Peak period large truck restrictions and a shift to off-peak operations: Impact on truck emissions and performance

Campbell, James F

Air pollution and excessive traffic congestion plague many metropolitan areas around the world.(1) One suggestion to reduce traffic congestion and improve air quality is to restrict large truck operations during peak periods, i.e., morning and evening rush hours. Regional truck bans have been considered in a number of cities, including London, Manila and, most recently, Los Angeles.(2) Potential air quality improvements were a key justification for the large truck restrictions proposed for Los Angeles, and air quality may be an important criterion for future restrictions. However, the effects of large truck restrictions on vehicle emissions and other performance measures are not well understood. Large truck restrictions could be counter-productive if they lead to an increase in emissions or otherwise degrade performance. This paper attempts to increase our understanding of the impact of such restrictions by estimating changes in truck emissions, fuel consumption, and utilization (vehicle-hours) that would result from a shift of large truck operations from the peak period to the off-peak period.

In response to peak period large truck restrictions (6 a.m.-9 a.m. and 4 p.m.-p.m.), a firm may shift truck operations to the daytime off-peak period (9 a.m. -4 p.m.) or to the nighttime (6 p.m.-6 a.m.). The daytime off-peak period would be most attractive to firms that wish to maintain a high level of service. Maintaining high service levels is a growing concern with the increasing levels of global competition and the emphasis on time-based production and operations systems, such as just-in-time.(3) Night operations are not feasible for many firms, and it would increase costs for firms that could switch, but are unaccustomed to night operations.

Another response to peak period large truck restrictions would be a switch to smaller vehicles. Smaller trucks that are not subject to the restrictions could allow a firm to maintain their schedules (e.g., early morning peak period deliveries). Campbell(4) analyzed impacts on truck emissions and performance of a switch to smaller trucks to circumvent large truck restrictions.

This paper considers trucking firms that shift to daytime off-peak operations in response to morning and evening peak period large truck restrictions. Because a wide variety of trucking firms and truck types would be affected by restrictions, this paper analyzes a general case for a trucking firm that operates large trucks on multistop tours during peak periods prior to the restrictions. The models presented in this paper apply to regional large truck restrictions that cover an area served by many truck tours. This may correspond to a single metropolitan area, as in Los Angeles (465 square miles) or Manila (636 square kilometers), or to a larger geographical area (e.g., Southern California). A good example of a large and important category of trucking firms to which this analysis applies is less-than-truckload (LTL) carriers.

The purpose of this paper is twofold. First, it presents methods to estimate changes in truck performance measures that are useful to evaluate the effectiveness of peak period large truck restrictions. Second, it identified the areas for which more accurate data and more careful analysis should be sought. This paper limits the analysis to the direct changes in truck performance measures. Indirect changes in the performance measures (e.g., emissions) of other vehicles as a result of changes in truck operations are not included. However, the final section of this paper addresses some of these important issues.

The remainder of this paper is organized in five parts. The first part describes some arguments for and against large truck restrictions and the second part provides background on the proposed Los Angeles large truck restrictions. The third part formulates the mathematical models and the fourth part presents results. The final part discusses some relevant issues regarding large truck restrictions.

ARGUMENTS FOR AND AGAINST LARGE TRUCK RESTRICTIONS

Proponents of large truck restrictions claim that reducing or eliminating large truck operations in congested peak periods will (1) increase peak period speeds for automobiles and other vehicles, due both to the absence of large trucks and the decrease in truck-related incidents; and (2) increase speeds for large trucks due to lower levels of congestion in the off-peak period (relative to the peak period). Because faster speeds generally produce smaller emission rates (grams/mile), depending on the range of speeds, pollutant emissions may decrease.

However, the issue of increasing peak period travel speeds by reducing peak period truck operations is very contentious. Latent demand from automobile travels may replace the trucks removed from peak periods with the net result that peak period speeds will not increase. Latent demand is caused by travelers who wish to travel in the peak period, but do not, largely due to excessive congestion.(5) This paper focuses on the effects on trucks of restrictions and does not address the unresolved issue of latent demand, nor the secondary effects on automobile operations (either in the peak or off-peak periods). However, a better understanding of the magnitude of any negative effects on trucks will help indicate the magnitude of any positive secondary effects on automobiles that would be needed to offset the negative effects.

A major operational disadvantage of a shift to off-peak operations is a possible reduction in the time available for operations. For example, the daytime off-peak period may be six hours long (9:30 a.m.-3:30 p.m.), which could force trucks to operate in a shorter time period than they did prior to the restrictions (e.g., 8 hours). This reduction in operating time may lead to greater total travel distances, since each vehicle will do less work. For example, a truck that could make 12 stops in an eight-hour tour may be limited to 9 stops in a six-hour tour. If trucks have shorter less efficient routes, then more trucks are needed and the total travel distance for all trucks would increase. An increase in travel distance may result in greater emissions and fuel consumption. Reduced operating time may also require modifying labor agreements that guarantee a minimum shift length.

Peak period truck restrictions would also be detrimental to many carriers, shippers, and receivers by restricting attractive early morning deliveries and late afternoon pick-ups. A survey of materials managers in Los Angeles showed that 58% of outbound shipments are sent in the p.m. peak and 27% of inbound shipments are received in the a.m. peak.(6) Restrictions that increase trucking costs will likely translate into higher costs to consumers. This is especially important in the United States, because of the pervasive role of truck transportation. Economic impact analyses of the proposed Los Angeles restrictions(7) suggest that delays would be unacceptable for many LTL carriers and specialized commodity carriers, because of the need to maintain high levels of customer service and just-in-time deliveries. In contrast, firms that currently receive shipments during the off-peak and night periods (e.g., retail department stores, auto dealers, some manufacturers) might see only minor effects due to a shift from peak to off-peak deliveries. The economic impact analyses discuss economic issues regarding a shift to off-peak operations in greater detail.

Finally, it has been suggested that peak period travelers might benefit from safe travel by reducing or eliminating large truck operations. Conversely, off-peak drivers may have to contend with greater concentrations of large trucks.

LARGE TRUCK RESTRICTIONS IN LOS ANGELES

In the United States, the problems of traffic congestion and unhealthy air quality are perhaps most serious and most closely linked in Southern California. It is estimated that 75% of the population exposure in the United States to unhealthy levels of ozone is in Southern California, and furthermore, that drivers in the Los Angeles area waste over 430,000 hours daily due to freeway congestion.(8) It is not surprising that Los Angeles has been at the forefront of recent efforts to implement large truck restrictions.

In response to the dual problems of traffic congestion and air pollution, the City of Los Angeles, with the strong backing of Mayor Tom Bradley, developed a draft ordinance to establish a pilot program to regulate large truck transportation during peak periods. This ordinance(9) is a detailed and lengthy legal document, but the restrictions can be summarized as follows. Seventy percent of the large trucks would be prevented from operating on city streets between 6:00 a.m. and 9:00 a.m., and 4:00 p.m. to 7:00 p.m. Large trucks are basically defined to be commercial vehicles with three or more axles, including tractor-trailer combinations (passenger carrying vehicles are not included). This corresponds to trucks over 26,000 pounds gross vehicle weight (GVW), which are class 7 and 8 vehicles in the United States.

There are numerous exemptions and implementation details of the Los Angeles draft ordinance that complicate the simple statement of the restrictions above.(10) Because the purpose of this paper is a general analysis, as opposed to a detailed study of the particular restrictions proposed for Los Angeles, details of the proposed Los Angeles restrictions are left for the interested ready to pursue.

Large truck restrictions in Los Angeles were originally proposed in 1987 as pat of a plan to reduce freeway congestion.(11) However, following a study of freeway congestion in Los Angeles,(12) the focus of the restrictions changed from freeways to city streets, and the primary justification for restrictions was expanded to include air quality improvement. The proposed restrictions in Los Angeles were very controversial and are no longer being considered, due to recent economic(13) and political developments. (Mayor Bradley did not run for re-election and several new City Council members were elected in 1993.) Further details of the Los Angeles truck restrictions and their evolution is provided in Campbell.(14) Although the City of Los Angeles is no longer actively pursuing large truck restrictions, the South Coast Air Quality Management District, which has broad authority regarding measures to improve air quality, still views truck restrictions as a viable transportation control measure.(15)

MODELS

Because a large number of trucks involved in a variety of different activities and operating modes would be affected by large truck restrictions (e.g., 65,000 to 100,000 trucks in Los Angeles),(16) this research employs an approximate analytic model of the average distance per shipment for a generic multistop truck tour. A number of authors have used similar approximate analytic models to address strategic planning issues.(17) In this paper we assume the underlying travel metric is Euclidean and that the truck delivery and pickup stops are randomly scattered over the region served. The formulation in this section is for a multistop tour delivering shipment from a single origin to many destinations. A multistop collection tour could be analyzed similarly. Define the following:

D = average distance per shipment (miles/shipment),

V = size of a truck load (shipments),

m = average number of stops on a tour (stops/tour),

n = density of delivery (or pickup) stops (stops/mile sup 2 ) and

A = area of region served (square miles)

The average distance per shipment can be formulated as follows:

(Equation 1 omitted)

using the tour distance expressions developed by Daganzo.(18) The values of the constants are k sub o = 0.382 and k sub 1 = 0.57. (Smaller values of k sub 1 should be used if there are fewer than six stops. The first term of the distance per tour expression can be viewed as the round trip distance from the origin to the vicinity of the stops. The second term of the distance per tour expression can be viewed as the incremental distance to make m stops.

The desire to maintain a high level of service is modeled in terms of the truck headways at the delivery (or pickup) locations. Define:

H = headway = time between visits to a delivery stop (days), and

q = average demand at a stop location (shipments/day).

The relationship between headway, vehicle size, and number of stops for a given demand q is:

H = V/(mq) (2)

From Equations (1) and (2) the average distance per shipment can be written

(Equation 3 omitted)

For a fixed level of service (headway), the distance per shipment is a decreasing function of truck size, as expected. Thus, large trucks are desirable to reduce distance and consequently transportation cost. The distance per shipment can also be viewed as a decreasing function of the number of stops, since for a given demand and headway (q and H), an increase in vehicle size is matched by a proportional increase in the number of stops (see Equation 2).

The final component of the model is a time limit. This is needed to analyze a shift to off-peak operations that reduces the time available for large truck operations. Define:

T = tour time limit (hours),

s = average truck speed (miles per hour), and

t = average time per delivery (or pickup) stop.

The time limit provides a constraint on truck operations.

travel time + stop time

(remainder of equation 4 omitted)

This can be written as a constraint on the number of stops:

(Equation 5 omitted)

The number of stops also cannot exceed the number of shipments carried by a truck:

m

Thus, the number of stops cannot exceed the minimum of V and the right-hand-side of Equation (5). The number of stops should be as large as possible to minimize the travel distance (see Equations 2 and 3). This implies that vehicles should be large enough that the time constraint, and not the vehicle size, limits the number of stops, so Equation (5) should be an equality. The vehicle size can then be written from Equation (2) using the right hand size of Equation (5) for m:

(Equation 7 omitted)

From Equations (3) and (7), the distance per shipment can be formulated as a function of the speed s and time period T:

(Equation 8 omitted)

Note that the distance D(s,T) increases as the time limit T decreases.

The demand characteristics (q and n) are assumed to be unchanged by the enactment of large truck restrictions. Likewise, the firms operating parameters (area A, stop time t, and headway H) are assumed to be the same before and after the restrictions. However, the speed and time limit values (s and T) are affected by the large truck restrictions. In the following equations the speed and time limit are varied to produce an estimate of the change in travel distance in response to peak period large truck restrictions. The change in travel distance is used to derive changes in the performance measures.

Let the truck operating time and average speed before implementing large truck restrictions be denoted T sub b and S sub b , respectively. Likewise, let the subscript a denote the conditions after implementing restrictions. The percentage change in the average distance per shipment is given by:

(Equation 9 omitted)

Let e sub i (s) be the emission rate for pollutant i at speed s (e.g., in grams per mile). The percentage change in the emissions of pollutant type i is:

(Equation 10 omitted)

Emission rates were obtained from Environmental Protection Agency (EPA) documents.(20) Emission rates depend on a variety of factors, including speed, age of equipment, installed emissions control devices, altitude, temperature, and operating conditions. No single data source includes all factors for all conditions. However, the EPA compiles air pollution emission rates for the major vehicle pollutants, hydrocarbons (HC), carbon monoxide (CO), and oxides of nitrogen (NOx) for several classes of trucks under various environmental conditions. NOx and HC emissions are especially important because they contribute to the formation of ozone, a major component of urban smog. NOx emissions are perhaps the most serious problem, because large trucks contribute more to regional NOx vehicle emissions than to HC and CO vehicle emissions (due to the nature of diesel engines).(21) The California Air Resources Board reports that in California large trucks cause 37% of NOx vehicle emissions, 14% of CO vehicle emissions, and 10% of CO vehicle emissions.

EPA emission rates are based on federally prescribed engine dynamometer test procedures for which the estimated average speed is 19.45 mph. The EPA also provides an equation to determine speed correction factors to allow emission rates to be estimated for other speeds (between 5 mph and 55 mph). The emission rates used in this paper are the EPA rates adjusted by the speed correction factors.

Let f(s) be the fuel consumption rate at speed s. The percentage change in the fuel consumption is then:

(Equation 11 omitted)

EPA documents also provide fuel consumption rates and speed correction factors, similar to those for emissions.(22)

The utilization in vehicle hours is given by the average distance per shipment, multiplied by the number of shipments per day and divided by the average speed:

U = D x nAq/s. (12)

The percentage change in utilization is then:

(Equation 13 omitted)

RESULTS

The models and equations presented in the previous section can be used to estimate changes in performance measures for a variety of environments. This section considers one such environment that corresponds to a 1,000 square mile region with 200 customers, where a customer receives on average one delivery of five shipments per day and the average stop time per delivery is 30 minutes. This situation is specified by the following set of data:

A = 1,000 square miles,

n = 0.2 destinations per square mile,

q = 5 shipments per day,

H = 1 day, and

t = 0.5 hours.

This might be viewed as representative of an LTL trucking firm providing a high level of customer service. (The service region of 1,000 square miles is approximately twice the size of the City of Los Angeles, but considerably smaller than the jurisdiction of the South Coast Air Quality Management District in Southern California) The constants are k sub o = 0.38 and k sub 1 = 0.57.(23) The optimal vehicle size, from Equation 7, depends on the speed and the tour time limit and is given by:

V = 5(sT - 24.03)/(0.5s + 1.27).

Suppose that prior to restrictions, trucks are operating for an eight-hour period (T sub b =8) at an average speed of 20 miles per hour (s sub b =20). The optimal vehicle size is then 60 shipments and the average number of stops per tour is 12. Now suppose that large truck restrictions create a tour time limit by imposing an off-peak period of seven hours (T sub a =7) (e.g., 9 a.m. to 4 p.m., as in the proposed ordinance for Los Angeles).

Figure 1 shows the change in distance per shipment, fuel consumption, and utilization as a function of the average speed in the off-peak period S sub a . (Figure 1 omitted) The reduced time for large truck operations increases the average distance per shipment by an amount ranging from 10.5%, if the off-peak speed is the same as the peak speed (20 mph), to 3.4% if the off-peak speed is 30 mph. Fuel consumption increases from 10.5% to 26%, due to reduced efficiency at higher speeds, Utilization may increase or decrease depending on the average speed in the off-peak period. Higher utilization in a reduced time period (seven hours versus eight hours) implies more trucks would be required.

Figure 2 plots the percentage change in emissions (Equation 10) for three major pollutants as a function of the speed S sub a , when the average speed before imposing restrictions is 20 mph. (Figure 2 omitted) This figure combines two competing factors: average travel distance increases due to the reduced operating time in the off-peak period, but emission rates tend to decrease with increasing speed over the range 20 mph to 30 mph. Thus, the net effect will be a decrease in emissions if the speed increase due to off-peak operations is large enough (e.g., a 4 mph increase for NOx). If shifting to the off-peak period does not result in an increase in average speed, then the emissions will increase 10.5%, due to the increase in the travel distance (Figure 1).

Figures 3 and 4 present results when the average speed prior to restrictions is 30 mph, (s sub b =30), instead of 20 mph as in Figures 1 and 2. (Figures 3 and 4 omitted) For an average speed of 30 miles per hour, the optimal vehicle size is 66.4 shipments and the average number of stops per tour is 13.3. Suppose as before, that trucks operate for 8 hours prior to restrictions (T sub b =8) and seven hours after the imposition of restrictions (T sub a =7).

Figure 3 shows that the average distance per shipment increases by an amount ranging from 9.5%, if the off-peak speed is the same as the peak speed (30 mph), to 6% if the off-peak speed is 40 mph. The results for fuel consumption and utilization in the range 30 to 40 mph are similar to the results for 20 to 30 mph in Figure 1, although the increase in fuel consumption is not as dramatic as in Figure 1. Figure 4 differs from the earlier results in Figure 2 because NOx emissions will increase at any resulting off-peak speed. This is because the emission rate for NOx does not decrease enough as the speed increases. In fact, the NOx emission rate actually increases for high enough speeds. Thus, no amount of speed increase in the off-peak period will reduce NOx emissions, when the initial speed is large enough.

If restrictions imposed a shorter time limit than seven hours, the impact would be greater. Figure 5 presents results for a situation as in Figure 2 (20 mph initial speed), but where the off-peak period is only six hours (instead of seven). (Figure 5 omitted) As expected, the emissions are worse, compared to Figure 2, and even a 10 mph increase in speed will result in increased NOx emissions.

DISCUSSION

This paper has developed analytical models of transportation to estimate the impact of a shift to off-peak operations in response to peak period large truck restrictions. Figures 1-5 indicate that the impacts of large truck restrictions are sensitive to the vehicle speeds, both prior to, and after, imposing large truck restrictions. This highlights the need to acquire accurate speed data before restrictions and to accurately estimate the speeds achieved after restrictions. The models in this paper can help to identify the magnitude of speed increase necessary to improve performance measures for any given speed before restrictions. The models may also indicate that no amount of speed increase will improve performance for certain measures (as with NOx in Figure 4).

The percentage results in Figures 1-5 apply to all vehicles shifted to the off-peak period. If a small fraction of the total number of large trucks are shifted to the off-peak period, then the net effect in the peak and off-peak period will be small, both because the percentage changes in Figures 1-5 are applied to a small base, and because any increase in peak period speed is likely to be small. A large shift out of the peak period would likely be required to produce even a small improvement in peak period speed.

Although the results in Figures 1-5 are for one particular scenario, the findings are generalizable to other situations. Because parameters such as the area of the service region (A) and the density of destinations (n) appear in the distance formula (Equation 8) as square roots, the results are insensitive to changes in their values. For example, suppose the service region was 250, instead of 1,000, square miles. Then, large truck restrictions that reduce operating time from eight to even hours increase travel distance by only 6.6%, compared to 10.5% for the 1,000 square mile service region (assuming a 20 mph speed before and after restrictions). Similarly, if the service region was 4,000, instead of 1,000, square miles, a reduction from eight to seven hours increases travel distance by 17.1% Thus, changing the size of the service region by a factor of four has a small effect on the travel distance increase. The results are even less sensitive to changes in the density of destinations. Changing the density of destinations (from 0.2 per square mile) by a factor of four changes the travel distance increase by only about 2%.

The impacts of large truck restrictions would be greater than shown in the example in this paper if the service region was larger than 1,000 square miles or the density of demand was greater than 0.2 destinations per square mile. A larger service area would also likely affect a greater number of trucks, and thus produce a greater net impact. Conversely, the impacts would be less than shown in Figures 1-5 if the service region or density of destinations were smaller than the values used in this paper.

To use the models presented in this paper, one needs to determine appropriate values for the parameters describing the demand (n and q) and operating characteristics (A, t, H and S sub b ). These values can usually be easily measured or estimated. The parameter that is difficult to determine is the average speed after large truck restrictions are imposed, s sub a . However, the type of sensitivity analysis presented in this paper using a range of speeds will indicate how large must be the speed increase for large truck restrictions to be beneficial.

Although the models presented in this paper indicate an improvement in some performance measures for certain scenarios, it is important to recognize that a shift to off-peak operations may result in delays, and additional inventories and costs that are not reflected in the models. For example, desirable late afternoon pickups may be replaced by morning pickups the following day as a result of evening peak period restrictions. Similarly, desirable early morning deliveries may be replaced by afternoon deliveries on the preceding day to ensure the needed materials are available at the beginning of the work day.

In summary, it is not at all clear that peak period large truck restrictions would reduce net emissions and improve air quality, as proponents have claimed. Reductions in truck emissions of HC and CO are likely if the speed differential between the peak and off-peak period is great enough. Truck emissions of NOx are more sensitive to the initial speed in the peak period and may not decrease, even for a large speed differential. Better data on peak and off-peak speeds are essential to allow better estimates of the magnitude of emissions changes. Even if the restrictions increase truck emissions, there could be a net benefit from reduced automobile emissions in the peak period. However, the unresolved and controversial role of latent demand in potentially canceling any emissions and congestion improvements needs to be better understood. Future growth in travel demand could also make any air quality and congestion improvements short lived.

NOTES

1 A primarily European perspective is provided in Martin Kroon, Ruthger Smit, and Joop van Ham, eds., Freight Transport and the Environment (Amsterdam: Elsevier, 1991). A wider view is presented in Asif Faiz, "Automotive Emissions in Developing Countries-Relative Implications for Global Warming, Acidification and Urban Air Quality," Transportation Research 27A (1991): 167-186.

2 Kenneth W. Ogden, Urban Goods Movement: A Guide to Policy and Planning (Brookfield, Vermont: Ashgate Publishing Co., 1992), Ch. 6.

3 Kant Rao, William Grenoble, and Richard Young, "Traffic Congestion and JIT," Journal of Business Logistics 12, no. 1 (1991): 105-121; Patricia J. Daugherty and Michael S. Spencer, "Just-In-Time Concepts, Applicability to Logistics/Transportation," International Journal of Physical Distribution and Logistics Management 20, no. 7 (1990): 12-18; and Randolph W. Hall and Janice G. Partyka, Peak Period Truck Restrictions: Impacts on the Los Angeles Economy (Walnut Creek, Calif.: Logisolve, 1991).

4 James F. Campbell, "Using Small Trucks to Circumvent Large Truck Restrictions: Impacts on Truck Emissions and Performance Measures," accepted for publication in Transportation Research.

5 Jim Mele, "Congestion Takes its Toll," Fleet Owner (September 1988): 59-72; and California Air Resources Board Report AB2595, Technical Advisory Group, Guidelines for Local Air Districts Considering Transportation Control Measures Directed at Heavy-Duty Truck Operations (Sacramento, Calif.: Business, Transportation and Housing Agency, Air Resources Board, California Highway Patrol, September 1990).

6 Hall and Partyka reference in Note 3.

7 Recht Hausrath & Associates: Hamilton, Rabinovitz & Alschuler, Inc.; The Kingsley Group, Economic Impact Analysis of the Proposed Truck Management Program, Los Angeles, California, 31 January 1993; Urban Freeway Gridlock Study (Cambridge, Mass.: Cambridge Systematics, Inc., 1988); same reference as Hall and Partyka in Note 3.

8 James D. Boyd, "A California and United States Perspective on the Impact of Air Quality Policies on Goods Movement by Heavy Duty Trucks," in Kroon, Smit, and van Ham reference in Note 1 at pp. 81-89.

9 The draft ordinance would have amended the Los Angeles Municipal Code by adding a new Article 3 to Chapter VII, Sections 73.00 to 73.13. The draft ordinance is entitled Truck Management Program and dated October 10, 1991.

10 Section 73.04 of the ordinance (Note 9) contains 8 pages defining exempt vehicles, including U.S. Postal Service trucks, U.S. military vehicles, U.S. government trucks from agencies whose jurisdiction preempts that of the City of Los Angeles, trucks carrying hazardous materials, trucks engaged in emergency operations, trucks powered by clean alternative fuels, etc. Implementation details in the ordinance include procedures for identifying and enrolling large trucks in the program, determination of fleet size for a firm, five options for fleet operators to operate a fraction of their enrolled fleet in the a.m. or p.m. peak period, and two options for independent operators to operate in the a.m. or p.m. peak period.

11 Tom Bradley, "Keep on Trucking--at Nighttime," Los Angeles Times, 11 December 1991.

12 Cambridge Systematics reference in Note 7.

13 Same references as Hall and Partyka in Note 3 and Cambridge Systematics in Note 7.

14 Same reference as Note 4.

15 Von Loveland, South Coast Air Quality Management District, telephone interview, 14 March 1994.

16 Cambridge Systematics reference in Note 7 and S. E. Rowe, "Approval of Peak-Hour Heavy-Duty Truck Management Program," City of Los Angeles Inter-Departmental correspondence, 22 October 1991.

17 Andre Langevin and Pontien Mbaraga, "Continuous Approximation Models in Physical Distribution: An Overview," under review at Transportation Research, 1994; and Carlos F. Daganzo, Logistics Systems Analysis (Berlin: Springer-Verlag, 1991).

18 Carlos F. Daganzo, "The Distance Needed to Visit N Points with a Maximum of C Stops per Vehicle: A Manual Tourbuilding Strategy and Case Study," Transportation Science 18 (1984): 331-350.

19 Carlos F. Daganzo, "The Length of Tours in Zones of Different Shapes," Transportation Research 18B (1984): 135-146.

20 United States Environmental Protection Agency, Supplement A to Compilation of Air Pollutant Emission Factors Volume II: Mobile Sources, AP-42 Supplement A (Ann Arbor, Mich.: Office of Mobile Sources, January 1991); and Paul A. Machiele, Heavy-Duty Vehicle Emission Conversion Factors II 1962-2000, Technical Report EPA-AA-SDSB-89-01, U.S. Environmental Protection Agency, October 1988.

21 Theo J. H. Shoemaker and Peter A. Bouman, "Facts and Figures on Environmental Effects of Freight Transport in the Netherlands," in Kroon, Smit, and van Ham reference in Note 1 at pp. 41-62.

22 Same reference as United States Environmental Protection Agency report in Note 20.

23 Same references as Notes 18 and 19.

ABOUT THE AUTHOR

James F. Campbell is associate professor of management science and information systems at the University of Missouri-St. Louis. He received his doctorate in operations research and industrial engineering from the University of California, Berkeley. His current research concerns mathematical models of logistics and distribution systems. His publications have appeared in numerous journals.

Copyright Council of Logistics Management 1995
Provided by ProQuest Information and Learning Company. All rights Reserved