructed in 2005 no rehabilitation work was performed. In 2013 you want to forecast the impact of each policy on the road network versus the cumulative costs for maintaining the network over the next 5 years (from 2013 to 2018). You have developed the following table to assist in comparing between policies. Assume no rehabilitation took place from 2005 to 2013.

Create a table for each policy to compare total costs.

Comment on the efficiency of each policy with regards to delivering a high level of service to users at least cost.

 Fair Poor Failing Year (20XX) Length of Road (m) Reactive Maintenance Costs (\$) Length rehabilitated (m) Rehabilitation cost (\$) Total Cost \$