october 1982
"tober 1982
G.
Economics Report 106
The Economic Efficiency
of Operating Transportation
Vehicles Empty or Full
Food and Resource Economics Department
Agricultural Experiment Stations
Institute of Food and Agricultural Sciences
University of Florida, Gainesville 32611
Richard P. Beilock
Richard L. Kilmer
TABLE OF CONTENTS
1. TABLE OF CONTENTS . . . .
2. LIST OF FIGURES . . . .
3. LIST OF TABLES . . . .
4. INTRODUCTION . . . .
5. BACKHAUL DECISION MODEL . . .
IMPACT OF TIME WHEN COMPARING SCENARIOS
MODEL SPECIFICATION . . .
6. SCENARIO ANALYSIS . . . .
DIRECT RETURN . . .. .
. . . i
. . . ii
. . . .iii
INDIRECT RETURN . . . . .
7. MODEL IMPLICATIONS AND EMPIRICAL EVIDENCE OF BEHAVIOR IN
U.S. TRUCKING INDUSTRY . . . .
EFFECT OF DISTANCE ON FULL OR EMPTY MOVEMENT DECISIONS .
ECONOMIC REGULATION OF TRANSPORTATION . . .
DIRECT SEARCH COSTS (DSC), EMPTY MILEAGE, AND REGULATIONS
RATE INFLEXIBILITY AND REGULATIONS . . .
8. SUMMARY . . . . . . .
9. FOOTNOTES . . . . . . .
. 1
. 2
. 3
. 6
. 8
8
. 8
. .. 9
S. 10
S. 10
. .15
. 17
. 21
. 22
LIST OF FIGURES
Figure 1. Scenarios for going from B to D via A or via C and A. 4
Figure 2. Future net return comparison across scenarios .... . 5
Figure 3a. Tariff rates and additional costs of securing and carrying
a load as implied by a positive full load distance
relationship .............. ......14
Figure 3b. The relationship between distance and the probability
of obtaining a loaded backhaul . . .... 16
LIST OF TABLES
Table 1. Percent empty vehicles by length of previous haul . .11
Table 2a.
Comparison of percent empty truck miles by type of
equipment and authority ........... ........19
Table 2b. Comparison of percent empty truck miles by type of
equipment, authority, and type of highway (Intrastate
or Interstate). ........................ .21
The Economic Efficiency of
Operating Transportation Vehicles Empty or Full
By Richard Beilock and Richard L. Kilmer*
INTRODUCTION
While it is generally recognized that virtually no transportation
system can operate without empty mileage, it is often assumed that a
system or any part of a system is operating more efficiently the smaller
the empty mileage incurred. This belief is often grounded in energy con-
cerns and in the common sense notion that if a vehicle could be loaded,
then it is a waste if it is not. This belief may be false. Minimizing
empty mileage will not generally maximize the economic benefit or social
welfare of the system. In this paper, a conceptual framework is
developed to determine the costs and benefits to carriers of running
empty or full. The implications of individual carrier behavior are
related to the performance of the transportation system. Backhaul
movements of over-the-road motor vehicles serve as the focus of the
analysis. Comparisons are made between what is theoretically
anticipated and empirical evidence from the U.S. trucking industry. It
is shown that this evidence generally conforms to the behavioral
expectations of the model.
Minimizing empty mileage is a technical, rather than an economic
goal. For any transportation system reducing empty mileage may be a
sound strategy to follow up to a point. Beyond that point, the costs
incurred in realizing further reductions would tend to outweigh any
benefits to be gained from the reductions. Under certain conditions it
becomes a rational strategy to opt for empty mileage even if a load
*Richard Beilock and Richard L. Kilmer are Assistant Professors,
Institute of Food and Agricultural Sciences, Food and Resource Economics
Department, University of Florida, Gainesville, Florida 32611.
could be obtained. Thus a system with more empty miles could be more
desirable than one with fewer empty miles.
BACKHAUL DECISION MODEL
Backhauls for over-the-road motor vehicles offer an excellent
framework in which to examine the empty mileage question. Most motor
vehicles operate from a home base (A) to which they must periodically
return for maintenance and/or the personal needs of the operator.
Selection of the outbound or fronthaul movement away from A is based
upon the carrier's perceptions or expectations regarding the
profitability of the entire trip. No doubt, when a carrier accepts a
load from A to B there is some expectation of the routing and loads
which will be taken to facilitate the return. Once at B, unless the
carrier is contractually obligated to follow some course of action, the
optimum strategy for the return trip should be reconsidered. It is at
this point that we will begin.
To facilitate the analysis of the operator's decision making
procedure the following simplifying assumptions are made: (1) the
carrier's objective is to maximize net returns, (2) the carrier is a
price taker, (3) loads may be taken to and/or hauled from only one
intermediate point (C) prior to returning to A from B, (4) regardless
of how the operator elects to return to A, he anticipates that the next
load outbound from A will be to D, (5) regardless of when D is reached,
the anticipated future earnings rate is the same, and (6) costs and
revenues are independent of one another. Any of these assumptions may
be dropped without altering the validity of the model but at the cost
of greatly increased complexity.
With only one possible intervening point (C), the operator's
choice of return strategies reduces to five scenarios (Figure 1): (1)
return empty from B directly to A, (2) return full from B directly to A,
(3) travel full to C and return empty to A, (4) travel empty to C and
return full to A, and (5) travel full to C and return full to A.
Being a maximizer of net returns, the optimum strategy is dependent'
upon: (1) the value or urgency of having the vehicle return to A, (2)
the revenues and costs associated with securing, transporting, and
handling freight at the various points (A, B, C, and D), and (3) costs
associated with running empty. Time is important because each scenario
takes different amounts of time to complete. In the next section, the
importance of time will be discussed.
Impacts of Time When Comparing Scenarios
If the net returns (wk) of two scenarios are being compared, and if
one scenario can be completed x days sooner, an amount must be added to
account for the anticipated interest and earnings (AIE) which would be
realized by the operator during those x days. AIE depends upon the size
of the time differential, the anticipated rate at which interest can be
made on money earned and the net returns from future trucking activities.
The natural log future net returns (FNRk) from each scenario are
plotted against time (Figure 2). The beginning time at B is to. The
time it will take the operator to return to A, secure and deliver a load
to D is tk units of time. The natural log of the net return associated
with tk is Inrk. At any point in time, the slope of the dashed lines
indicates the rate at which it is anticipated that interest and earnings
will be made.2 Therefore, line FNRK represents the future or t5 value
of returning to A, delivering a load to D, and being free to engage in
other productive activities t5 tk (t k) units of time sooner than
jk
Figure 1. Scenarios for going from B to D via A or via C and A.
KEY
Full =
Empty = -- --
Scenarios = 1, 2, 3, 4, 5
Figure 2. Future net return comparison across scenarios.
Lnr5
O m -
Lnir2
Lnr, -
LT I /_ ,
to tl
-o -M 4
Lnir3
-d
w g- M
o-
400 SOM
Ln 4
, M
- U -I s I
t3 t4
LnFNR2
LnFNR3
LnFNR1
LnFNR4 LnAIE51
Time
*Ln = natural logarithm
*LnTk,
LnFNRk
LnAIE5k,
__
m
a
would be the case if loads had been acquired at both B and C (Scenario 5).
The vertical distance between rk and FNRk represents the total net earnings
to be realized in t5k, denoted AIE5k. The most attractive scenario is
3
that for which the FNRk (equal to r5 if Scenario 5) is the highest.
Model Specification
Employing the above methodology for comparing all scenarios at t5,
the amount of time necessary to complete scenario 5, the decision process
may be stated as a net return maximization problem as follows:
(1) MRNR = Maximum {FNR1, FNR2, FNR3, FNR4, FNR5}
where:
(2) FNR1 = -ERCBA + (CTCAD)(CCFI) DSCAD -PLUAD FRCAD
RC1 RISK1 + AIE51
CTCBA DSCBA LUBA -
DSCAD PLUAD FRCAD -
CTCBC DSCBC PLUBC -
SCAD PLUAD FRCAD
-ERCBC + (CTCCA)(CCF4) -
(CTCAD)(CCF4) DSCA -
AIE54
CTCBC DSCBC PLUCA -
DSC PLUCA FRCCA +
CA CA CA
FRCBA
RC2 -
FRCBC
RC3. -
DSCCA
PLUAD
AD
+ (CTCAD)(CCF2) -
RISK2 + AIE52
- ERCCA + (CTCAD) (CCF3)-
RISK3 + AIE53
- PLUCA FRCCA +
- FRCA RC4 RISK+
AD
FRCBC + (CTCCA)(CCFt) -
(CTC D)(CCF5) DSCAD -
PLUAD FRCAD RC5 RISK5
(3) FNR2 =
(4) FNR3 =
(5) FNR4 =
(6) FNR5 =
where: MRNR is the maximum future net returns among all scenarios measured
at time t5; t5 is the length of time to complete the longest scenario (Scen-
ario 5); FNRk is the future net returns from scenario k at time t5; and
ERC.. is the total empty running cost between i and j which includes fuel,
labor costs, on-the-road meals and lodging, scale fees, tie down checks,
etc. CTCij is the current (t ) total compensation received for hauling a
load from i to j, and CCFk is the expected compensation change factor asso-
ciated with scenario k (assumed to be 1 for CTCBA and CTCBC). For example,
CCFk equals .8 if a 20 percent decrease is expected in CTC. DSC.i is the
direct search costs associated with locating a load to haul from i to j
including telephone costs, brokerage fees, costs of lodging and meals, and
labor costs during the search; PLUij represents the positioning, loading,
and unloading costs associated with hauling from i to j; FRCij is the total
full running cost between i and j (includes same costs as ERC); RCk is
the cost of being away from home base A for the amount of time associated
with scenario k and includes delayed vehicle maintenance, overtime charges,
and personal costs of being away from home, etc.; RISKk is the risk asso-
ciated with scenario k to include weather and road conditions, crime and
uncertainties related to price expectations and search success; AIESk
is the anticipated interest in nk and future trucker earnings after
delivery at D for an amount of time equal to the difference between the
time it took to go from B to D in scenario k as opposed to scenario 5;
,k is the net return from scenario k up to tk; CCFk is the expected com-
pensation change factor associated with scenarios 4 and 5 between B and C.5
SCENARIO ANALYSIS
Scenarios 1 and 2 (direct empty and direct full return to A) will be
discussed first. Next, the indirect return scenarios (3, 4 and 5) will be
discussed. The operator would, however, compare all five possibilities
and select the most attractive one, i.e., the one with the highest FNR.
Direct Return
If the vehicle were to return directly to A, deciding whether or not
to carry a load would depend upon the relative net returns. Subtracting
FNR1 from FNR2 yields:
(7) FNR2 FNR1 = AFNR21 CTCBA + CTCAD (CCF2 CCFI) +
(AIE52 AIE51) (FRCBA ERCBA) DSCBA
PLUBA RISK2 RISK) (RC2 RC1)
If AFNR21 is positive, then a full return (scenario 2) would be preferable
to. an empty return (scenario 1).
AFNR21 will be algebraically greater (smaller) if it is anticipated
that during the added time necessary to search for, secure and handle a
full return to A, the freight rates for hauling a load from A to D will
increase (decrease) (CCF2 increases (decreases) relative to CCF1). An
operator naturally prefers to arrive at A when rates are higher. If
rates from A to D are expected to rise, the search for a full backhaul
from B to A becomes attractive as a delaying tactic.6
If the costs of remaining away from home base for the additional
time necessary to attain a full load (AIE2 minus AIE1 and RC2 minus
RCi) or the added risks (RISK2 minus RISK1) are large, then the incentive
to return full is smaller (i.e., AFNR21 is smaller). For motor vehicles
a more rapid return may be desirable because of the personal needs of the
driver or vehicle maintenance requirements. In addition, if the risks
associated with search are greater away from home base due to lack of
familiarity with potential shippers, this will encourage foregoing the
search and returning empty (assuming risk averseness). Finally, AFNR21
is greater the smaller the added linehaul cost associated with running
loaded rather than empty (FRCBA ERCBA).
When a vehicle and load are matched at a given location an exter-
nality is created in that search costs (DSCBA) generally rise for remain-
ing vehicles. This is true because the number of places to search remains
the same, but the number of potential loads is decreased (by one). At a
certain point, all carriers will balk and go elsewhere rather than search
at length for a load in a well picked over market. This is not to say
that remaining loads will never be picked up, but that they must wait
until the density of available loads increases back to a point where
searches once more become economical at the locale. Therefore, in a world
of nonzero search costs some empty mileage is efficient even if matching
fronthaul and backhaul loads exist. This implies that economically
efficient transportation systems generally must be technically
overcapacity. Reductions in this "necessary" empty mileage may be
realized if the costs of search related information could be lowered.
Indirect Return
If the alternative of returning from B to A via C is considered, the
selection of Scenario 1, 2, 3, 4, or 5 depends on which is expected to
yield the highest return. An examination of Equations 4, 5, and 6 reveals
that, as with direct returns, the decision to seek a load or not on each
leg of the journey is dependent upon the differences between full and
empty running costs, the costs of locating and handling loads, the magni-
tude and direction of anticipated rate movements at points down-the-line
during the time necessary to acquire and handle loads, and the relative
risks and other (road) costs associated with loading or not loading. The
operator will choose the scenario or course of action which is most
attractive. This corresponds to the scenario with the highest FNR given
the assumption of net return maximization.
In the next section of the paper some implicationsof themodel and
empirical evidence regarding observed behavior will be presented. The
impacts of economic regulations will be of particular concern. Observed
empty movement patterns and rate structure-cost relationships, and impli-
cations of vehicle speculation will also be addressed. Next, as a brief
aside, the implications of positive levels of empty mileage to a society
where energy is highly valued will be discussed. It will be shown that
a carrier's decision to run empty may not be at variance with society's
desire to reduce energy consumption. Finally, the results will be sum-
marized and conclusions drawn.
MODEL IMPLICATIONS AND
EMPIRICAL EVIDENCE OF BEHAVIOR
IN U.S. TRUCKING INDUSTRY
Effect of Distance on Full or Empty Movement Decisions
In an analysis of the National Motor Transport Data Base, Paxson
(1979)7 found that the percentage of empty trucks was negatively related
to the length of the previous loaded haul. This relationship held
regardless of the type of vehicle or the authority class, i.e., under
ICC regulations or exempt, (see Table 1). The reason for the observed
positive distance-full truck relationship may be discovered by taking the
Table 1. Percent empty vehicles by length of previous haul.
Previous
500 1000- 1500-
<500 1000 1500 2000
Carrier Type
Regular Route
Common Carriage
Irregular Route
Common Carriage
Private Carriage
Contract Carriage
Exempt* Carriage
10 7 3
33 18 14
2 N/A
10 8
All Types 31 20 15 11 8 6 19
Trailer Type
Regular Van 24 16 12 9 7 4 17
Reefer Van 34 17 12 9 7 7 13
Flatbed Trailer 33 22 17 15 11 6 29
Tanker Trailer 44 28 31 35 24 N/A 39
Moving Van 27 20 16 5 7 7 12
Special Trailers 38 22 20 15 14 N/A 20
All Trailers 32 19 14 11 8 7 19
An "N/A" denotes that the category has no observations or only a
small number (less than 20) of observations.
*Includes Agricultural Cooperative Hauls.
Source: Paxson [1979].
Length
2000-
2500
of haul
<2500
(miles)
all
mileage
N/A
5 18
partial derivative with respect to distance (DBA) of the difference between
the future net returns from scenarios two and one (AFNR21: Equation (7)).
8AFNR21
(8)
( DBA
As it does not seem
a load would change
between scenarios 2
8CTCBA CTCAD(CCF2 CCF1) t21
+ +
3DBA t21 _DBA
8(AIE52 AIE51) 3t21 (FRCBA ERCBA)
at21 DBA aDBA
DSCBA PLUBA RISK2 RISKj)
3DBA DBA aDBA
a(RC2 RC1) 3t21
3t21 3DBA
likely that the time required to search for and handle
systematically with distance, the time difference
and 1 (t21) is not assumed to be a function of distance.
Therefore, Bt21/SDBA would be approximately zero, which eliminates the
second, third, and eighth right-hand side elements in Equation (8).
Likewise, there is no obvious reason to hypothesize that direct search cost.
(DSC) or positioning, loading and unloading costs (PLU) would be system-
atically related to distance. This eliminates the fifth and sixth right-
hand side terms. Finally, it seems reasonable to assert that risks would
be only weakly related to distance, which allows the seventh right hand
side element to be dropped.8 This reduces Equation (8) to:
8AFNR21 3CTCBA B(FRCBA ERCBA
(9) =D
DBA aBA DBA
The first right-hand side term is the rate of compensation per mile (or
per unit distance). This would normally be expected to be positive,
ceteris paribus. The second term is the per mile (or per unit distance)
additional costs associated with running full as opposed to empty (made
up primarily of added fuel costs).9 If the per mile freight rate were
larger on average than the costs of running full rather than empty,
then the incentive to return full would increase with distance (see
Figure 3a).
As the vehicle is already at B and must return to A, the cost of an
empty return (ERC) is a sunk cost. Therefore, regardless of distance,
this cost should not affect full versus empty backhaul decisions.
Rather, in the short-run, the decision to return full depends upon
whether the compensation (CTC) is at least as great as the tntil
variable cost (TVC) associated with securing, handling, and transporting
a load. TVC is made up of two components: terminal or distance-
unrelated costs and running or distance-related costs. Distance-related
costs are composed primarily of added fuel and labor costs from carrying
a load rather than traveling empty (FRC ERC). This component gives
total variable cost (TVC) its upward slope across distance (see Figure
3a). The zero distance TVC intercept (O1) is the terminal cost and is
made up of direct search cost (DSC), positioning, loading, and unloading
costs (PLU),and added risk cost (RISK) and road costs (RC) due to
handling the load. If the current total compensation (CTC) over
distance is as shown in Figure 3a, beyond distance OM the carrier will
seek a full return, while at a shorter distance (from A) the carrier
will elect to return empty.
If all carriers face the same costs and revenues, then at distances
larger (smaller) than OM all carriers will return full (empty). If,
as would seem to be more realistic, carriers face different costs, then
there would be differences in the critical (OM) distance. Within one
Figure 3a. Tariff rates and additional costs of securing and carrying
a load as implied by a positive full load distance
relationship
FRC + other costs
P CTC (Rate)
ERC + other
costs
Backhaul Distance
ITotal variable costs equal full running costs (FRC) minus empty
running costs (ERC) plus direct search costs (DSC) plus positioning,
loading and unloading costs (PLU) plus risk cost (RISK) plus road costs
(RC) of attaining a load running full rather than empty.
01 = DSC + PLU + RISK + RC.
Tariff
Rate,
Costs
mode, carrier-to-carrier variations in total variable running costs
(FRC ERC) would not likely be great. That is, the added fuel and labor
costs associated with carrying a load are probably similar from truck to
truck. Therefore, the slope or increase in total variable cost (TVC)
across distance is similar between trucks.
Current total compensation (CTC) also is likely to be similar among
truckers at any given distance (at least within equipment and regulatory
classes). On the other hand, terminal or distance-unrelated variable
costs probably vary significantly among carriers. Some trucks would
perform their own brokerage services or sleep in their truck sleepers
or be generally adept at positioning and loading in unfamiliar
surroundings. Others would require brokerage services or motel, or have
difficulties with positioning and loading.
If a survey of truckers were taken, it would reveal a frequency
distribution of total variable costs (TVC's) with variations in terminal
costs accounting for virtually all of the variation. In Figure 3b a
hypothetical frequency distribution has been assumed. In this situation
the proportion of operators opting for a full return would increase
with distance from home as a logistic function (or a logistic-like
function if the frequency distribution were unimodel and symmetric about
the mean-see Figure 3b). In a recent study of haulers of perishable
goods from Florida, evidence was found which suggested that the incidence
of the full backhauls is positively related to distance by a logistical
function (Kilmer, Ramirez and Stegelin, 1982, p. 16-23).10
Economic Regulation of Transportation
The model facilitates examination of the impacts of economic
regulation on transportation. Regulations may affect rate levels and
Figure 3b.
CTC,
TVC
I
Probability
of a
Backhaul
.5
1.0
The relationship between distance and the probability
of obtaining a loaded backhaul.
i
g
restrict rate variations, control entry, and determine permissible
routes and load types.
Direct Search Costs (DSC), Empty Mileage, and Regulations
Higher search costs (DSC) discourage full movements (see Equation 7).
Direct search cost (DSC) depends upon the volume and types of goods
available in a region to be hauled, the types of goods which vehicles
may legally and physically carry, and factors influencing the ability of
carriers and shippers to make themselves known to one another.
Regulations may lower direct search cost (DSC) by providing mechanisms,
such as published tariffs and routes, and licensed and bonded brokers
which reduce information costs. In a recent study of agricultural
truck brokers in Florida, (Beilock, Freeman, and Stegelin, 1982)11 there
was some evidence that direct search cost (DSC) for carriage of
agricultural goods may have been increased by the dropping of broker
bonding and licensing requirements. Without these standards, a broker's
value as an information source and logistics coordinator is eroded.
In another study (Beilock and Freeman, 1982)12 a similar result was
suggested with regard to household goods carriers in Florida. Since
the removal of uniform rate control and entry restrictions for intrastate
traffic on July 1, 1980, the majority of the already established
household goods carriers surveyed reported being able to raise rates,
despite the fact that rates in the State have generally been stable or
falling. These rate increases are thought to stem from the ability of
established household goods carriers to charge for a service charac-
teristic which was previously taken for granted reliability.
Regulations may affect the degree of vehicle specialization. If
carriers are restricted with regard to commodities which may be carried,
they will tend to operate fleets with equipment specialized for carrying
those goods (Miller, 1973, p. 9).13 This in turn, further restricts the
types of goods which an operator may carry. In general, the more
specialized a vehicle, given the amount of authority held, the higher
are direct search costs (DSC), and the more empty mileage which would be
expected (Curve D, Figure 3b). The converse should also be true. Since
holding an authority does not exclude one from carrying exempt cargoes;
within equipment classes, vehicles with authority would be expected to
have lower direct search cost (DSC) and less empty mileage than those
without. The findings of the 1976 Interstate Commerce Commission (ICC)
14
survey of trucks on interstate highways (ICC, 1977),14 generally support
these expectations. In Table 2a, it can be seen that for every category
of equipment, save for tank trucks, vehicles under ICC authority had the
lowest percent of empty miles. Moreover, as one moves from the most
flexible vehicle (refrigerated vans) to the least flexible (flats and
tank trucks), the percentage of empty vehicles tends to increase.
ICC authorities are licenses or permits to haul interstate cargo.
Those holding such authorities have an advantage (lower search costs -
DSC) in competing for interstate commerce which they do not possess with
respect to intrastate commerce. For operators without ICC authority,
the reverse would be the case, with a competitive advantage over or on
a roughly equal basis for intrastate hauls and at a disadvantage to ICC
carriers for interstate hauls. Therefore, within equipment types, it
would be expected that ICC carriers would be more apt to run empty when
traveling within a state than between states relative to those without
ICC authority (Curve D, Figure 3b). Evidence of this relationship may
be seen by examining the empty miles, recorded in the ICC study, for
Table 2a. Comparison of percent empty truck miles by type of equipment
and authority.
Lower Upper
No. of Limit Percent Limit
Equipment Authority Trucks (Percent) Empty (Percent)
Refrigerated ICC 1,008 9.1 11.0 13.0
Van
Exempt 586 10.9 13.7 16.5
Private 560 18.5 24.2 29.9
Van ICC 3,909 10.4 12.2 13.9
Exempt 443 23.2 27.4 31.6
Private 2,266 23.9 26.7 29.6
Flat or Lowboy ICC 1,322 12.8 16.6 20.4
Exempt 124 11.4 18.5 25.6
Private 847 18.8 23.2 27.6
Tank ICC 529 38.4 41.0 43.7
Exempt 85 12.1 20.1 28.1
Private 456 28.6 37.5 46.3
1
Ninety percent confidence interval
Source: ICC "Empty/Loaded Truck Miles on Interstate Highways
During 1976," April, 1977, pp. 8,9.
van and refrigerated vans of the authority groups by interstate and
intrastate roadways (see Table 2b). Refrigerated vans with ICC
Authority were almost six times more likely to be running empty if they
were on intrastate as opposed to interstate roads versus twice as likely
for refrigerated vans of exempt carriers and only half again more likely
for those of private carriers. Similarly, for unrefrigerated vans those
with ICC Authority were two and a half times more likely to be running
empty if on intrastate roads versus nine percent less likely for exempt
carriers and twenty-eight percent more likely for private carriers.
Rate Inflexibility and Regulations
It was argued that anticipated rate changes at a point to which one
will or may go influences the urgency of the journey. In particular,
if rates for loads secured at such a point are expected to rise (fall),
then there is an incentive to delay (expedite) the trip to that point so
as to be able to secure a load there with a higher remuneration (see
Equation 7). Therefore, there are different levels of urgency for
vehicles to go to a point as demands for freight rise and fall. This
translates into differing economically optimum amounts of empty (and
direct) returns as-conditions change.
This points up an interesting implication for regulation. As rate
regulation has traditionally implied price rigidity, regulations may lead
to greater or smaller amounts of empty mileage than would be economically
optimal. Without rate flexibility it becomes difficult for shippers to
signal carriers of unusual demand conditions. Indeed, carriers would
have to be made aware of changing direct search cost (DSC) due to changing
15
probabilities of securing loads at the going, regulated rate. It
seems doubtful that such information could be as readily communicated as
Table 2b.
Comparison of percent empty truck miles by type of equipment,
authority, and type of highway (Intrastate or Interstate).
Lower1 Upper
No. of Limit Percent Limit
Equipment Authority Trucks (Percent) Empty (Percent)
Refrigerated
Van
(Interstate)
Refrigerated
Van
(Intrastate)
Van
(Interstate)
Van
(Intrastate)
ICC
Exempt
Private
ICC
Exempt
Private
ICC
Exempt
Private
ICC
Exempt
Private
942
547
421
6.8
9.2
15.6
64 40.1
36 17.5
137
3,322
348
1,769
23.8
8.1
21.8
21.8
20.5
94 19.9
485
27.9
Ninety percent confidence interval
Source: ICC "Empty/Loaded Truck Miles on Interstate Highways
During 1976," April, 1977, pp. 8,9.
9.1
12.5
20.5
54.5
24.4
34.7
10.0
26.7
24.7
26.0
30.1
34.9
11.4
15.7
25.4
68.9
31.2
45.7
11.9
31.6
27.7
31.6
40.4
41.9
changing rate levels. Therefore, with regulated rates more vehicles than
would be economically optimal would be expected to be returning empty to
a region whose demand for transport is rising, and the reverse when
demands are falling. Thus, the same regulations can generate too much or
too little empty mileage in the same region for the same commodities as
demands peak and ebb.
SUMMARY
In this paper a theoretical framework has been developed to analyze
the determinants of decisions to move vehicles empty or to seek out and
carry a load. Backhauling of over-the-road motor vehicles was employed
as an example to facilitate the discussion. Whenever possible, compari-
sons were made between theoretical expectations and empirical evidence.
In general, the evidence corresponds to these expectations. It was argued
that minimizing empty mileage may not be economical or even energy effi-
cient. Decisions to operate empty or full were found to be dependent upon
several factors including rate levels and expected rate levels, search
costs, risk, and the relative costs of operating empty or full. Regula-
tions may alter search costs by commodity, route or other restrictions or
raise rates by granting monopoly rights, etc. Regulations may promote
specialization of operations and equipment which, in turn, reduce the
opportunities for full roundtrip hauls. Rate rigidity commonly associated
with regulations also may reduce the ability of shippers to signal car-
riers of swings in their demand for carriage, resulting in uneconomically
large amounts of empty movements to points where demands are rising and
the reverse when demands are falling.
FOOTNOTES
1. The underlying justification for assumptions 5 and 6 is that an oper-
ator's expectations regarding the costs and returns from future acti-
vities become less specific the more remotely into the future those
activities become. Therefore, the carrier will be assumed to have
fairly specific short term expectations regarding rate levels at B,
C, and A. He (she) expects, however, to go to D regardless of how
the return trip to A from B is accomplished. The time and costs
associated with the haul from A to D are anticipated to be the same
regardless of when the trip is taken. Finally, since the arrival at
D, regardless of routing and loads handled, will be fairly distant
in time, the rate of earnings after D has been reached is not assumed
to depend upon the timing of the arrival.
2. The nonlinear curves in Figure 2 are based on the assumptions that
the rate of interest is equal across scenarios, and that the net
returns from future trucking operations (after arriving at D) are
linear with respect to time and equal across the scenarios.
3. The approach described in this paragraph is conceptually equivalent
to that first employed by Fisher (I. Fisher, The Theory of Interest,
(MacMillan Press, New York), 1930), to compare alternative projects
or the same project with an adjustable duration.
4. As CCF describes the anticipated proportional change in the current
(to) rate CTC, CTC times CCF is equal to the anticipated future rate.
5. It might be well to note that any or all of the above cost and reve-
nues elements could be specified in more detail. For example, a
wealth of literature exists concerning queuing theory, risk, price
expectations formation, etc. However, the purpose of this paper is
to present the basic model and its implications.
6. This type of behavior is similar to that of a grain speculator who
attempts to withhold stocks from the market until prices are at their
highest. In so doing both the operator and the grain speculator serve
society by rationing the product until the need is the greatest.
7. D. Paxson, "Motor Carrier Deregulation and Opportunities for Reducing
Empty Truck Mileage," Association of American Railroads Staff Paper
79-2, 1979.
8. The argument can be made that the time necessary for DSC, PLU, and
RISK may be positively related to distance due to less familiarity
with more remote regions. If this were the case, there would be an
added per mile cost element associated with Equation 9.
9. The extra weight of a cargo normally reduces the gallons per mile.
For example, Boles has estimated the reduction in miles per gallon
associated with running full rather than empty to be .7 (5.2 MPG full,
4.5 MPG empty: Boles, P. Owner-Operator Costs of Hauling Fresh
Fruits and Vegetables in Refrigerated Trucks, Washington, D.C.: USDA
Report No. 82, 1980). Labor costs may also be incurred if the
vehicle must go somewhat slower or if the driver required additional
compensation for monitoring the load and the increased difficulty
in vehicle unloading.
10. R. Kilmer, H. Ramirez and F. Stegelin, Economic Impact of Empty
Backhauls in Florida Fresh Fruit and Vegetable Truck Transportation,
Florida Agricultural Experiment Station Bulletin No. (to be assigned), ,
Gainesville, (in press).
11. R. Beilock, J. Freeman and F. Stegelin, "Agricultural Truck Brokers
and Deregulation: The Case of Florida," (Gainesville, Unpublished
manuscript), 1982.
12. R. Beilock and J. Freeman, "An Analysis of the Effects of Florida
Motor Carrier Deregulation," (Gainesville, Unpublished manuscript),
1982.
13. E. Miller, "Effects of Regulation on Truck Utilization, "
Transportation Journal, (Fall 1972): 5-14.
14. U.S. Interstate Commerce Commission, Empty/Loaded Truck Miles on
Interstate Highways During 1976, ICC Bureau of Economics, Washington,
D.C., 1977.
15. The probability of obtaining a load may not change if the unusual
demand condition is not volume related. For example, suppose a
shipper customarily sends a certain quantity of a good to a receiver
each week. One week the receiver may be willing to pay a premium
to carriers in order to expedite their services.
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