# Use of Life Cycle Cost Analysis and Multiple Criteria Decision Aid Tools for Designing Road Vertical Profiles

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## Abstract

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_{2}emissions. Therefore, this paper describes a proposed design procedure that starts by finding feasible alternatives with different grades. Then, a microsimulation traffic tool is used to simulate the movement of predicted vehicles (volume and type) over the different alternatives. The microsimulation tool provides reliable estimates of travel times, fuel consumption, and CO

_{2}emissions for the different alternatives. With these data, it is possible to use life cycle cost analysis (LCCA) or multiple criteria decision aid (MCDA) tools to select the “optimal” alternative. The proposed procedure was used on a case study involving a 6-km highway section with different proposed grades ranging from 2% to 8%. Using LCCA and an MCDA tool, it was revealed that the current design alternative is not the optimal alternative in most considered scenarios (various fuel values for LCCA and different “Cost” weights for MCDA).

## 1. Introduction

_{2}-equivalent [1]. In the U.S., in 2017, CO

_{2}emitted from fossil fuel combustion in the transportation sector was estimated at 1794 megatons of CO

_{2}-equivalent [2]. In their Transportation Energy Data Book, Davis and Boundy presented many facts about fuel consumption in the transportation sector in the U.S. [3], including the following main facts:

- In 2016, there were 113 million cars and 133 million light trucks;
- In 2016, light vehicles accounted for 90% of the 3.2 trillion driven vehicle miles;
- In 2016, there were 11,499,000 heavy trucks;
- In 2016, heavy trucks and buses accounted for 10% of the 3.2 trillion driven vehicle miles;
- In 2017, transportation petroleum use was 70% of total petroleum use;
- In 2017, petroleum comprised 92% of transportation energy use;
- In 2016, cars and light trucks accounted for 63% of transportation petroleum use;
- In 2016, medium trucks accounted for 4% of transportation petroleum use;
- In 2016, heavy trucks and buses accounted for 19% of transportation petroleum use;
- In 2017, transportation energy use accounted for about 29% of total energy use;
- In 2016, cars and light trucks accounted for 59% of transportation energy use;
- In 2016, medium trucks accounted for 5% of transportation energy use;
- In 2016, heavy trucks and buses accounted for 19% of transportation energy use.

_{2}emissions as criteria during the initial design of the vertical profile of roads. The conventional design recommendation to follow the terrain profile to minimize cut/fill quantities might be revisited in certain situations. For instance, a decrease in the longitudinal grade from 6% to 3% would certainly increase the initial construction cost; however, benefits from significant reductions in fuel consumption and CO

_{2}emissions, improved service to motorists, and reduced accidents might justify such an investment. This paper presents a case study where traffic microsimulation software was used to simulate traffic on a 6-km, four-lane divided highway section (two lanes per direction). Five alternatives were considered for the longitudinal profile of the studied section. Life cycle cost analysis (LCCA) as well as a multiple criteria decision aid (MCDA) tool were used to select the “optimal” alternative. Based on the considered costs for the fuel/CO

_{2}emissions or the weights attributed to the criteria, the alternative with the lowest earthwork cost was not found to be the optimal solution.

## 2. Methods

#### 2.1. Life Cycle Cost Analysis

_{j}or C

_{i}) or a benefit (B

_{j/i}) is applied. The EUAW is a conversion of the NPW into a series of equal annual amounts. This is achieved mathematically using Equation (2). As shown in Equation (3), the BCR of alternative j with respect to i (BCR

_{j/i}) is the ratio of the discounted present benefits of project j with respect to project i to the difference in the discounted present costs of both projects. If the higher cost alternative, j, yields a BCR equal to or greater than 1, it is retained and the lower cost alternative, i, is eliminated. With all three methods, the discount rate should be assumed depending on risk of investment and economic conditions. The IROR is the discount rate for which the NPW is equal to zero. If the IROR exceeds the minimum attractive rate of return, the higher cost project is retained; otherwise, it is eliminated and the lower cost alternative is selected.

_{2}and consumed fuel were considered. Uncertainties in other variables were deemed similar for all alternatives, which will not affect the performed comparative study.

#### 2.2. Multiple Criteria Decision Aid

_{j}is the weight associated with criterion j and k is the total number of criteria. A value of π(a, b) close to zero indicates a weak global preference of a over b, while a value close to 1 indicates a strong global preference of a over b. Then, each alternative a belonging to the total set of alternatives A is faced with the n − 1 of other alternatives by calculating two indices—the positive and negative outranking flows—as shown in Equations (6) and (7), respectively. The net outranking flow, Equation (8), is then used to rank all the alternatives. The alternative with the highest net outranking flow is considered the “optimal” alternative for the project.

#### 2.3. Rakha–Pasumarthy–Adjerid (RPA) Car-Following Model

_{n}(t), as shown in Equation (9).

#### 2.3.1. First Order Steady-State Car-Following Model

_{f}is the free-flow speed expressed in m/s, and c

_{1}(m), c

_{2}(m

^{2}/s), and c

_{3}(s) are constants used for the Van Aerde steady-state model that have been shown to be directly related to the macroscopic parameters defining the fundamental diagram of the roadway. A speed formulation is adopted for the Van Aerde model, as demonstrated in Equation (11), which is derived from Equation (10) using basic mathematics.

#### 2.3.2. Collision Avoidance Model

_{n−1}(t) is the speed of the leading vehicle and b is the maximum allowed vehicle deceleration.

#### 2.3.3. Vehicle Dynamics Model

_{a}), rolling (R

_{r}), and grade (R

_{g}) resistances.

_{ta}is the vehicle mass on the tractive axle. The acceleration computed using the dynamics model is then used to calculate the maximum feasible speed ${u}_{n}^{DYN}$ using a first Euler approximation.

#### 2.4. Virginia Tech Comprehensive Power-Based Fuel Consumption Model (VT-CPFM)

_{0}, α

_{1}, and α

_{2}are the model parameters, which are vehicle-dependent and are obtained using any drive cycle as long as both the drive cycles and the total fuel consumed for those drive cycles are reported. Prior research has shown that the VT-CPFM is simple, accurate, and easily calibrated [21]. The instantaneous power, in kW, is calculated as presented in Equation (16) by computing the instantaneous resistance forces R(t) in N, the instantaneous acceleration a(t) in m/s

^{2}, the mass of the vehicle m in kg and its driveline efficiency η

_{d}, and the instantaneous vehicle speed v(t) in km/h. The resistance force on the vehicle is computed as the sum of the aerodynamic R

_{a}, rolling R

_{rl}, and grade resistance R

_{G}forces as expressed in Equation (17). In this equation, p is the density of air at sea level at a temperature of 15 °C, C

_{d}is the vehicle drag coefficient (unitless); C

_{h}is a correction factor for altitude (unitless) and is computed as (1–0.085H) where H is the altitude in km; A

_{f}is the vehicle frontal area in m

^{2}; C

_{r}, C

_{1}, and C

_{2}are rolling resistance parameters that vary as a function of the road surface type, road condition, and vehicle tire type; and G(t) is the instantaneous road vertical grade in m/m.

_{2}emissions generated by the vehicles. To address this issue, expected values within specific distributions can be adopted [22,23]. The model used in this paper is deterministic to simplify the evaluation. A future version of the simulation software will consider all these uncertainty aspects. However, for the current comparative study, all these parameters were kept the same for all treated alternatives and only the grade value (variable of interest) was varied between alternatives.

## 3. Proposed Evaluation Procedure

_{2}emissions. If the decision maker can estimate other measures of effectiveness (such as accidents and emission of other pollutants as NO

_{x}, SO

_{x}, PM

_{10}, and PM

_{5}) between the proposed alternatives, then he/she should include them in the analysis.

_{2}emissions are established. The benefits are the saved user costs associated with one alternative versus another multiplied by the considered unit cost. Other criteria, such as accidents (crashes, injuries, deaths) could be taken into account if they can be estimated within a certain level of reliability. Once the costs and benefits of one project versus another are all established in dollar values for the whole analysis period, an economic indicator, as discussed above, can be calculated to select the best cost-effective alternative. For this study, the IROR is used.

_{2}emissions and fuel consumption to be most important. For this reason, a sensitivity analysis is always recommended, wherein the weights are changed to study the effects on the final selection.

## 4. Case Study: Description, Results, and Discussion

_{2}emissions) results.

_{2}emissions). Table 1 shows the main assumptions used for the traffic simulations. The infrastructure was modeled as a 2 × 2 highway. Simulating uphill and downhill movements is very important, as many researchers think that consuming more driving fuel uphill would be compensated for by consuming less fuel when driving downhill, and hence designers should always follow the terrain grade. Results of the simulations can be used to show whether this argument is valid. The modeled vehicles were a car with a mass of 1550 kg and a power of 132 kW and a truck with a total mass of 27,500 kg and a power of 354 kW. These represent typical characteristics for cars and trucks in the U.S. However, the used vehicles do not have the modern engines that cut the injection when driving downhill since the available software does not model engine cut offs, at this time. This feature could be added in future versions of the software.

_{2}emissions for all treated alternatives as predicted by INTEGRATION. In terms of travel time, all the alternatives resulted in similar values for cars of around 324 kilo-vehicles times hour (kveh. × h) per year. This is explained by the average travel speed of around 115 km/h, which did not differ as a function of grade. Average travel speed for trucks, on the other hand, was found to differ as a function of grade, with a value of 58.2 km/h at 8% uphill, 86.2 km/h at 4% uphill, 101 km/h at 2% uphill, while the average truck speed traveling on leveled grade or downhill was around 113 km/h. This difference in travel speed going downhill or uphill explains the difference in total travel time per year for trucks for the different alternatives. The total travel time per year for trucks predicted for Alt. 1 was 72.5 kveh. × h and decreased to 60.6 kveh. × h for Alt. 5.

_{2}emission trend is similar to that for fuel consumption given that CO

_{2}emissions are equal to a constant multiplied by the fuel consumption. The constant used varies depending on the vehicle type. Cars (trucks) traveling on a road as designed for Alt. 1 are expected to emit 9.7 (14.1) kilotons (kt) of CO

_{2}per year. These numbers decrease to 7.6 kt (11.6 kt) per year for cars (trucks) traveling on a road designed for Alt. 5.

_{2}emissions, Alt. 3 outperformed Alt. 1 by 14.2%, while Alt. 4 reached savings as high as 20%.

_{2}emissions. The next question is whether these savings outweigh the increase in cost associated with earthwork needed to bring the road level to the proposed values for each alternative. This question can be answered based on the results of the LCCA and MCDA tool presented in the following sections.

#### 4.1. LCCA Results

^{3}and the average unit price for regular excavation used in the State of Virginia (20 $/m

^{3}). It was assumed that the cut material is of acceptable quality to be used in the fill areas for Alt. 3 and Alt. 4. The fuel cost per liter and the CO

_{2}cost per ton were varied, as shown in the table, in order to study the sensitivity of these values on the calculated IROR. The analysis period was taken to be equal to 50 years. Alt. 1 was taken as the basis alternative since it is the common geometric design and the least expensive alternative.

_{2}emissions for Alt. 2 as compared to Alt. 1. The CO

_{2}emissions prices included the lowest (3 $/t) and highest (900 $/t) published values as reported by Nocera et al. [11]. If a 4% discount rate were assumed to be the minimum attractive rate of return, then Alt. 2 would be preferred over Alt.1 for a fuel value higher than 1.25 $/L, 1.12 $/L, 1.0 $/L, 0.76 $/L, 0.55 $/L, and 0 $/L for CO

_{2}emission prices per ton of $3, $50, $100, $200, $300, and $900, respectively. The 0.75 $/L represents the approximate current average sale price of fuel (diesel and gasoline) in the U.S. The authors believe that the value of fuel is much more than its sale price and should include the concept of sustainability, since a liter saved today would be available for use by future generations. Using a value of 4 $/L results in IROR values greater than 13%. Therefore, given these results, Alt. 2 is preferred over Alt. 1.

_{2}emissions for the most costly alternative (Alt. 5) as compared to Alt. 1. The decision to select this high-priced alternative over Alt. 1 starts for fuel prices of about 2.3 $/L. Therefore, the decision to select even this high-cost alternative over Alt. 1 is highly recommended, especially given that other criteria that add to the benefits of this alternative were not considered. These include a reduction in fatal crashes, injuries, and physical damage to vehicles during accidents. It is known that the probability of accidents on 8% grades is higher than the probability at lower grades for driving in both directions (upgrade and downgrade). At high grades, trucks create moving bottlenecks that result in different vehicle speeds along the roadway. This speed differential causes higher crash rates. Driving downhill on an 8% grade increases the probability of truck braking mechanism failures. The addition of supplementary lanes for trucks driving upgrade and the construction of escape ramps for trucks driving downgrade would increase the cost of the base design. These additional costs and benefits were not considered in this case study to make it simpler and to show that the alternatives are more attractive than the base solution even when ignoring these parameters.

#### 4.2. MCDA Tool Results

_{2}” criteria were equally varied from 5% to 30%. Table 3 shows the performance table as used with PROMETHEE. The indifference and preference thresholds were set as recommended by the software, with the exception of the Cost criterion, where values of 4 and 10 M$ were used as thresholds to ensure a strict preference for Alt. 1 with respect to all other alternatives for this criterion. In Table 3, the green values show the best performing alternative with respect to a given criterion, while the red values show the worst preforming alternative.

## 5. Conclusions

_{2}emissions. Geometric road designers are accustomed to following the terrain profile in rolling and mountainous areas, considering only minimizing the initial cost of the road. However, on steep grades, cars and trucks emit more CO

_{2}and consume more fuel. Therefore, it is recommended that several feasible alternatives with different reduced slopes be included in the initial design of the vertical profile of roads. The designer should then use a traffic simulation tool to simulate the traffic that will be using the designed road to estimate the performance measures for the different alternatives. Once the performance measures are estimated, the designer can use either LCCA or an MCDA tool to select the “optimal” alternative. The proposed procedure was tested with a case study and the findings led to the following conclusions:

- The least cost alternative with the lowest required earthwork may not be the “optimal” design.
- As compared to a leveled road (0% grade), the rate of car and truck fuel consumption and CO
_{2}emissions is much higher when going uphill than when going downhill. Therefore, the idea that excess fuel consumed uphill is compensated by lesser fuel consumed downhill is inaccurate. - Currently, vertical profiles of roads are the role of a geometric designer who is an expert on surveying and geometric road properties. This study recommends that transportation engineers consider a project from all perspectives (planning, design, management, etc.) and understand concepts related to traffic engineering and management.
- A design software could be developed to help the analysis described in this paper. The input to such a software is the associated costs for all alternatives (excavation, filling, transportation, materials, extra lane construction, etc.) as well as the measures of performances predicted for each alternative. The software output would be the LCCA indicators and/or the ranking of the different alternatives using any MCDA tool. Different types of uncertainties could be added to the software analysis tool.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 3.**Measures of performances for the different alternatives: (

**a**) travel time; (

**b**) fuel; (

**c**) CO

_{2}.

**Figure 5.**Internal rate of return (IROR) as a function of fuel and CO

_{2}prices for (

**a**) Alt. 2 vs. Alt. 1; (

**b**) Alt. 5 vs. Alt. 1.

**Figure 6.**Calculated net outranking flow for the different alternatives for the various considered Cost weights.

Characteristics | Value |
---|---|

Average annual daily traffic | 2000 |

Percentage of trucks | 15% |

Directional distribution | 50/50 |

Proportions of daily traffic occurring during the peak hour | 15% |

Free flow speed | 120 km/h |

Speed at capacity | 90 km/h |

Jam density | 160 veh./km/lane |

Saturation flow rate | 1800 veh./h/lane |

Item | Cost |
---|---|

Earthwork cost Alt. 1 (M$) | 4 |

Earthwork cost Alt. 2 (M$) | 60 |

Earthwork cost Alt. 3 (M$) | 44 |

Earthwork cost Alt. 4 (M$) | 88 |

Earthwork cost Alt. 5 (M$) | 120 |

Value of travel time ($/(veh. × h), cars | 30 |

Value of travel time ($/(veh. × h), trucks | 56 |

Value of fuel ($/L) | 0.75–4 |

Value of CO_{2} emissions ($/t) | 3, 50, 100, 200, 300, 900 |

Cost (M$) | Fuel per Year (kL) | CO_{2} per Year (t) | Time per Year (kveh. × h) | |
---|---|---|---|---|

Alt. 1 | 4 | 10,300 | 23,800 | 396.4 |

Alt. 2 | 60 | 8500 | 19,900 | 387.1 |

Alt. 3 | 44 | 8700 | 20,400 | 391.0 |

Alt. 4 | 88 | 8200 | 19,100 | 385.3 |

Alt. 5 | 120 | 8200 | 19,200 | 384.2 |

Indifference threshold (q) | 4 | 600 | 1600 | 3.6 |

Preference threshold (p) | 10 | 1600 | 4000 | 9.6 |

Weight | 50–300 | 5–30 | 5–30 | 5 |

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## Share and Cite

**MDPI and ACS Style**

Loulizi, A.; Bichiou, Y.; Rakha, H. Use of Life Cycle Cost Analysis and Multiple Criteria Decision Aid Tools for Designing Road Vertical Profiles. *Sustainability* **2019**, *11*, 7127.
https://doi.org/10.3390/su11247127

**AMA Style**

Loulizi A, Bichiou Y, Rakha H. Use of Life Cycle Cost Analysis and Multiple Criteria Decision Aid Tools for Designing Road Vertical Profiles. *Sustainability*. 2019; 11(24):7127.
https://doi.org/10.3390/su11247127

**Chicago/Turabian Style**

Loulizi, Amara, Youssef Bichiou, and Hesham Rakha. 2019. "Use of Life Cycle Cost Analysis and Multiple Criteria Decision Aid Tools for Designing Road Vertical Profiles" *Sustainability* 11, no. 24: 7127.
https://doi.org/10.3390/su11247127