The author describes the use of the "Lokset method" for routing and scheduling deliveries, with special emphasis on data requirement.Agribusiness,

Kriebel, Wesley R.

English

Research Papers in Economics

Management of Routing and
Scheduling Company Trucks
Presented by DR. WESLEY R, KRIEBEL
The author describes the use of the “Lokset
method” for routing and schedtding deliveries, with
special emphasis on data requirement.
DR. WESLEY R. ICRIEBEL, Extension Transportation Econo-
mist and Associate Professor of Agricultural Economics,
has been a member of The Pennsylvania State University
stafl since 19(33, He has conducted many private fleet cost
studies in the Midwest and East; and he has pub-
lished numerous articles on transportation economics
-ml fleet management, Current areas of study include
wuck routing and scheduling, urban food distribution
problems, and the inbound trafic problems associated
with grocery wholesaling. He is a member of the Ameri-
can Society of Traffic and Transportation, and past presi-
dent of the Altoona Chapter, Delta Nu Alpha.
Higher prices for new equipment and escalating wage
rates have resulted in rising distribution costs for firms
in the food industry. With this trend, managers have
been searching for better ways to evaluate their present
distribution methods and to guide them in making de-
tiisions about possible changes in route operations.
Routing and scheduling is a key task in food dis-
tribution. If this is not done appropriately, more trucks
and drivers will be required than necessary and thus
the cost of distribution will be excessive. I think that
many companies are more upset over a drop in miles
per gallon than the discovery of a few poorly-routed
trips. A few relatively minor misroutings by a dispatcher
can be much more expensive than a major decrease
in overall gas or diesel mileage.
Routing and scheduling is also a very difficult task
for most food distributors because of t~e magnitude
of the logistical task itself and because of the many
restrictions imposed on the distribution problem — e.g.,
some customers may be located in congested metro-
politan areas while others are located in rural areas so
that driving conditions in different parts of the service
area vary; some customers can be served only during
certain times of the day and/or with only certain types
of trucks; for many companies the fact that drivers are
unionized may impose special restrictions on the dis-
tribution problem,
During the past few years researchers have developed
a scientific method which can be used by management
to determine efficient multiple-customer routes, deter-
mine the appropriate sequence of customers on each
route, and allocate a specific delivery vehicle to each
route while considering all of the special restrictions
imposed on the distribution problem. This technique can
be used without the aid of a computer on relatively
small problems. However as the distribution task becomes
more complex, a computer will be essential for its applica-
tion.
Data Requirements
one technique, known as the “Lockset method,” has
been thoroughly clescribed elsewhere’ and will not be
detailed here. The data requirements for an applica-
tion of the technique, however, deserve special mention.
TO do a good job of routing, a substantial amount
of information is required and it must be as accurate
and detailed as possible. This is true regardless of
whether the routing task is accomplished manually or
by computer. The information required falls into two
general categories – fixed and variable.
Variable Data Requirements
This type of data consists of that information relating
to the delivery problem which may well change from
day-to-day or from routing-to-routing. It will include the
quantity of product or products to be delivered to each
customer, the time required to serve each customer,
and any other special services required by each CUS-
tomer. The special services required by a given customer
might inchlde:
1. Delivery must be made within a certain period of
the day,
2. Order must be delivered on a refrigerated truck, or
3, Only a certain size of truck can be used because
of the customer location.
Fixed Data Requirements
The fixed data required consists of data that does
JOURNAL OF FOOLILXWRIBUTION RESEARCH JULY 72/page 89not change in a relatively short period of time — informa- Indeed this is whv it is categorized as fixed data. It
tion on delivery vehicles and &ivers, list of customers,
and customer and plant location.
Delioq vehicles and Drivers.
The ‘details required on delivery vehicles include the
types and number of trucks available and their capacity,
The fleet may contain trailers, straight-trucks, and panels.
Some may be refrigerated while others are not. Some
may have mechanical lifters while others may not, The
capacity of some may be different than others.
One of the crucial decisions to be made by man-
agement concerns the units in which to express truck
capacity — pieces, cases, pounds, or cube, As far as
the use Qf the routing technique is concerned, any two
of the three can be used, The choice, however, will
be different for different applications and will depend
on the number of different types, sizes, and/or weight
of packages delivered. For example, if only milk is to
be delivered the appropriate unit of measurement could
be either weight, quarts, or cases. If, on the other
hand, fresh vegetables are to be delivered on the same
truck with milk, thp appropriate unit of measurement
might well be cube.
Another concern of management is to plan an appro-
priate work day for drivers – i.e., a full day’s work
for every deliveryman, In so doing any special restric-
tions imnosed bv union contracts will need to be con-
sidered: 1the number of stops a driver can make, the
total pounds or pieces a driver can deliver in one day,
a guaranteed minimum time for a daY’s work.
Consumer and Plant Location
It is obvious that to determine how and when cus-
tomers are to be served, their location relative to each
other and relative to the plant or distribution center
must be known. The easiest way to reflect this type
of information is to determine how far, either in terms
of driving distance or minutes driving time, each cus-
tomer is from all other customers and from the plant.
This is precisely the type of information needed by
the routing technique.
To appreciate the magnitude of this requirement,
assume a delivery problem with only eight customers.
The data required may be as indicated in Table 1.
Table I. Minutes Driving Time Between Indicated Customers
and Plant
Customer
Customer Plant 1234567
60
; 80 100
3 20 20
4 60 1% 20
5 % 80 100 30 50
30 50 10 30 20
; :: 90 40 20 40 50 20
8 70 50 100 70 60 80 30 50
In Table 1 it is seen that to travel from Customer 2 to
Customer 7 requires 40 minutes and to travel from the
plant to Customer 4 requires 50 minutes.
In this example only 36 measurements were required.
However for 20 customers 210 measurements would be
required, for 200 customers 20,100 measurements would
be required, and for 1,000 customers 500,500 measure-
ments would be required.’ Thus even for medium sized
routing problems, the task is not a simple one.
Fortunately, these data will need to be obtained only
once. That is, this basic set of data will be used for
the initial as well as all subsequent routing problems.
will only need to’ be modifie~ as new customers are
addecl or as old customers are dropped.
There are several sfiortcuts that can be used to ob-
tain these data, In the first place it may be known
before hand that certain customers are not to be
linked together on the same route. If this is the case,
the distance or driving time separating these customers
may be ignored altogether since these data are only
useful in determining the sequence of customers on
routes.
Rarely are exact distances or times necessary. Thus
a second shortcut would be to approximate these data
by (1) locating each customer and the plant by X-Y
coordinates or by longitude-latitude coordinates, and
(2) calculating “crow-fly” distances between customers
and between customers and t~e plant.”
Finally, there is available ~ computerized technique
for calculating the shortest distance between two points
through a network of straight-line segments. Thus if
well-defined road network with road intersections scat-
tered throughout and with customers located at inter-
sections is available, the distance data may be obtained
accurately and efficiently by computer.
Applications
The routing technique we have been discussing is
not a panacea — it will not eliminate all your distribution
problems, Nor will it necessarily eliminate the need for
a dispatcher. It will, however, make the dispatcher’s
job much easier, and help management to better control
costs. This it will do by serving as a tool with which
to consistently design the most efficient local delivery
system.
In addition to designing efficient routes for actual
deliveries, the routing technique can be used by man-
agement to examine ‘the imp>ct of various changes in
the delivery system. For example, what would be the
impact of adding different types of trucks to the fleet?
If the service time of a few key customers was changed,
could we design more efficient routes? Is it really worth
serving that one customer located 20 miles farther from
the warehouse than any other customer? Could we save
money by paying our drivers overtime to run the newly-
organized routes? What would be the impact of changing
the frequency of delivery? -.
We have used both manual and computer routing
techniques. Several applications inchlded ice cream, re-
tail milk delivery, bulk milk assembly and grocery prod-
ucts distribution. The results have been encouraging.
Routes discovered by the scientific routing method have
produced potential savings. In one grocery c~ain, for
example, deliveries for a specific day were accomplished
with one less truck and driver, plus 160 minutes less
driving time for the remainder of the fleet. The $70
savings obtained for that day were immediate and the
benefits required no additional capital outlay
Distance savings of 12 percent in milk assembly routes
~Tere found in work with a Pennsylvania dairy. This
relatively small dairy estimates a $3,000 annual savings
for bulk milk assembly.
In another dairy 10 home delivery routes were ex-
amined. The technique was used to reorganize the
entire delivery system into new routes to see what
savings, if any, co-uld be achieved in retail home delivery
of m~k. A d“elivery system was designed assuming that
the deliveries were made to each customer twice-a-week
as opposed to three-times-a-week. The advantages of
JULY 72/page 90 JOUFiNAL OF FOOD msmurwmoiv LZESEARCHthe reorganized system over the existing delivery system Similarly the advantages of the two-day-per-week de-
were achieved by: livery system over the reorganized delivery system were
1, eliminating the use of two trucks principally by achieved by:
utilizing trucks more efficiently 1. eliminating one more truck,
2. eliminating two drivers, and 2. eliminating the relief driver, and
3, reducing the number of miles driven to serve the 3. further reclucing the number of miles driven.
customers.
LITERATURE CITED
1 See M, C. Hallberg and G. T. Gentry. “Efficient Routing 3 That is, using the fact that the hypotenuse of a right
Systems for Retail Milk Delivery.” Dept. of Agr. Econ. triangle is equal to the square root of the square of
and Rural Sot., The Pennsylvania State University, A.E.
& R.S. #91, June 1970.
its base plus the square of its height.
4 We have been discussing the routing techniques applica-
2 The number of measurements required is determined by bility to delivery systems only. Nevertheless it can be
the formula N(N+l)/2 where N = the number of cus-
tomers.
applied to pickups as well, It will not design routes
involving both pick-ups and delivery.
JOURNAL OF FOOJIIXSTRIBLJTION RESEAtKX JULY 72/page Q1

Efficient Routing 3 That is, using the fact that the hypotenuse of a right Systems for Retail Milk Delivery.” Dept. of Agr. Econ. triangle is equal to the square root of the square of and Rural Sot., The Pennsylvania State University,

The number of measurements required is determined by bility to delivery systems only. Nevertheless it can be the formula N(N+l)/2 where N = the number of customers. applied to pickups as well, It will not design routes involving both pick-ups and delivery.

MANAGEMENT OF ROUTING AND SCHEDULING COMPANY TRUCKS

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