A Probabilistic-Based Approach to Evaluate Winter Maintenance Vehicle Wash Water Management Options

Abstract

When locating new facilities, departments of transportation must consider how the wash water generated during routine winter operations will be managed. Previous research has shown that two options are likely to be the most cost-effective: (a) collecting and hauling off-site for disposal (C_DISPOSE) or (b) connecting to an existing sanitary sewer system (C_SAN). In this article, the cost-effectiveness of these two strategies for Ohio Department of Transportation (ODOT) maintenance facilities was evaluated probabilistically using Monte Carlo simulation. The probability C_DISPOSE was the most cost-effective option was greater than 90% for existing ODOT facilities without sanitary sewer access if the sanitary sewer capital cost exceeded US$172,000. Considering all ODOT facilities, there was 90% probability C_DISPOSE was the most cost-effective option if the sanitary sewer capital cost exceeded US$280,000. These results can be used to guide facilities management decisions regarding wash water management options for both existing and future facilities.

Keywords

winter maintenance wash water management probabilistic analysis Monte Carlo simulation transportation facility management

Introduction

Snow and ice removal is essential to minimize the impact of winter events on the transportation network within the state of Ohio. The Ohio Department of Transportation (ODOT) has a fleet of 1,583 trucks equipped with salt spreaders located at 88 county and 136 outpost garages to address the needs for snow and ice removal. On average, ODOT spreads 600,000 tons of salt throughout the 43,000 lane miles of highways (ODOT, 2011). In an attempt to minimize corrosion, trucks are washed after every outing.

The waste water generated from washing the trucks after winter events has been identified to contain elevated concentrations of suspended solids, dissolved solids, oil and grease, and heavy metals (Alleman, Partridge, & Yeung, 2004; Fitch, Smith, & Bartelt-Hunt, 2004; Miller, Schneider, Kennedy, & Sullivan, 2014). Where available, oil/water separators treat the wash water before it is discharged directly to the sanitary sewer. Unless it is cost-prohibitive, this is the preferred management strategy for many state Departments of Transportation. Connecting the facility to the sanitary sewer has many benefits, including minimized annual operating costs, maintenance, and labor. This strategy also eliminates the need for collection, storage, and disposal of truck wash water. Although the capital costs to connect to an existing sanitary sewer system can be high, any evaluation of management strategies should include connection to the sanitary sewer due to its benefits.

However, more than 40% of the ODOT maintenance facilities involved in routine truck washing do not have access to a sanitary sewer system, and alternate management methods must be utilized. Due to increasing regulations, current management strategies are becoming substandard, and facilities are in need of an alternative management strategy that is both cost-effective and able to meet all disposal regulations. These factors should be considered when the management strategy of a facility completes its life cycle or a new facility is established.

Previous research has identified and evaluated strategies to manage waste water (Alleman et al., 2004; Fitch, Craver, & Smith, 2006, 2008; Fitch et al., 2004; Miller et al., 2014). Miller et al. (2014) determined six feasible management strategies for implementation by the ODOT: (a) connection to an existing sanitary sewer system, (b) the use of a contractor to pump and haul stored wash water for off-site disposal, (c) disposal of wash water at a waste water treatment plant using ODOT equipment (e.g., trucks) and personnel for hauling, (d) collection and off-site disposal at a nearby ODOT maintenance facility, (e) media filtration and disposal at a nearby ODOT maintenance facility, and (f) media filtration and reuse for brine. Preliminary cost assessments for the management strategies determined collecting and disposing of wash water at a nearby ODOT maintenance facility is a more cost-effective management strategy than commercial disposal or disposal at a waste water treatment plant (Miller, Schneider, & Kennedy, 2015). Filtration and disposal or reuse are predictably costlier than collecting and disposing due to the additional step of filtration. Because the five options all share similar cost factors, any changes to the input variables will affect the feasibility of all five options and have the same relative effect on the cost. Therefore, disposal at an ODOT facility will almost always be the less costly option than commercial disposal, disposal at a waste water treatment plant, filtration and disposal, or filtration and reuse.

The previous research focused on cost assessments of typical county and outpost garages and uses point values in all calculation; this does not accurately predict or provide probabilities for each strategy’s annual cost. ODOT trucks involved with snow and ice removal are located throughout the state of Ohio at 88 county and 136 outpost garages. Fleet sizes per location range from one to 24 trucks. The number of trucks at each facility varies, based on the site-specific conditions, and directly affects the volume of wash water generated. Deterministic estimates utilizing single values can be unreliable, but probabilistic ranges improve the cost estimate reliability, and this will allow government agencies to make more informed decisions when deciding which management strategy is best suited for each situation (Chou, Yang, & Chong, 2009).

The objective of this project is to evaluate wash water management strategies to determine the most cost-effective option, using a probabilistic-based approach and factoring in the range of values that may be encountered based on varying site characteristics and uncertainty in unit costs. The evaluation was performed by calculating the probabilities that select management strategies will be cheaper than others, using a three-step approach: (a) define probability distributions in the cost equations for the input variables that have uncertainty or variability, (b) determine each strategy’s cost sensitivity for each variable, and (c) calculate the probabilities that select strategies will be cheaper than the others, based on specific site conditions, and assess the influence of those site conditions on the calculated probabilities.

Although six feasible management strategies for use by ODOT have been identified, previous research suggests disposal of truck wash water from an ODOT facility to another ODOT facility with sewer access or connection to an existing sanitary sewer system are cheaper than the other alternatives (Miller et al., 2015). However, a research need exists to examine the cost factors in more detail. Therefore, the objective of this article was to perform a probabilistic-based cost evaluation of two viable wash water management strategies: (a) connection to an existing sanitary sewer system, and (b) collection and off-site disposal at a nearby ODOT facility using ODOT personnel.

Method

Previous research on wash water management used deterministic values based on typical values. Deterministic values are best used when detailed or specific values are available. A probabilistic approach uses probability distributions for one or more variables in a risk equation to quantitatively characterize variability. Variability may occur due to a large deviation of values, uncertainty, or a lack of available data (United States Environmental Protection Agency [USEPA], 2001). Although a probabilistic approach is often used in risk assessments, and this project is not a risk assessment, the techniques can be applied to the uncertainty and variability encompassing wash water management strategies.

Monte Carlo simulation, a numerical technique that relies on repeated random sampling to obtain results, is the most widely used probabilistic method (USEPA, 2001). Monte Carlo simulations define cost uncertainty with input distributions often derived from technical experts or historical data. The ultimate goal of the Monte Carlo simulation is to estimate a cumulative distribution function for the final cost, which includes all the uncertainty (Khodakarami & Abdi, 2014).

The Monte Carlo simulation process consists of the following steps: (a) identify the major and uncertain work components, (b) define statistical distributions of each uncertain item, and (c) use the model to calculate the desired output parameters with a predetermined number of iterations for the desired confidence and simulation error. Cost estimates are composed of both fixed and variable parameters; therefore, not every input must be defined by probabilistic distributions (Carr, 1989).

Monte Carlo simulations can be used to calculate a distribution for a final cost when variables are defined as probability distributions. Computer software enables simulations with numerous calculations to be performed. Monte Carlo simulations were performed using Palisade’s @Risk software, a risk analysis and simulation add-in for Microsoft Excel that enables input variables to be defined by probability distributions. Probability distributions were applied to the nine inputs defined in Table 1. Not all inputs had distributions associated to their value.

Table 1.

Summary of Cost Factors Defined by Distributions in the Collect and Dispose or Sanitary Sewer Annualized Cost Calculations.

Cost factor	Distribution	5 Percentile value	Average	95 Percentile value	Source
Discount rate (decimal)	Histogram	0.0443	0.0740	0.1143	Office of Management and Budget (2013)
Cost of disposal of wash water (US$/gal)	Lognormal	0.0060	0.0121	0.0199	Ohio Environmental Protection Agency (2013)
Number of trucks	Discrete histogram	2	8	16	ODOT
Hose flow rate (gpm)	Uniform	4.1	5.0	5.9	ODOT
Wash time per event per truck (min)	Normal	40.3	60	79.7	ODOT
Number of winter events	Discrete histogram	16	32	54	ODOT
Roundtrip distance of hauling (miles)	Histogram	16.3	49.2	109.7	ODOT
Labor cost (US$/hour)	Gamma	33.44	56.37	87.11	ODOT Bureau of Labor Statistics (2012) Social Security Administration (2014)
Fuel cost (US$/gal)	Normal	3.665	4.315	4.965	U.S. Energy Information Administration (2013)

Note. Values are based on all ODOT county and outpost garages. ODOT = Ohio Department of Transportation.

Cost Equation

A spreadsheet was created to calculate and evaluate costs for the two options. In a typical Excel model, the input variables are defined as a deterministic value that results in a single output. With the @Risk software, the models can be modified to provide probabilistic distributions for the input variables. The program then runs a simulation that performs the calculations for a predetermined number of iterations (10,000 for this article) of the calculations. The resulting output value is also in probabilistic distribution form.

Annualized costs were calculated to evaluate both options at a common basis for comparison, and cost equations were created for the two strategies. For future discussion purposes, the two strategies will be referred to as the Sanitary Sewer option and Collect and Dispose option (C_SAN and C_DISPOSE). The annualized costs are composed of capital costs and operational costs, as shown in Equations 1 and 2.

C_{S A N} = A n n u a l i z e d C a p i t a l C o s t + O p e r a t i o n a l C o s t,

C_{D I S P O S E} = A n n u a l i z e d C a p i t a l C o s t + O p e r a t i o n a l C o s t,

where,

C_SAN = Annualized cost of the tying into an existing sanitary sewer;

C_DISPOSE = Annualized cost of collection and off-site disposal at a nearby ODOT facility using ODOT personnel.

Capital costs must be put in annual terms by calculating the annualized capital cost factor, as shown in Equation 3. The annualized capital cost is then the product of the capital cost and annualized capital cost factor, as shown in Equation 4.

A n n u a l i z e d F a c t o r = \frac{i}{{(1 + i)}^{n} - 1} + i,

where,

i = discount rate;

n = planning horizon in years.

A n n u a l i z e d C a p i t a l C o s t = C a p i t a l C o s t \times A n n u a l i z e d F a c t o r .

The number of years used in the annualized capital cost calculation differed between the two management strategies based on the planning horizon of each option. The Sanitary Sewer option utilized a 50-year planning horizon, based on the useful life expected for a sanitary sewer (Bizier, 2007). The Collect and Dispose option utilized a 30-year planning horizon. This length was selected based on the useful life of the storage tank used to hold the wash water until disposal, as ODOT indicated storage is achieved through the use of an underground fiberglass storage tank (Kennedy, 2013), and the life expectancy of this type of storage system is typically assumed to be 30 years (Xerxes Corporation, 2014; Yale Environmental Health & Safety, 2011). The annualized cost equation is summarized in Table 2. The Sanitary Sewer option is composed of a capital cost for the construction of sanitary sewer to connect to the existing system and an annual operational cost for disposal. The Collect and Dispose option consists of a capital cost for storage and annual operational costs for water quality monitoring, hauling, and disposal.

Table 2.

Capital and Operating Cost Factors Used in the Calculation of the Annualized Wash Water Management Costs.

Management options	Capital cost	Operating cost(s)
Sanitary sewer (C_SAN)	Construction	Disposal
Collect and dispose (C_DISPOSE)	Storage	Water quality monitoring
		Disposal
		Hauling

Definition of Input Variables

Variables were defined by probability distributions when a value was uncertain or demonstrated variability. This may occur due to a lack of available information or differences among the population of values. This approach accounts for the range of feasible values (minimum through maximum) for each variable that may occur at an ODOT maintenance facility. Subsequently, calculations utilizing the distributions will provide a range of annualized costs and associated probabilities for both strategies. Comparing the two management strategies in probabilistic terms can help determine which management strategy has the lesser annualized cost.

An important variable in any cost model is the discount rate. The proper selection of a discount rate can be a difficult proposition for governmental agencies (Veneziano, Shi, & Ballard, 2010). As funds for winter maintenance are reserved exclusively for winter maintenance activities, no alternative investments or minimum rates of return exist. Therefore, the discount rate can be defined by the Office of Management and Budget (OMB) “Discount Rates for Cost Effectiveness, Lease-Purchase, and Related Analyses” guidance (Veneziano et al., 2010). This document, an appendix in “Circular A-94: Guidelines and Discount Rates for Benefit-Cost Analysis of Federal Programs,” sets the discount rates to be used in calculations by most federal programs.

Using historical data from the OMB document, the distribution was defined as a histogram based on the discount rate of a 30-year maturity from 1979 to 2013. The discount rate is defined as a probabilistic distribution based on the nominal interest rates on treasury notes and bonds of a specified maturity. The specified maturity is based on the planning horizon of the project. Planning horizons for durations of 30 years or longer use the 30-year interest rate from Appendix C in the OMB Circular No. A-94 (OMB, 2013). The discount rates set by the OMB varies yearly.

The Collect and Dispose option requires a holding tank system to store the truck wash water until it can be hauled to and disposed at another ODOT facility. The storage tank system will be the only capital cost for this management option. The cost of the storage system will be approximately US$30,000 based on systems recently purchased by ODOT (Kennedy, 2013). The system includes a 3,000-gallon underground fiberglass storage tank, a 500-gallon oil/water separator, and associated electrical components. A 3,000-gallon tank was selected to provide more storage capacity than the available hauling capacity of the tanker trucks used to transport the wash water to a nearby ODOT facility with sanitary sewer access. Truck size is assumed to be 2,000 gallons, based on the current fleet of ODOT vehicles.

Operational costs are a summation of the disposal, monitoring, and hauling costs. The annual water quality monitoring cost was set as a fixed cost of US$1,385 (Kennedy, 2013). This cost is based on the annual cost of an existing truck wash water quality monitoring program, approved by the Ohio Environmental Protection Agency (Ohio EPA), at the Henry County Garage in District 2.

Disposal and hauling costs are a function of the wash water volume generated. Each ODOT maintenance facility will generate different volumes based on the site-specific conditions, such as the number of winter events that occur in a year. The calculation of the annual volume, in gallons, is shown in Equations 5 and 6.

\begin{array}{l} A n n u a l v o l u m e (g a l l o n s) = N u m b e r o f t r u c k s \times h o s e f l o w r a t e (g p m) \times \\ w a s h t i m e p e r e v e n t (m i n) \times n u m b e r o f w a s h c y c l e s . \end{array}

Each truck goes through one wash cycle during a typical winter event. ODOT personnel estimated approximately 10% of winter events will require an additional wash cycle. To incorporate this variable, the number of winter events is multiplied by a factor of 1.1 to generate the number of wash cycles.

N u m b e r o f w a s h c y c l e s = N u m b e r o f w i n t e r e v e n t s \times 1.1 .

The number of trucks and the number of winter events are defined as distributions. The distributions are discrete histograms based on the data provided by ODOT. The number of winter events was determined by historical data provided by ODOT, based on the number of winter events from 2008 to 2011. The data quantifies the number of trucks per ODOT facility and includes both county and outpost garages. County garages are larger, with a mode of 12 trucks per facility. Outpost garages are significantly smaller, with a mode of three trucks per facility.

Correspondence with ODOT personnel reported the hoses used to wash the trucks have flow rates ranging from 4 gallons per minute to 6 gallons per minute. The model input utilizes a uniform distribution of 4 through 6 gallons per minute for hose flow rate to account for the potential variation in the flow.

ODOT personnel reported wash times ranging from 30 to 90 min per truck. A typical wash time of 60 min was reported. To incorporate the range of values, a uniform distribution with a standard deviation of 12 min and a mean of 60 min was applied to the variable for wash time.

Cost of disposal was based on the volume of water multiplied by the disposal rate. The distribution for the cost per gallon of disposing wash water is based on data from the Ohio EPA 2011 Sewer and Water Rate Survey (Ohio EPA, 2013). A histogram was created for the price per gallon from the 461 municipalities and sewer districts in Ohio. The histogram provided the full range of values and the likelihood of occurrence for the sewer rate throughout the state. To incorporate the uncertainty of future costs of disposal, @Risk was utilized to calculate a distribution of expected disposal rates over the next 12 years using the historical increase of yearly rates data. The distribution was calculated by combining a histogram of sanitary sewer rates for the entire state of Ohio multiplied by the rate increase factor shown in Equation 7. For the disposal rate calculations, the midpoint of the planning horizon is 15 years, and the rate increase factor is based on a histogram of rate increases obtained from historical data (Ohio EPA, 2013).

r = {(1 + i)}^{n},

where,

r = Rate increase factor;

i = Rate increase; and

n = Midpoint of the planning horizon.

Hauling costs were calculated on a per trip basis. The cost is based on the labor and operational expenses of the vehicle for each trip. Labor cost is based on the truck driver’s compensation, and labor cost per hour was calculated by multiplying the hourly rate of the truck driver by a factor of 1.55 to account for salary and benefits (Bureau of Labor Statistics, 2012). ODOT District 2 personnel indicated an hourly wage of US$17.50 per driver. The distribution for labor cost per hour was fit by @RISK based on the hourly wage supplied by ODOT (US$17.50/hr), multiplied by a factor of 1.55, and multiplied by the rate increase factor in Equation 7. The rate of increase is a distribution of the Average Wage Increase from 1951 to 2013 (Social Security Administration, 2014). The total labor cost per trip is based on Equation 8.

L a b o r C o s t = \frac{D i s t a n c e}{S p e e d} + T i m e t o l o a d a n d u n l o a d t r u c k \times L a b o r R a t e .

Each roundtrip was defined as the distance between garages based on street addresses supplied by ODOT. The average roundtrip hauling distance is 49.2 miles, and speed was assumed at 45 mph. The time to load and unload the truck is approximately 1 hr.

The cost of operating a truck to haul the wash water to a location for disposal includes fuel, depreciation, purchase, insurance, maintenance, and permits. The diesel fuel cost was defined as a distribution. The distribution was derived using low, likely, and high predictions for the cost of 1 gallon of diesel fuel in the year 2020 (U.S. Energy Information Administration, 2013). The average fuel efficiency used in the calculations was 7 miles per gallon (Barnes & Langworthy, 2003). An additional US$0.53/mile was added to the fuel cost to account for depreciation, purchase, insurance, maintenance, and permits as shown in Table 3.

Table 3.

Costs of Operating a Truck (Excluding Fuel and Labor) to Haul Wash Water to Disposal at an off-Site ODOT Facility.

Parameter	Cost (US$/mile)	Source
Cost of vehicle	0.235	American Transportation Research Institute (2011)
Insurance	0.060	Trego and Murray (2009)
Repair/maintenance	0.105	Barnes and Langworthy (2003)
Tires	0.030	Trego and Murray (2009)
Depreciation	0.080	Barnes and Langworthy (2003)
Permits/licenses	0.023	Barnes and Langworthy (2003), American Transportation Research Institute (2011)
Total cost	0.530

Note. ODOT = Ohio Department of Transportation.

To determine the total annual hauling cost, the number of trips for disposal must be calculated. This number is calculated by dividing the volume of wash water at a facility by the capacity of truck, assuming the capacity of the truck is less than the capacity of the storage tank. Calculations are based on a 2,000-gallon tanker truck.

The capital cost for the Sanitary Sewer option is the cost of constructing the sanitary sewer connection. This cost is site specific. Factors influencing this cost include the distance from an existing sanitary sewer system and site topography, both of which will affect if a gravity sewer can be utilized to meet the existing sewer system. Calculations were performed with capital costs ranging from US$100,000 to US$1,000,000. For reference, in 2011, ODOT District 4 constructed a connection to a sanitary sewer system in Conneaut, Ohio, that required 3,000 linear feet of 8″ sanitary sewer and cost US$330,000; a Greensburg, Ohio, connection construction utilized 600 linear feet of 6″ sanitary sewer and cost US$100,000.

Disposal of the wash water is the only operational cost for the Sanitary Sewer option. The disposal rate of the Collect and Dispose option was also used for the Sanitary Sewer Option.

Definition of Input Variables for Facilities Without Access to Sanitary Sewer

Approximately 40% of the ODOT maintenance facilities currently lack access to a sanitary sewer system. Many of these facilities require a revised approach to managing wash water to meet regulations. Separate analyses of cost for the facilities lacking sanitary access were performed to provide insight for the selection of a new management strategy. These facilities tend to be outpost garages and in rural areas; therefore, input variables must be revised to match the site-specific characteristics of these garages.

New probability distributions were defined for the number of trucks and the roundtrip hauling distance. The data provided by ODOT indicated which facilities lack access to sanitary sewer. Using this information, the histograms were revised to include only data from facilities lacking the sewer access.

The remaining input variables maintained the distributions or point values as described in the previous section. Values for discount rate, water quality monitoring, and labor cost are uniform throughout the state. The facilities lacking sanitary sewer connections are apportioned throughout the state; therefore, the distribution for winter events will still apply.

Results

The impact of each of the input variables on the cost-effectiveness of the wash water management strategies was assessed using a single variable sensitivity analysis. Four variables with the greatest impact were identified and further evaluated using Monte Carlo simulation. The probability that the Collect and Dispose option would have a lower annualized cost than the Sanitary Sewer option was determined as a function of each of these high impact variables, and charts were developed to assist decision makers in selecting the most cost-effective management strategy. An assessment of the cost-effectiveness of these management strategies for current ODOT facilities lacking access to sanitary sewer was also conducted.

Sensitivity Analysis of Input Variables

The sensitivity of the annualized cost of the Collect and Dispose option to each of the operational cost variables was assessed by varying each input parameter, one at a time, from 5% to 95% of its defined distribution and calculating the annualized cost. All other variables were held constant at their mean values. The range was limited between 5% and 95% to eliminate statistical outliers. As shown in Figure 1, the number of trucks had the biggest impact on the annualized cost of the Collect and Dispose Option, followed by number of winter events, roundtrip hauling distance, wash time per event per truck, hose flow rate, discount rate, wage rate, cost of fuel, and disposal rate. The top three variables were selected as high impact variables for additional evaluation.

Figure 1.

Sensitivity analysis of cost factors on annualized costs calculated for the Collect and Dispose option (C_DISPOSE).

Because the only operational cost of the Sanitary Sewer option is the disposal rate of the wash water, which was shown to have very little impact on the annualized cost of the Collect and Dispose option (Figure 1), the sensitivity of the annualized cost of the Sanitary Sewer option to non-operational costs was assessed. The non-operational costs included the capital cost of the sanitary sewer and the discount rate. As a distribution could not be defined for the capital cost of the sanitary sewer, a sensitivity analysis for the discount rate was performed for the capital cost of the sanitary sewer at US$100,000 increments. As shown in Table 4, for capital costs of US$300,000 and greater, the difference or range between the annualized cost at 5% and 95% is greater than any other range between minimum and maximum values in the Collect and Dispose calculations, indicating that the discount rate has the potential to have a high impact on the annualized cost of the Sanitary Sewer option, and should be evaluated further.

Table 4.

The Range of Values for the Annualized Cost of the Connection to an Existing Sanitary Sewer System Based on the Capital Cost of the Sewer Construction.

Capital cost of sanitary sewer (US$)	Annual cost
Capital cost of sanitary sewer (US$)	Minimum valve (US$)	Maximum value	Range
100,000	5,949	12,428	6,479
200,000	10,971	23,929	12,958
300,000	15,967	35,404	19,437
400,000	20,975	46,892	25,916
500,000	25,982	58,377	32,395
600,000	30,984	69,859	38,875
700,000	35,991	81,345	45,354
800,000	40,999	92,832	51,833
900,000	46,002	104,314	58,312
1,000,000	51,008	115,798	64,791

Note. The minimum and maximum values were calculated by an advanced sensitivity analysis in @Risk, where the discount rate was varied between 5% and 95% of its defined distribution.

In-Depth Analysis of Important Wash Water Cost Variables

The sensitivity analysis identified four variables that are likely to have a large impact on the cost of wash water management: the number of trucks, the number of winter events, the roundtrip hauling distance, and the discount rate. To evaluate the effect of each of the selected variables on the cost of wash water management, the same process was followed. First, the range of the distribution for the selected variable was extended beyond the range defined in Table 1 to ensure that trends would be identifiable. Next, 10,000 values were randomly selected from this new distribution and the defined distributions for all other variables (Table 1) and the annualized cost of the Collect and Dispose option and the Sanitary Sewer option were calculated for sanitary sewer capital costs of US$100,000, US$300,000, and US$500,000. The probability that the Collect and Dispose option was less costly than the Sanitary Sewer option was then calculated for each of these scenarios as a function of the variable of interest.

Number of trucks

The impact of the number of trucks was evaluated over the range of one to 24 trucks. As shown in Figure 2, the probability that the Collect and Dispose option is more cost-effective for the statewide average number of trucks (eight) versus a sanitary sewer at a capital cost of US$100,000, US$300,000, and US$500,000 is 37.0%, 95.9%, and 99.5%, respectively. A significant observation is the difference in the slopes of the output at capital costs US$100,000, US$300,000, and US$500,000 (Figure 2). The slope of the US$100,000 line vastly differs from the slopes of the other two lines. At a capital cost of US$100,000, the probability that the Collect and Dispose strategy is more cost-effective drops significantly as the number of trucks increases. At five trucks, the probability that Collect and Dispose is more cost-effective is less than 50%, which indicates that for a location of five or more trucks, tying into the sanitary sewer is a cost-effective management strategy if the capital cost is approximately US$100,000.

Figure 2.

The probability that the annualized cost for the sanitary sewer option (C_SAN) is greater than collecting and disposing wash water at a nearby ODOT facility (C_DISPOSE) as a function of the number of trucks at a facility.

When sanitary sewer capital costs are US$300,000 or greater, the Collect and Dispose strategy is more cost-effective. Regardless of the number of trucks at a facility, the probability of the Collect and Dispose strategy being more cost-effective is approximately 60% or greater. For capital costs of US$300,000, minimal change is observed in the probability until the number of trucks exceeds 10. Likewise, minimal change is observed for any number of trucks for capital costs of US$500,000 (i.e., the probability that Collect and Dispose is more cost-effective remains approximately 90% at the upper limit of this variable). This demonstrates the importance of the capital cost of the sanitary sewer; as this cost increases, the number of trucks has little significance in determining which option is more cost-effective.

These findings indicate that, at low capital costs of sanitary sewer tie in, the number of trucks can have a substantial effect on the cost-effectiveness of the wash water management options. The number of trucks at a given location is dependent on the type of garage. A typical outpost garage will have only three trucks, whereas a typical county garage has 12 trucks. For an outpost garage, Collect and Dispose is nearly 100% probable to be more cost-effective when capital cost of the sanitary sewer is US$300,000 or more. At capital costs of US$100,000, the probability is still nearly 80%. These results indicate the Collect and Dispose option is the more cost-effective strategy for nearly all outpost garages.

County garages have much lower probabilities for Collect and Dispose option as the more cost-effective option. The typical county garage of 12 trucks has probabilities of 21%, 88%, and 98% that the Collect and Dispose option is more cost-effective with sanitary sewer capital costs of US$100,000, US$300,000, and US$500,000, respectively. If the cost is approximately US$100,000 for a county garage to connect to the sanitary sewer, the construction of the sewer connection is likely to be the more cost-effective strategy.

Number of winter events

After the number of trucks per facility, the annual cost of the Collect and Dispose option was most sensitive to the number of winter events. As shown in Figure 3, the cost-effectiveness of wash water management for one to 60 winter events was evaluated. Similar to the observed trend for the number of trucks, the probability that the Collect and Dispose option is more cost-effective than Sanitary Sewer sharply decreases as winter events begin to increase when the capital cost is US$100,000 (Figure 3). For capital costs US$300,000 or greater, the probability remains high that Collect and Dispose is more cost-effective than Sanitary Sewer up to the average number of winter events, then shows a slight decrease as the number of events increases.

Figure 3.

A key observation from Figure 3 is that the Collect and Dispose strategy has probability greater than 70% for being the more cost-effective strategy when sanitary sewer capital costs are greater than US$300,000, regardless of the number of winter events. This means that for a facility in the snowiest part of Ohio the Collect and Dispose option would still likely be more cost-effective than tying into the sanitary sewer at capital costs greater than US$300,000. However, when capital costs are closer to US$100,000, the number of winter events must be taken into consideration.

Because most areas served within a district or county will have similar snowfall totals, a facility cannot necessarily be strategically placed in a particular location to experience fewer winter events. Although this factor cannot be managed, it must be understood when making the decision between the Collect and Dispose or Sanitary Sewer options. The greater the number of winter events, the less likely the Collect and Dispose option is the more cost-effective strategy.

Hauling distance

After number of trucks and number of winter events, roundtrip hauling distance had the greatest impact on the annualized cost of the Collect and Dispose option. Whereas the number of trucks and number of winter events affects the cost of disposal, which is a factor in both Collect and Dispose and Sanitary Sewer options, an increase in the roundtrip distance increases the cost for the Collect and Dispose option only.

Despite this variable being less sensitive, roundtrip distance is important because it can be managed by controlling where a new garage is located. As per previous discussions, the location of a new facility can influence the number of winter events experienced and number of trucks required. Likewise, existing garages may already be connected to the sanitary sewer, giving other facilities places to haul to. The effect of this variable was evaluated for distances of zero to 120 miles. Figure 4 shows that only a 10% change in the probability that Collect and Dispose is more cost-effective than Sanitary Sewer is observed when the roundtrip distance is increased from 60 to 110 miles when the capital cost is US$100,000. When the capital cost is US$300,000 or more, the probability is more than 70% that the Collect and Dispose option is more cost-effective at travel distances as great as 120 miles. Therefore, at high capital costs, hauling distance can be greater while still maintaining cost-effectiveness. At low capital costs, the probability is marginally sensitive to distance; this means fewer garages need to be connected to the sanitary sewer because the water can be hauled longer distances without incurring high costs. Therefore, greater distances should not hinder the decision in choosing a wash water management strategy. This indicates a need for district-wide facilities with sanitary access that all other county and outpost garages can use for disposal.

Figure 4.

Discount rate

The last variable considered was the discount rate, and its impact was evaluated for values of 0.01 to 0.12 (1%-12%). Although the discount rate is used in calculating the annualized cost for both management strategies, its importance varies greatly between management options. The Collect and Dispose option has limited change based on the discount rate. This is due to the much smaller capital cost. For the Sanitary Sewer option, the discount rate plays a more significant role, attributed to the sanitary sewer capital cost as the main factor in the cost equation.

The Discount Rate impact is shown in Figure 5. This continues to show that the probability of the Collect and Dispose option being the more cost-effective strategy increases as the capital cost of the sanitary sewer increases. As the discount rate increases, the annual capital cost also increases, making the Collect and Dispose option a more cost-effective strategy. The capital cost of the Collect and Dispose option is much smaller than the capital cost of the Sanitary Sewer option. The discount rate is a function of the interest rate of the 30-year treasury note. Current interest rates are at the lower limit of rates recorded from 1979 to 2013, which correlate to the period used in the discount rate probability distribution. Rates have decreased for almost 10 consecutive years. The 2013 interest rate was 3.0%. If low interest rates remain common, the probability of the Collect and Dispose option being the more cost-effective strategy decreases. At the 2013 interest rate of 3.0%, the probability that Collect and Dispose was the more cost-effective option than a Sanitary Sewer with a capital cost of US$100,000, US$300,000, and US$500,000 was 8.6%, 74.4%, and 91.8%, respectively.

Figure 5.

Evaluation of Management Alternatives for Locations Without Sanitary Sewer Access

After analyzing the key input parameters individually, a clear trend developed. The trend shows that if capital costs are US$300,000 or more, the Collect and Dispose option is almost always the most probable management strategy to have a lower annualized cost. To further investigate this trend, a cumulative distribution function of the probability that the Collect and Dispose option is more cost-effective than the Sanitary Sewer option versus the capital cost of the sanitary sewer was created. To create an overall cumulative distribution function, 10,000 calculations were run at capital costs of sanitary sewer ranging from US$0 to US$800,000. All other identified parameters were set at the defined probability distributions. Figure 6 shows a steep increase in probability for capital costs of US$75,000 to US$300,000. At US$300,000, the Collect and Dispose option is approximately 90% probable to be the more cost-effective strategy. By the time the capital cost approaches US$700,000, the probability that Collect and Dispose is more cost-effective is almost 100%. This means that the Collect and Dispose option is an easy decision to make when capital costs are more than US$300,000 (Table 5, Figure 6).

Figure 6.

The cumulative distribution function for Collect and Dispose as best management strategy based on the capital cost of the sanitary sewer connection for ODOT facilities without current sanitary sewer access.

Table 5.

Comparison of the Probability That Collect and Dispose Is Least Costly Management Strategy for All ODOT Maintenance Facilities and Facilities Lacking Access to a Sanitary Sewer System.

	Probability that Collect and Dispose is least costly management strategy
Capital cost of sanitary sewer (US$)	All facilities (%)	Facilities without sanitary sewer (%)
61,000	7	10
65,000	10	17
100,000	40	60
172,000	73	90
280,000	90	98
300,000	92	98
500,000	98	99

Note. ODOT = Ohio Department of Transportation.

The probability of both management strategies being cost-effective is approximately 50% when the capital cost of the sanitary sewer approaches US$120,000. This may further complicate the strategy selection decision. However, focusing on the site characteristics and referring to Figures 2 to 5 can provide the decision maker with more considerations when selecting a more cost-effective management strategy.

To account for facilities without access to a sanitary sewer, the simulation was repeated, with distributions for the number of trucks and roundtrip hauling distances that varied from what was used in the statewide analysis to describe the distributions for only facilities lacking sewer access. As expected, the results from this simulation increased the probability from the statewide calculations that Collect and Dispose is the more cost-effective strategy (Table 5). This was not unexpected, as garages without sanitary sewer access are defined by distributions with fewer trucks and shorter roundtrip hauling distances. The results from this analysis indicate that in a statewide approach, locations without sanitary sewer access would find Collect and Dispose to be the more cost-effective option.

Conclusion

The purpose of this research was to evaluate two wash water management strategies incorporating uncertainty through probabilistic analysis. The four variables having the greatest impact on the cost-effectiveness of wash water management were identified using sensitivity analysis. Probability distributions were defined for all variables in the analysis, and 10,000 simulations were conducted for each high impact variable to evaluate its influence on the cost-effectiveness of alternative management strategies. The impact of the capital cost of sanitary sewer on the cost-effectiveness of alternative strategies was also evaluated and the probability that the Collect and Dispose option would be more cost-effective for existing facilities lacking access to sanitary sewer was determined. The following conclusions can be drawn from this research:

Single variable sensitivity analysis indicated that the number of trucks, number of winter events, roundtrip distance of hauling, and discount rate have the greatest impact on the annualized cost of wash water management.

When the capital cost of tying into the sanitary sewer is greater than US$300,000, there is a high probability than the Collect and Dispose option is more cost-effective than the Sanitary Sewer option for all scenarios evaluated.

When the capital cost of tying into the sanitary sewer is less than US$100,000, the cost-effectiveness of alternative strategies is highly affected by the number of trucks, number of winter events, and roundtrip hauling distance, indicating that these factors should be considered when the capital cost of tying into the sanitary sewer is less than US$100,000.

The probability distribution graphs and/or approach developed as part of this research can be used by decision makers to determine the most cost-effective management strategy at a specific location or single garage by using specific values for the highest impact variables.

The type of garage can be an important consideration for selecting the optimal management strategy. Analysis showed that there is an 80% probability that Collect and Dispose is more cost-effective than Sanitary sewer for an outpost garage, regardless of the capital cost of the sanitary sewer, whereas the probability of Collect and Dispose being more cost-effective at a County Garage is only 21% when the capital cost of the sanitary sewer is low (US$100,000).

For ODOT facilities currently lacking access to sanitary sewer, Collect and Dispose is generally the most cost-effective management strategy when the capital cost of connecting to the sanitary sewer exceeds US$100,000.

Footnotes

Acknowledgements

The authors thank the U.S. Department of Transportation and Ohio Department of Transportation for their generous support.

Authors’ Note

The research was performed at the University of Akron, and the contents reflect the views of the authors, who are responsible for the facts and the accuracy of the data presented herein. The contents do not necessarily reflect the official views or polices of the U.S. Department of Transportation or Ohio Department of Transportation.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Author Biographies

Christopher M. Miller is an associate professor in the Civil Engineering Department at the University of Akron and a registered professional engineer in the State of Ohio. His research areas include winter maintenance transportation operations including facilities and equipment management and material usage optimization to minimize corrosion and environmental impacts.

Joshua Slaga is an engineer at GPD Group and a registered professional engineer in the State of Ohio. His background includes design and analysis of public infrastructure and research in winter maintenance.

Marla J. Kennedy is a PhD candidate in the Civil Engineering Department at the University of Akron. Her research areas include process optimization, water treatment, and winter maintenance.

William H. Schneider IV is an associate professor in the Civil Engineering Department at The University of Akron as well as a registered professional engineer in the State of Ohio. His research areas include traffic data collection, archiving, management, and analysis; winter maintenance operations; and crash prediction and injury-severity modeling.

References

Alleman

J. E.

Partridge

B. K.

Yeung

(2004). Innovative environmental management of winter problems at INDOT yards (Publication FHWA/IN/JTRP-2001/27) (Joint Transportation Research Program). West Lafayette: Indiana Department of Transportation and Purdue University.

American Transportation Research Institute. (2011). An analysis of the operational costs of trucking: 2011 update. Retrieved from http://www.atrionline.org/research/results/Op_Costs_2011_Update_one_page_summary.pdf

Barnes

Langworthy

. (2003, June). The per-mile costs of operating automobiles and trucks. Minnesota Department of Transportation Office of Research Services. Retrieved from http://www.lrrb.org/media/reports/200319.pdf

Bizier

(2007). Gravity sanitary sewer design and construction, Second edition: ASCE manuals and reports on engineering practice no. 60 wef manual of practice no. fd-5. Reston, VA: American Society of Civil Engineers.

Bureau of Labor Statistics. (2012, September). Employer costs for employee compensation, (USDL-12-2404). Retrieved from http://www.bls.gov/news.release/archives/ecec_12112012.pdf

Carr

R. I.

(1989). Cost estimating principles. ASCE Journal of Construction Engineering and Management, 115, 545-551.

Chou

J. S.

Yang

I. T.

Chong

W. K.

(2009). Probabilistic simulation for developing likelihood distribution of engineering project cost. Automation in Construction, 18, 570-577. doi:10.1016/j.autcon.2008.12.001

Fitch

G. M.

Craver

V. O.

Smith

J. A.

(2006). Potential use of reverse osmosis in managing saltwater waste collected at road-salt storage facilities (VTRC 06-R26). Charlottesville: Virginia Transportation Research Council.

Fitch

G. M.

Craver

V. O.

Smith

J. A.

(2008). Recycling of salt-contaminated stormwater runoff for brine production at Virginia Department of Transportation Road-Salt Storage Facilities (VTRC 08-R17). Charlottesville: Virginia Transportation Research Council.

10.

Fitch

G. M.

Smith

J. A.

Bartelt-Hunt

(2004). Characterization and environmental management of stormwater runoff from road-salt storage facilities (VTRC 05-R15). Charlottesville: Virginia Transportation Research Council.

11.

Kennedy

M. J.

(2013). Evaluation of management alternatives for truck wash water generated during winter maintenance activities. Akron, OH: University of Akron.

12.

Khodakarami

Abdi

(2014). Project cost risk analysis: A Bayesian networks approach for modeling dependencies between cost items. International Journal of Project Management, 32, 1233-1245.

13.

Miller

C. M.

Schneider

W. H.

IV Kennedy

M. J.

(2015). Evaluation of management alternatives for truck wash water generated during winter maintenance activities. Public Works Management and Policy, 20(1), 80-100.

14.

Miller

C. M.

Schneider

W. H.

IV Kennedy

M. J.

Sullivan

(2014). Snow removal wastewater disposal alternatives (State Job Number 134629). Akron, OH: Ohio Department of Transportation, Office of Statewide Planning & Research.

15.

Office of Management and Budget. (2013). Discount rates for cost effectiveness, lease-purchase, and related analyses. Washington, DC: Author. Retrieved from http://www.whitehouse.gov/omb/circulars_a094/a94_appx-c

16.

Ohio Department of Transportation. (2011). Snow and ice practices. Columbus, OH: Division of Operations, Office of Maintenance Administration.

17.

Ohio Environmental Protection Agency. (2013). 2011 Sewer and Water Rate Survey. Columbus, OH: Office of Fiscal Administration. Retrieved from http://epa.ohio.gov/Portals/43/Rate%20Reports/Ohio_EPA_2011_Sewer_and_Water_Rate_Survey.pdf

18.

Social Security Administration. (2014, March 9). National Average Wage Index. Retrieved from http://www.ssa.gov/oact/cola/AWI.html#Series

19.

Trego

Murray

. (2009). An analysis of the operational costs of trucking. Retrieved from http://www.atri-online.org/research/results/ATRITRBOpCosts.pdf

20.

U.S. Energy Information Administration. (2013). Annual energy outlook 2013 with projections to 2040. Washington, DC: U.S. Department of Energy.

21.

United States Environmental Protection Agency. (2001). Risk Assessment Guidance for Superfund: Volume III—Part A, Process for Conducting Probabilistic Risk Assessment. Washington, DC: Author.

22.

Veneziano

Shi

Ballard

(2010). Development of a toolkit for cost-benefit analysis of specific winter maintenance practices, equipment and operations: User manual. Bozeman, MT: Clear Roads.

23.

Xerxes Corporation. (2014, March 17). Fiberglass underground water tanks. Retrieved from http://corerosion.thomasnet-navigator.com/Asset/Water-Brochure.pdf

24.

Yale Environmental Health & Safety. (2011). Underground storage tanks. Retrieved from http://ehs.yale.edu/sites/default/files/undergroundstorage.pdf