Assessing the effects of several variables on freight train fuel consumption and performance using a train performance simulator

Trompn. Res..A. Prmred in Great

Vol.2%. No. ?. pp. 99-112,1990

0191.:607~90 s3 cQ+ .ca D 19% Pergamon Press plc

Bnram.

ASSESSING THE EFFECTS OF SEVERAL VARIABLES ON FREIGHT TRAIN FUEL CONSUMPTION AND PERFORMANCE USING A TRAIN PERFORMANCE SIMULATOR EUGENE V. HOYT Union Pacific Railroad Company, 24125 Aldine Westfield Road, Spring, TX 77373, U.S.A. and REUVEN R. LEVARY Department of Management Sciences, Saint Louis University, Saint Louis, MO 63108, U.S.A. (Received 6 November 1987; in revised form 26 May 1989)

Abstract-The impact of several variables on freight train fuel consumption and performance are assessed using a train performance simulator. These variables include: wind, precipitation, number of cars, and number and type of locomotives. The input to the train performance simulator includes data related to train characteristics and data related to external conditions such as weather. The simulator output represents fuel consumption expected under a given set of conditions. Graphical and cost/benefit approaches were used to assess operations alternatives.

1. INTRODUCTION

and the rising trend of fuel costs that operational efficiencies and subsequent profitability can only be realized with an accurate knowledge of operating costs. Some parameters which affect fuel usage are described in Think Fuel (Union Pacific Railroad, 1981). The application of an effective procedure that allows for a reasonably accurate determination of fuel usage as a function of desired train performance while considering external random events, offers several distinct advantages; (1) An effective base from which to enter into contractural arrangements with shippers and consignees dependent on train performance, (2) A method for evaluating the impact of increased/decreased traffic on specific trains over a range of various conditions with respect to overall profitability, and (3) The ability to most appropriately allocate limited locomotive resources. The procedures employed in this study essentially address the following sequence of processes; (1) Selection of an operating corridor, (2) Determination of representative freight trains operating in the corridor, (3) Collection of data representing the physical characteristics of the selected trains and having a direct impact on fuel usage, (4) Analysis of collected data to derive train parameters and characteristics, (5) Application of the derived characteristics to the Train Performance Simulator over varying external conditions, (6) Analysis of simulator results and the development of methodology to assess optimal alternatives. Two different methods which may be used to assist the tactical planning process in rail freight transportation were described by Crainic (1984). Assad (1980) reported on the existing models for rail transporta-

Since the early 197Os, several economic and legislative events have taken place affecting the operations of American Rail Carriers with respect to their costs and their ability to transact business. For example, the recognition of petroleum fuel as a limited resource has served to dramatically increase the cost of freight train operations via diesel fuel prices which have risen nearly 430% between 1970 and 1985. Diesel fuel, once an abundantly cheap resource having minimal impact on profitability, has become a major cost item in the scheme of rail operations. Legislative action, too, has affected the operations of American Rail Carriers. For example, the Staggers Act has resulted in the deregulation of rail carriers permitting them to individually negotiate prices and services with shippers and consignees on a contractual basis. Furthermore, prices that were once established and maintained through tariffs issued by the Interstate Commerce Commission, are now individually negotiable and tied to service contracts complete with penalties affecting realizable revenues. The outcome of these economic and legislative events has required management to address the profitability associated with the operation of dedicated freight train service. Dedicated train service specifically refers to those trains which operate in a consistent manner according to a published schedule of operation. Generally, competing carriers will normally offer an alternative service within a similar frame of operation. Such trains are representative of those hauling service sensitive type traffic due to the consistency of their operation. It becomes apparent that within the environment of deregulation 99

E. V. HOYTand R. R. LEVARV

100

tion. A discrete event simulation model of a railway line, in which different dispatch goals or criteria can be included, was developed by Petersen and Taylor (1982). Turnquist and Jordan (1983) developed a dynamic network optimization model for distribution of empty freight cars. Roy and Ravacley (1982) described how customer selectivity was used as a means to integrate the activities of freight transportation at CN Express. Background information on the relationship between braking and train movement was given by The Air Brake Association (1974). The following presentation is organized in five general sections: (1) Data Collection, (2) Data Analysis and Train Characteristics Development, (3) Train Performance Simulator Application, (4) Simulator Output Analysis and Methodology for Assessing Alternatives, (5) Conclusions and Comments. This paper attempts to illustrate some procedures relevant to the U.S. rail transport system. In the U.S., virtually all rail carriers are either privately owned or held publically through stock. In contrast, most rail carriers outside the U.S. are controlled by a government agency or mininstry. The difference in ownership creates different research objectives. A major objective of the U.S. rail transport companies is to minimize the operational costs. No consideration is given to such items as conservation of natural resources (petroleum) or the impact of such resources on the budget of a nation. In societies where rail transportation is nationalized, however, national resources and the national budget are considered important. 2. DATA

COLLECTION

Train and corridor selection

To be included in this study trains had to be service sensitive, dedicated, and consistant in operations. Furthermore, the corridor over which they would operate had to permit nonstop operations. Several candidate trains sharing the same corridor were examined for consistancy of operations with the intent of arriving at two choices operating in opposing directions. The rationale for opposing directions stems from the fact that the characteristics of physical terrain will have differing effects on train operations dependent on train direction. For example, operations in one direction could be predominantly downhill suggesting operation in the opposite direction generally uphill. Obviously, the direction of train operation in any given corridor can have significantly different effects on fuel usage and performance, even for two trains with identical physical characteristics. The selection of only two trains to be analyzed was made entirely with respect to maintaining the simplicity of the analysis, but in reality, could have included any number of trains. The selections made were: (1) Train CKZ, operating from Chicago and Kansas City, and (2) Train LCB, operating from Little Rock to Chicago. The

symbol conventions of CKZ and LCB are indicative of those used by the Union Pacific System at the time of the analysis. The first letter of the symbol indicates the origin city, the second letter indicates the destination, and the third acts as a modifier indicating some particular aspect of the train. In this case, the ‘Z’ shows that the train is to be expedited and the ‘B’ means that the train is to be delivered, intact, to the Belt Railway at Chicago. The corridor of operation selection was that portion of each train’s route between Chicago and Villa Grove, IL, a distance of 127.1 miles. Since neither train is required to perform service within this corridor, the corridor essentially meets the criteria initially defined for the analysis. The direction of operation for train CKZ will be south and for LCB north. Data selection

The selection of data to best represent train characteristics required that the parameters inherrent in the data be controllable in nature and have a direct affect on fuel consumption and performance. Data characteristic of such qualities included: the number of cars on a train, the tonnage being hauled, and the length of the train. Data of this nature was collected for 100 consecutive days of train operation for each of the trains under study over the corridor of interest. This was accomplished by manually transcribing the necessary information from a batch generated computer report known as the ‘Train Statistics Performance Report’ (TSPR). This report is generated monthly and reveals train statistics for each train on the rail system. A representative example of the report is included as Appendix 1. Although other factors such as terrain and weather impact fuel consumption and performance, the collection of such data is unnecessary as physical terrain characteristics are programmed into the Simulator logic (see Section 4) and unpredictable events (e.g. weather) may be entered into the simulator by the user as needed. The number and types of locomotives used on a given train also affect fuel and performance but this will be addressed in the next section. The data collection efforts used, thus far, were made entirely to determine the characteristic physical parameters of the trains under study. 3. DATA

ANALYSIS

CHARACTERISTICS

AND

TRAIN

DEVELOPMENT

The evaluation of collected data and its application towards determining individual train characteristics were accomplished through the use of statistical procedures. The procedures addressed distributions for each train (i.e. car, tonnage, length) and correlations between them. A description of these procedures follows. Distribution of data

To determine the physical parameters of the trains under study, it was necessary to determine how car.

Freight

train fuel consumption

ships. Since tonnage and length are directly dependent on the number of cars on a given train, it was initially reasonable to assume that train length and tonnage varied linearly as a function of the number of cars on a train. Linear regression was used to test this assumption. The empirical relationships follow:

tonnage, and length data were distributed among each train. It was important to assess physical characteristics of each train and the probabilities associated with these characteristics. Accumulated data was sorted and relative frequency of occurrence with respect to number of cars, gross tons, and length was determined. Results were plotted in a histogram and a visual assessment of type distribution was made. Figure 1 is the histogram obtained from plotting car data for train CKZ and LCB. As can be observed, the plots readily suggest the characteristics of a ‘normal’ distribution. Similar histograms for tonnage and length data (not shown), were also plotted with results similar to that of Fig. 1. In all cases, a Chi-Squared Goodness-Of-Fit test was performed to further verify the assumption of normality. The test results, in each case, were strongly positive towards the distributions being normal.

1. Train CKZ: T (tonnage) = 55.203X + 201.73 Coefficient of Correlation = 0.910 L (length) = 64.126X + 535.48 Coefficient of Correlation = 0.957 2. Train LCB:

Data correlation

(1)

T (tonnage)

After characteristic distributions were obtained, elements of car, tonnage, and length data were correlated in order to derive some empirical relation-

.25

101

= 58.750X + 311.86 Coefficient of Correlation = 0.898

X=66cws 6=24CARS

0

12

24

36

96

48

108

(No. OF CAPS)

.25

(No. OF C?GS)

Fig. 1. Histograms

of car distribution

data for trains CKZ and LCB.

E. V. HOYTand R. R. LEVARY

102

L (length)

= 70.661X + 274.03 Coefficient of Correlation = 0.981 where X is the number of cars in all cases. Notice that the coefficients of correlation in each of the above relationships strongly suggest the conditions of linearity. Linearity will be used in accordance with the relationships developed above. The use of these equations will be instrumental in the application of train characteristics to the simulator. 4. TRAIN PERFORMANCE

SlM_JLATOR APPLICATION

As it is infeasible to apply the derived characteristics to actual train operations over repeated trials, computer simulation provides for analyses that are reliable and reasonably accurate. The Train Performance Simulator (TPS), (Missouri Pacific Railroad Co., 1986), is the result of some initial work started by R. W. Drucker in 1974, while a graduate student at the University of Illinois. His primary research and developments were acquired by the Industrial Engineering Department of the Missouri Pacific Railroad Company and, since then, have been extensively modified and redesigned as a FORTRAN based program of considerable sophistication. The TPS is composed of several physical and empirical deterministic equations designed to calculate the following quantities: (1) tractive effort, (2) train resistance, (3) accelerative force, (4) distance for acceleration, (5) time for acceleration, (6) breaking distance and time, and (7) fuel consumption. The time needed for simulation runs ranges between lo-15 seconds on IBM 32/370. The Simulator is a software package which has been customized to include data regarding the characteristics of the various physical territories of the rail system. Such data includes: grades, curves, track characteristics, speed limits, slow orders, and sundry elements which define operating conditions. Data regarding the various types of railroad rolling stock and locomotives is also included as part of the Simulator’s logic. This type of data relates to: physical dimensions of cars, rolling resistances, IOCOmotives characteristics (tractive effort, HP ratings, etc.), and other relevant data which defines car and locomotive characteristics. The Simulator also facilitates the input of various external conditions affecting train operations. The TPS allows for the input of a wide variety of user identifiable data related both to train characteristics and external events. Its output provides a representation of that which is expected under given conditions. Locomotive data inpur The TPS logic contains data which is descriptive of all types of locomotives used on the rail system. This data is based on manufacturer specifications

and is periodically modified to reflect actual historical operations. Invariably. railroads employ many classes of locomotives. Each class is characterized by the individual manufacturer, horsepower rating. and other specifics such as upgradings and modifications. The classes are more conveniently characterized by the type of service for which they are intended. The three basic types of service for which locomotives are utilized and the locomotive characteristics necessary for each type of service are listed below: 1. YARD SERVICE requires locomotives which are designed for use in a very limited operation such as yard switching. These locomotives have quick response to throttle and are capable of moving significant tonnages over short distances for a short period of time. 2. ROAD FREIGHT SERVICE requires locomotives designed to move large tonnages for long periods of time over long distances. These locomotives are less responsive to throttle (lower geared). 3. LOCAL FREIGHT SERVICE requires locomotives which compromise between items (1) and (2) above. They are generally utilized in services which require limited amounts of yard switching and road freight service. For the purposes of this study, interest focuses on the classes of locomotives utilized in Road Freight Service. Among the classes available for selection in the study, the following widely used locomotives were selected: CLASS

HORSEPOWER

SD40 GP40 u3oc GP50

3000 HP 3000 HP 3000 HP 3500 HP.

Experience indicates that optimal locomotive operations are obtained by grouping locomotives of the same class in situations requiring the use of two or more units. Thus, all simulated runs were performed with locomotives of the same class in two. three, and four unit consists (i.e. configuration). Application of train characteristic data To introduce data regarding various train characteristics into the simulator, random numbers representing number of cars should be generated. It was shown earlier that the number of cars per train is normally distributed with given mean and standard deviations. Therefore, normally, distributed random numbers, generated for a given train. are used in eqn set (1) to obtain tonnage and length data which are then used for input to the simulator. A table of normally distributed train characteristics (Table 1) was obtained through use of a simple

103

Freight train fuel consumption Table 1. Table of normally distributed train characteristics TRAIN CKZ #CAQSRJi~KO. .-FINS 101 5774 6425 113 4027 69 4223 73 70 4533 52 3072 3424 50 4163 :; 3453 43 2583

II LEXXH 6907 7652 4909 5134 5488 3818 4220 5065 4253 3258

11

TRAIN LCS

t CY.BS RW

II

algorithm which generates normally distributed random numbers (Fig. 2). A simple BASIC program was written to generate normal random numbers and to calculate tonnage and length values.

NO.

‘IONS

LFXXH

109

6741

8007

87 69

5442 4349 3159 7217 4260 4747 4002 6562 5696

6444 5130 3698 8579 5023 5609 4712 7791 6750

1:: 67 75 1:: 92

tervals. The wind was consistently at an angle of 45” to train movement (see diagram below). TRAIN DIRECTION

Application of external random data

The application of external data focuses on the effects of noncontrollable events on train operations (e.g. precipitation and wind). Wind conditions have impact on train operations in terms of performance and fuel use. Impact varies with wind speed and with wind direction in relation to the direction of train movement. The TPS allows for the input of various wind speeds and differing wind angles in relation to train movement. In this study, wind speeds were varied from zero to twenty miles per hour in five mile per hour in-

WIND DIRECTION

Wind speeds were chosen that could realistically be expected. A wind angle was chosen which was neither entirely restrictive nor permissive to train forward movement. Precipitation acts to reduce the tractive effort of locomotives (i.e. the ability of a locomotive fo pull tonnage in terms of its adhesion to the rails). In train operations, wet rail sometimes creates a situation known as ‘wheel slip.’ Under conditions of heavy operation, one or more of the wheels on any of the locomotives on a train may begin to slip and spin continuously upon contact with wet rail conditions. The results of ‘wheel slip’ is a momentary loss of train momentum and speed which causes the train weight to act as a drag which would not be present had the slipping action not occurred. Since most modern locomotives are equipped with wheel slip features which can sense slipping and redistribute power more evenly to other wheels, this problem has become less severe. For application to the simulator, conditions of wet and dry rails are input as a Locomotive Adhesion Percentage, which is actually a limit on the maximum tractive force (specified as a percentage of locomotive weight) transmitted to the rail by the locomotive consist (configuration of locomotives). Generally, dry conditions are specified as an Adhesion percentage of 23% to 25%, while wet conditions at approximately 18.5%. The percentages used were those mentioned above and specified in the TPS manual’s recommended values. Simulator application process

Fig. 2. Algorithm

for generating normally train characteristics.

distributed

To obtain the necessary output for the full range of conditions specified, data was applied to the sim-

E. V. HOYT and R. R. LEVARY

10-t

ulator according to a sequential process of steps which were iterated repeatedly. A flowchart presented in Fig. 3 describes the process. The process provides simulated runs for each class of locomotives over each set of train characteristics for various wind speeds. This is done for both dry (23%) and wet (18.5%) conditions. The figures appearing in parenthesis on the flowchart indicate the cumulative number of simulation runs generated up to that point. 5.

SIMULATOR

OUTPUT

2). Each table is divided into three sets (i.e. one for each locomotive class) and indicates simulated output results for a specific class. Each set contains data regarding fuel consumption and running times achieved for various wind velocities for two, three, and four unit consist configurations. For the sake of clarity, all figures are rounded to the nearest gallon and minute. Data in the tables is representative of output achieved under dry conditions (Adhesion limits = 23%). Since the differences between results obtained under wet conditions and results obtained under dry conditions were extremely small (i.e. running times were identical and fuel consumption varied by less than 0.5 gallons in all cases), simulated output under conditions of precipitation were excluded. As previously indicated, most modern locomotives are

ANALYSIS

Results of the TPS output for the simulated ten days of operation of Train CKZ and LCB, each having various class locomotives, were tabulated. Only the TPS output data for train CKZ having SD-40 class locomotives, however, are given here (Table

SEX AtHFSIoN % = 23 I

,GET

1st

SET

TFA.IN

CHAR.1

Fig. 3. Flowchart of data application process to train performance simulator.

105

Freight train fuel consumption Table 2. TPS output data for train CKZ-SD-40

i& 174 148 73 684 716 766 824 889 147 149 78 709 744 794 853 919 149 152 52 563 591 629 684 748 142 143 58 599 629 671 730 793 143 144 72 678 710 761 818 883 147 149 59 604 636 677 736 799 143 144 431 5021 5301 5621 6151 672111411 141 AVGI 6671 7001 7461 8051 87411149 1151 -

y F

T?.AINCXZ -THREE 0. FmLcoNsuMpTIoN(GALs) WIND SPEED (MPH) 0F ARS 0 5 10 15 20 101 977 1022 1090 1180 1275 113 1039 1086 1161 1249 1344 69 775 818 872 952 1040 73 800 847 899 980 1075

class locomotives

10

15

174 185 183 195 151 158 154 161 157 165 143 146 146 149 153 160 146 150 141 142 155 in - f

SD-40 UNITS RUNNING TLYE (MIXSS) WINDSPEED (MPH) 0 5 10 15 146 148 151 157 149 151 156 163 142 142 143 143 142 142 143 144 143 144 146 150 140 140 141 141 141 141 141 142 142 143 144 147 141 141 142 143 139 139 143 144

TRAIN CKZ - FCYJRSD-40 WIT'S ;Jo. r FUEL COXSUWTION (GALS) RuNNIoIG'I-IYFS (>IINS) OF WIND SPEED (MPH) WINDSPEED (?.lPH) CARS 0 5 10 15 20 0 5 10 15 20 101 1088 1140 1230 1336 1457 143 144 144 146 149 113 1161 1223 1313 1422 1543 144 145 146 149 155 69 852 903 958 1055 1164 141 141 141 141 142 933 997 1087 1204 141 1411 1411 142 11421 973 1041 1142 1255 141 142 142 142 143 757 795 875 973 139 139 140 140 140 809/ 851 936 1046 140 140 140 140 140 928 984 1080 1195 141 141 141 141 142 817 863 944 1057 140 140 140 140 140

I!?lEwE , 975 1065 1176

equipped

with wheel slip features

which significantly

reduce the effects of precipitation on train operations. In addition, investigation also revealed that wet operations have minimal impact on train operating in excess of 15 MPH (TPS MANUAL). Analysis of output under wet conditions was not purposeful and therefore was eliminated from further consideration. Observation of the results for train CKZ shows that the lowest average fuel consumption alternative is two U30-C units under all wind velocity conditions. However, this alternative does not provide for the best running time. In the two unit category, best running time is achieved by the use of two GP-50 locomotives. In the three and four unit categories, both the best running times and the best average fuel are achieved through the use of GP-50 class locomotives. It should be noted that a shift from three unit consists to four unit consists produces only a minimal reduction in running time. This suggests that operations with four units may not be efficient under any circumstances. Some contrasts become apparent when comparing the results for train LCB to train CKZ. In the two,

141

three, and four unit categories for train LCB. none of the lower fuel consumption alternatives provide for the best running times. Furthermore. a shift from a three to four unit operation does provide for some substantial reductions in running times. It becomes clear, in this case, that the selection of the best combination of alternatives is not readily apparent from the TPS output data alone. In order to facilitate the selection of optimal alternatives, particularly as in cases such as this where substantial amounts of output data are present, the TPS data must be further analyzed and manipulated so as to afford a more manageable method of presentation. Such analyses may be conducted by using graphical analysis approach and cost/benefit analysis. These approaches are described below. Graphical analysis approach

This method provides for the assessment of alternatives through the discrete use of simulator output data. Applications consistant with the use of this approach primarily address the need to determine an optimal locomotive consist for a specific train and number of cars. First, a set of characteristics curves

106

E. V. HOYT and R. R. LEVARY

is plotted for each of the locomotive classes in their two, three, and four unit configurations. Both fuel consumption and running times are plotted as a function of the number of cars. Then, the curves are used to determine both the approximate fuel consumption for a given number of cars and the desired running time. The lowest fuel consumption alternative can then be selected accordingly. There are two methods by which a graphical analysis may be conducted. The first requires the plotting of curves for fuel consumption and running times for each category of wind velocity. This necessitates the plotting of some 110 curves per train, 220 in all. The second method requires the plotting of one set of curves for zero wind velocity conditions, and separate sets of curves for the average increase in percent of fuel consumption and for the running times over the entire range of wind velocities (from zero to twenty miles per hour). This method necessitates the plotting of only 48 curves. The second alternative appears more desirable because it requires less work and because it allows for a determination of fuel use and running times over the entire range of wind velocities (1 mph to 20 mph). Using the second method, a set of characteristic curves has been prepared for train CKZ for various class locomotives. These curves represent: (1) fuel consumption vs. number of cars, (2) running

time vs. number of cars, (3) average percent increase in fuel consumption vs. wind speed, and (4) average percent increase in run time vs. wind speed. These curves for locomotives class SD-40 are given in Figs. 4-7. The practical use of these curves is offered in the following example: Assume that a particular CKZ train will operate between Chicago and Villa Grove with 85 cars. It is desired that the running time not exceed 145 minutes. In addition, it is expected that wind conditions will average approximately 10 MPH from the Southwest (45 to train direction). A reasonable determination of both the optimal locomotive consist and the approximate fuel use based on CKZ’s operating characteristics is desired.

One must first determine which of the locomotive classes and consist configurations would be capable of completing the trip within the time specified for the number of cars given. This may be accomplished by consulting those graphs (which represent running time vs. number of cars (Fig. 5)). All locomotive classes in the two unit category will be eliminated, since none are able to complete the trip within 145 minutes with 85 cars. While all classes except the GP-40’s in the three unit category are able to complete the trip and all classes in the four unit category can complete the trip, three unit consists are favored as they use less fuel than the four unit consists.

Fig. 4. Fuel use plots train CKZ: Wind = 0 MPH - SD-40 Units.

Freight train fuel consumption

40

50

50

70

90

80 If

0,

107

100

110

ems,

Fig. 5. Running time plots train CKZ: Wind = 0 MPH - SD-40 Units

Since the alternatives obtained so far are representative of zero wind speed conditions, it is necessary to adjust the running times according to the average percent increase that can be expected for wind conditions at 10 MPH. By consulting the graphs which represent average percent increase in running time vs. wind speed (Fig. 7), it is possible to determine the average percent increase in running time for wind speed of 10 MPH as compared to zero wind speed. The adjustment calculations are presented as follows:

# of LOCO

CLASS LOCO

RUN TIME 0 WIND

% INCR. 10 MPH WIND

ADJUSTED RUN TIME

3 3 3

SD40 GP50 u3oc

143.5 Min 142.8 Min 143.8 Min

0.5% 1.0% 1.5%

144.2 Min 144.2 Min 147.9 Min

At this point, the U3OC’s may be eliminated and the SD40 and GP50 alternatives should be considered. Selection of the optimal alternative will now be based on fuel consumption. Using the same approach that was used to adjust running times, the graphs which represent average percent increase in fuel consumption vs. wind speed (Fig. 6) are consulted to determine increases in fuel consumption as they result from increases in wind speed (0 to 10 MPH). The calculations follow.

# of LOCO

CLASS LOCO

FUEL USE 0 MPH WIND

3 3

SD40 GP50

900 GAL 880 GAL

% INCR. 10 MPH WIND + +

ADJUSTED FUEL USE

12.0% = 1008.00 GAL 12.0% = 985.60 GAL

The obvious choice, in this case, is the use of three GP50 class locomotives at an approximate fuel consumption of 985.6 GAL and running time of 144.2 MINs. In this example, it would have been necessary to address the use of four unit consist configurations had the adjusted running times resulted in a figure in excess of 145 MINs. This graphical approach can be a valuable planning tool, but the user should be cautioned not to conclude that the results are indicative of all CKZ trains operating with 85 cars under 10 MPH wind speeds. It must be emphasized that the simulator output is based on characteristic data obtained from train operations over a period of time and that actual wind speeds may be more permissive or restrictive to train movement than that used in the simulation. Under actual operating conditions, train tonnage, and length as well as wind velocity and direction, must be considered separately. Costlbenefit analysis approach

This method, in contrast to the previous method, assesses the selection of alternatives on the basis of

E. V. HOYT and R. R. LEVARI~

108

10

5

15

10 (WIND SPEED - MPH)

Fig. 6. Percent increase in fuel-Train

simulator output averages. Applications focus on selecting the overall best long-run alternative for a range of desired running times. First averages of fuel consumption and running times are obtained from the TPS output tables for each class of locomotives (in the two, three, and four unit configurations). Next, fuel consumption is ranked from lowest to highest. Then, using the lowest consumption alternative as a BASE, the next best consumption alternative is indicated. Calculations are performed to determine the additional fuel used (COST), the running time gained or lost (NET BENEFIT), and the incremental fuel usage as a function of running time (INCREMENTAL COST in GAL/MIN). The data in Table 3 was obtained by performing this analysis for both trains under conditions of zero wind velocity. To illustrate the table’s construction with the results from train CKZ, the lowest cost alternative (BASE) was two U3OC locomotives at an average fuel consumption of 655 GALS and running time of 150 MINS. The next lowest alternative is two GP50 class locomotives at 661 GALS and 146

i? s

CKZ

-

SD-40

Units.

MINS. The additional fuel used (COST) was 6 GALS with a reduction in running time (NET BENEFIT) of 4 MINS, resulting in an incremental cost of 1.5 GALS per MIN. The remainder of the table is constructed similarly with the next best alternative always compared to the base. With Table 3 complete, it is possible to determine optimal locomotive consist configurations on the basis of desired running times and the lowest incremental cost available to achieve that time. Table 3 includes a completed COST/BENEFIT ANALYSIS for trains CKZ and LCB based on data calculated in Table 4. Figures in the Table 4 indicate the optimal locomotive consist arrangements for various running times over the long-run of train operations. Since this method essentially addresses long-run optimality, the introduction of wind effects would imply that such wind velocities were generally consistent in everyday train operations. This is unlikely as wind velocities and directions are variable in nature. If it is determined that wind is indeed a constant, however, wind effects may be easily included

5

3 UNITS 4 UNITS

/

O5

10

15

20

(WINDSPEED-MPH) Fig. 7. Increase

in run time-Train

CKZ

-

SD-40

Units.

Freight train fuelconsumption

:

109

Table3. Cost/benefit analysis results fortrains CKZ and LCB COST

xs -TFAI ii- CKZ 4DDITICN?U RIJNTIME WEL USED EWIT/Los, (Mw (Gw _----___ + 4.0 + 1.0 1;:: 0.0 29.0

CNEFIT ANAI

(GAL) 655 661 667 684

AVERXE RUN TLm 0.w 150 146 149 150

3 - GP50 3 - tJ3oc 3- SD40 3 -GP40

764 773 786 798

141 143 143 143

109.0 118.0 131.0 143.0

4 4 4 4

841 858 872 876

141 141 141 141

+ 186.0 + 203.0 + 217.0 221.0 _I- +

AVEFWE

03NsIST CWE'IG. / 3-u 2 - u3Oc 2 -850 2 - SD40 2 -840

EuELa USED

- 650 - u3Oc - SD40 -840

CONSIST 03NF'IG. #crpss 2 I u3oc 2 - SD40 2 - 850 2 - 840

FUEL USED

(GAL) 698

717 723 733 844 853 862 877

145 143 144 145

146.0 155.0 164.0 179.0

4 - u3oc 4 -GPso 4 - SD40 4 - GP40 --

949 951 971 976

142 140 142 142

251.0 253.0 273.0 278.0

AND

COMMENTS

This study attempts to present a unique approach for identifying relationships between train operating costs and performance. The uniqueness of the ap-

12.1 16.8 18.7 20.4 20.7 22.6 24.1 24.5

9.0 9.0 9.0 9.0

I

1CNCREMFNTA

COST (GAL/MlN) -_-_19.0 4.2 ----

+ + + +

11.0 13.0 12.0 11.0

13.3 11.9 13.7 16.3

+ + + +

14.0 16.0 14.0 14.0

17.9 15.8 19.5 19.8

preach lies in the generation of simulated operating statistics based on individual freight train physical characteristics. Wind and precipitation effects were considered in an attempt to broaden the dimension of the analysis and, thus, to allow for the assessment of alternatives in a more realistic framework that allows for a wide range of uncontrollable, external random events. To the knowledge of the authors,

Table 4. Optimal locomotive selections based on cost/benefit

EQUIPED AVG UNNINGTIM? WN) 150 149 148 147 146 145 144 143 142 141

1::; --

i

by using Figs. 6 and 7 to adjust fuel use and running times.

r

I

CGZLN ---__

+ 9.0 + 7.0 + 7.0 + 7.0

-IT ANAiFi ;1s - TRX [N Im iWDITICNAI AVERPGE rr RUN TIME FXJNTIME 1?UEL USED BI3iEFITfIKlS: (MIN) (GAL) ( ) _____--lzN + 1.0 19.0 155 + 6.0 25.0 150 - 1.0 35.0 157

3 - u3oc 3 - GP50 3-SD40 3 - GP40

6.CONCLUHONS

IXCREMENTAl

T , ,

analysis

AINIc8

EXPECTED WG FUEL US 655.0 656.5 658.0 659.5 661.0 715.5 727.6 739.7 751.8 763.9

EQUIPED AVC OPTLW EXPmD rJNNINGTI.YzCONSIST AVG F'UELUSE 156 155 154 153 152 151 150 149 148 147 146 145 144 143 142 141 140

2 - u3oc 2 -850 II 11 II II I, 3-850 I, II 11 1, 11 II 4 -GP50 II II

698.0 702.1 706.3 710.5 714.6‘ 718.8 723.0 781.3. 793.2 805.1 817.0. 828.9 840.8 852.7 919.2 935.0 950.8

110

E. V. HOYT and R. R. LEVARY

no previous study relating fuel usage and performance on the basis of physical train characteristics has been attempted. It should be noted that the simulations were conducted under the best possible operating conditions with all factors remaining constant except wind speed and precipitation. This means that no consideration was given to such typical operating situations as trains meeting one another, holding, or temporary slow orders. By not addressing these factors, fuel consumption and running times could differ from those under actual operating conditions. It was felt, however, that these factors would have minimal impact on simulator results, given a sufficient period of time, unless they occurred on a relatively consistent basis. At the time of data collection, there was no evidence of any consistency with these items. It should be noted, too, that the graphical plots of fuel use vs. number of cars, obtained from TPS output data, (Fig. 4) contain both linear and nonlinear characteristics. Throughout the mid-portions of the curve, particularly around the mean of car distribution data, fuel consumption increases with a constant rate. At the upper end of the curves, however, consumption increases at a decreasing rate. As tonnage and length are increased, additional amounts of drag are placed on the forward motion of the train. This situation necessitates the requirement for additional horsepower which results in an increase in tractive effort by the locomotive consist to maintain velocity. This is usually accomplished by increasing throttle. which provides these elements at the expense of added fuel consumption. There is a limit to the amount of horsepower available for any specific locomotive consist and class. Continued addition of length and tonnage to a train will eventually place the locomotive consist at the limits of its feasible operation, with fuel use becoming constant and velocity continually decreasing until the train actually stalls. Consider the graphical presentation in Figs. 8A, B, and C which were based on the data obtained for 2 unit SD-40 consists for train CKZ under zero wind conditions. Figure 8A illustrates a plot of Total Fuel Consumption vs. number of cars. As can be observed, at approximately 65 cars, fuel consumption begins to increase quite linearly (i.e. at a constant rate). This linear characteristic can be expected as long as sufficient horsepower is available to maintain train movement. As cars are added (tonnage and length), the locomotives will eventually reach their feasible operating limits. At that point, additional power would result in possible component damage (maximum loading). Figure 8B presents plots of Running Time and Velocity vs. number of cars. Observation of the plots indicates that they intercept each other at approximately 83 cars. At this point, the running time and velocity are at equilibrium (i.e. speed and trip time are in balance). At counts below and above 83 cars,

desired velocity and/or running time cannot be attained without a respective increase or decrease in one or the other. The 83 car level might be regarded as an optimal operating point with respect to these two parameters. Continued addition of cars (tonnage) would result in the velocity curve decreasing to zero (stall) and the running time curve approaching infinity. Figure 8C represents plots of Fuel Burn Rate and Fuel Use per Car vs. number of cars. These plots may be likened to those which characterize economic factors, particularly operational costs. The Fuel Bum Rate illustrates the amount of fuel consumed per unit of time (a function which may be easily translated in terms of cost) for specified car counts; the Fuel Use per Car depicts an economical evaluation of the average fuel cost associated with the movement of each car on the train. Similar to the plots of Fig. 8B, an interception point of these two functions may be observed at approximately 6.5 cars. Again, this is indicative of a level at which these functions are in equilibrium. Operations at car counts above or below this level could only occur at the expense of fuel burn rate or fuel per car. The 65 car count level may also be consideered an optimal operating level from an economic perspective. The continued addition of cars (tonnage) would result in the fuel burn rate becoming a constant (maximum available horsepower being delivered). Fuel burn rate, however, would drop to zero at stall or engine shut-down. Alternatively, the fuel per car would continually fall (due to the constant fuel burn rate and increasing number of cars). It, too, would drop to zero at engine stall or shut-down. Two points suggesting optimal operating parameters have been defined. However, each represents optimality for a different set of conditions (i.e. speed, time, and cost). Since these points do not occur at a similar car count, it is not possible to gain the optimal advantage of all conditions. Nevertheless, it is possible to recognize an advantageous range of operations with respect to car counts. From Fig. 8B, it is clear that desired operations should occur at a point at or below 83 cars. From Fig. 8C. it is clear that operations may be conducted above or below the 65 car point since the overall cost of operations at any one point would be the same. However, below the 65 car point, economic operations would begin to deteriorate. Limited resources (locomotives) would be engaged in moving fewer cars. This would result in increased costs per car, a factor which would substantially affect the cost passed on to shippers. This additional cost to shippers would eventually affect the competitive posture of the business. In conclusion, it would appear that the most beneficial operating conditions for the specified IOCOmotive configuration for this train would be attained between the 65 car and 83 car counts. This would place operations within the limits of optimal time, speed, and cost constraints.

Freight train fuel consumption

111

I 800.

700. :

600'

: A : L

500.

optimal

3 NO.

cars

Fig. 8. (A) Fuel consumption vs. number of cars. (B) Runtime and velocity vs. number of cars. (C) Fuel burn rate and fuel per car vs. number of cars.

Both graphical and cost/benefit approaches have been presented here so that some reasonable inferences can be made regarding operating costs and performance. Each approach is applicable to a specific short or long run outcome. Throughout this paper, it has been emphasized that all outcomes and conclusions were based on the physical characteristics of the individual freight trains selected for the study. This study was meant to illustrate methods of analysis which are applicable to other trains and other corridors. Any change of a consistent nature for the trains being studied (whether it is related to tonnage, length, or number of cars), requires the physical characteristics be reWI(A)24:2-C

defined and reapplied to the simulator. Additionally, changes in physical terrain or modifications to locomotive power necessitate a reapplication of simulation parameters.

REFERENCES Assad A. A. (1980) Models for rail transportation. Transpn. Rex. 14A, 205-220. Crainic T. G. (198-l) A comparison of two methods for tactical planning in rail freight transportation. Opt-r. Rex ‘84, (Netherlands), 707-720. Missouri Pacific Railroad Co. (1986) Train Performance Simulator Manual. Saint Louis, MO: Industrial Engineering Department.

E. V. HOYT and R. R. LEV.ARY

112

Peterson E. R,. and Taylor A. J. (1982) A structured model for rail line simulation and optimization. Transpn. Sci.. 16 (2). 192-206. Roy J. and Ravacley M. (1982) A customer selectivity appreach to operations at CN Express. INFOR, 20, (1) 2839. The Air Brake Association. (1974) Management of Train

Operarion and Train Handling. Railway Exchange Building. Chicago. IL. Sec. 8, 2-t-t-250. Turnquist M. A. and Jordan W. C. (1983) A stochastic dynamic network model for railroad car distribution. Transpn. Sci.. 17 (2) 123-115. Union Pacific Railroad Co. (1981) Think Fuel. Omaha. NE: Union Pacific Railroad Co.

APPENDIX TRANSPORTATION Detailed

***Includes

Train Catgy

Train Symbol

Trn Day

Trn Depart MO-Da-Time

Expedit

CKZ

01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 I8 19 20 21 22 23 24 25 26 27 30 31

05-01-0320 05-02-0122 05-03-0055 0.5-04-0500 05-05-0400 05-06-0155 05-07-0155 05-08-0052 05-09-0230 05-10-0105 05-l l-0345 05-12-0130 05-13-0235 05-13-2355 05-14-2345 05-16-0037 05-17-0310 05-18-0350 05-19-0250 05-20-0155 05-20-2145 05-21-2347 05-23-0115 05-24-0420 05-25-0402 05-26-0220 05-27-0207 05-30-0330 05-31-0325

TOTAL

TSYMBOL

Representative

example

DEPARTMENT

Train Stats For Reported Trains Between CIRC7 ZA003 And CIRC7 ZBl45 During May, 1985 All Records

(Field

Trn Arrive MO-Da-Time 05-01-0822 05-02-0535 05-03-0410 05-04-0848 05-05-1020 05-06-0535 05-07-0705 05-08-0355 05-09-0825 05-10-0635 05-l l-0937 05-12-0535 05-13-0725 05-14-0400 05-15-0420 05- 16-0555 05-17-0715 05-18-0905 05-19-0700 05-20-0640 05-21-0045 05-22-0409 05-23-05 10 05-24-0850 05-25-0810 05-26-0625 05-27-0635 05-30-0635 05-31-0815

output

Reported

Plus CPU Events)

C P U

Run Time (Mins)

Orig Tons

Dest Tons

Orig

Lds

Orig Mty

Dest Lds

Dest Mty

Orig Lgth

N N N N N N N N N N N N N N N N N N N N N N N N N N N N N

302 253 195 228 380 220 310 183 355 330 352 245 290 245 275 318 245 315 250 285 180 262 235 270 248 245 268 185 290

3613 5013 3950 -1762 4526 3785 1S99 -1998 17-17 -1S99 4873 4173 6207 3075 I368 1OS3 5% 1 525 1 3991 5296 3132 7389 -192-1 5976 5279 5703 6819 -3975 5069

3613 5013 3950 4762 4526 3785 -1899 4998 4747 4899 4873 1173 6207 3018 -1368 1083 5581 5251 3991 5296 3132 7389 4924 5976 6600 5703 6819 1975 5069

38 48 30 44 40 40 49 51 42 45 46 39 52 24 42 36 46 46 33 55 21 69 49 53 43 50 79 52 47

28 27 21 37 50 20 32 35 25 43 39 36 83 31 28 51 25 45 32 42 32 30 31 38 49 39 29 31 46

38 18 40 J-l 10 10 -19 51 13 45 46 39 52 23 12 36 16 46 33 55 21 69 19 53 53 50 79 52 -t7

28 27

4934 5355

:: 50 20 32 35 25 13 39 36 83 31 28 51 25 45 32 12 32 30 31 38 62 39 29 31 46

:z 6008 4297 5546 6482 4766 6204 5969 5237 810-l 3979 5444 5711 5120 6043 4440 7243 4325 7611 5923 6222 6287 6263 8390 6157 6707

268

4871

1918

45

36

-16

37

5841

CKZ of computer

1

PLANNING

used in obtaining

car, tonnage.

and length

data.