A NOTE OF RESIDENTIAL HEATING OIL INVENTORY POLICIES
-. April 1975
Walter P. Fischer*
Energy Laboratory
in association with
Sloan School of Management
Working Paper No. MIT-EL-76-022WP
* M.I.T. Visiting Scientist, IBM Scientific Center Staff, on leave from
the University of Munich.
This work was conducted in part under an M.I.T./IBM Joint Study in
association with the M.I.T. Energy Laboratory, the M.I.T. Sloan School
of Management's Center for Information Systems Research, and the NEEMIS
Project. NEEMIS is supported by the New England Regional Commission.
Trhequestion whether present inventory olicies of residential heating
.)il
consumers are stable or likely to change as a result of higher oil
prices or a shortage situation is investigated on the basis of a model
which xplains heating energy cost as a function of a consumer's tank
capacity, the size o oil deliveries, his choice of a safety level of
,)Oilin his tank, and on the basis of data for Massachusetts. For the
,onst comlmon situation
(:onslmoes
of a
1000 to 2000 gallons
consumer who owns
per hating
a 270 gallon
eason,
tank and
the result is:
UInlessthe consumer expect substantial fluctuations in the price of
o(ilto occur during each year throughout the depreciation period of
the tank, there is little incentive to change the present inventory
policy: One 270 gallon tank and the avoidance of policies which reduce
the delivery size through partial fills or a large safety level, are
'ta1,
le policies.
Table of Contents
.
2.
I{.
T t rod
Oil
Liction...................
a
istribution Cost..........
Cost of Investment
in Tank and
...
Oil.
5 .
Resu its ........................
Conclusion
.....................
Appendix:
.9
O
a.
*
.
.
a a aa
aa
. ..
* .a .a ..
a
.
-a a
aa
a a *a--
*
a
l
*
-
lmo
*
@ o-l
.
.
0
.........
Data Used to Compute Figure
1
.4
14
-l
..... a 28
l........
1...
.....
i
.... . 19
.
.
.
..... a 17
a. aa
*.l
*
.
.
.a...........
a a a a aa
The Cost of Oil ................
.
a
......
...............30
A NOTE ON RESIDENTIAL
1.
HEATING OIL
INVENTORY POLICIES
Introduiction
T'rhe
question whther present inventory policies of rsidential
hating
oilconsumers are stable or likely to change as a result of higher oil
prices or a shortage situation
is of importance to:
(1) The policy maker, since additional
demand to build up inven-
tories will worsen an already tight supply situation.
(2)
The consumer who would like
to keep the cost
of home heating
low'.
(3) The oil distributor
who faces
changes in distribution
as a resultof changes in inventory
costs
policies.
'his papsr models heating energy costs as a function of consumer deci·;ions on:
(1)
The tank capacity.
(2) The delivery size (the amount of
oil put into the tankwhe-
never the delivery truck comes around).
(3)
The ;afoty lcevel(the
minimum amount
wi;hs o k'p)in his tnk
for safety
of oil
reasons)
the consumer
INTRODUCTION
'he cost items considered are:
(1) Oil delivery costs from the oil supplier's bulk storage facility to
the
consumer.
These costs depend on
the size of
the delivery to each consumer.
(2)
cost of investment
in the tank and the average
kept in the tank.
These costs dependon all
amount
of oil
three varia-
bles: tank capacity, delivery size and safety level).
(3) cost of oil.
These costsdependon the tank capacity in
case the oil price changes during
Tf the decision criterion
of our
tank,
studiy is:
xpects
year.
is the sum of these costs,
Unless a consumer,
substantial
the
fluctuations
the main result
who owns the usual
in the
270 gallon
price of oil
to occur
,luring each year throughout the depreciation period of the tank, there
is little
incentive to change the present inventory policy.
ne 270
gallon tank, and the avoidance of policies
r;izo
through partial
Data for
this
who serves
'oston.
study
fills
which reduce the delivery
or a large safety level,
arestable poli-
was provided by a large heating oil
astern Massachusetts and
distributor
the Better Home Heating Council,
T lI T P;1 DI[CT ION
'3
ehction 2 investiates
Size of
the dependency
delivtries to
-;toring oil
in a
price fluctuations
home.
of
consumers. Section
Section 4
during the year.
various inventory situations.
oil distribution
3 deals
describes
a
cost on the
with the
way to
Section 5. presents
ccst of
consider
oil
results for
4.
OIL. DISTRIBUTION COST
- 2.
Oil Distribution
Tr this
:;j7. of
section
il
Cost
we model oil distribution
deliveries
to the residential
resnlt. of this effort.
-?sin delivery
size.
cost as a function
consumer. Figure
of the
1 is the
It showsthat this cost is sensitive to changFor example: an increase
per delivery reduces the
from 200 to 400 gallons
delivery cost per gallon by .
cent or 20%.
A decrease of the delivery size from 200 to 100 gallons means a deliv-
,-ry
cost increase of 1 cent per gallon or 40%.
rom Figure
1 alone an important
of residential
size is
inventory
the 270 gallon
lons. The oil
conclusion
situations:
follows
At present the
tank and a delivery
either through partial
most commontank
size of around 200 gal-
distributor has reason to strongly
of this delivery size
for the evaluation
resist a reduction
fills
of a tank or the
increase of safety levels.
Figur
1 was derived as follows:
oil distribution
trucks.
The bulk of truck
if distribution
operates
cost are mainly the cost to operate the delivery
5 trucks.
cost
is time proportionalin the sense that
times can be reduced by 20%and the
oil distributor
one truckcan be saved. A smaller part of the truck
cost is proportional to the mileage driven. Both distribution time and
mileage
driven to serve a given
number of customers
with given con-
sumptiorns per year depend on the delivery size to the individual customer.
Fig.urc 1:
Oil Distribution
Cost (in Cent per Gallon)
3.28
Cent
Per
Gallon
2.28
1.7
I
7
200
-
.I i
.
400
600
800
Delivery
Size
[Gal. ]
,6 t,~~~~~~~~
OILISTPTBUTTIO
COST
i4e use (ldata ol:
Dr =
Quantity of oil
distributed
(in gallons per truck per
year) .
DR
Delivery
=
size average
(in gallons
per consumer per
delivery)
.ost. associated with th( operation of one truck (in $ per truck per
yar).
These costs are divided into two segments:
TC
Costs that are
=
time proportional in the sense defined
above (wages and related cost,
50% of
truck repairs,
depreciation, insurance, registration).
MC
Truck cost that are proportional
=
to te
mileage driven
(50% of truck repairs, tires, gas and oil).
T'he time- and mileage proportional distribution
ci.
ated with the delivery size DR are:
TC
(2.
+
cost per gallon asso-
MC
1)
DIS
rn ordeor to write
r'lice
the
not at ion:
(2.1) as a function
of the
delivery
size we intro-
O)IT, DSTRIBUTION
!3
=
7
COST
Variable
delivery size
(in gallons
per customer and
delivery).
T (D)
=
to deliver one
Time spent
truckload
of
deliveries
of
size D (in minutes per truckload).
M(D)=
Mileage driven
to deliver one truckload
of deliveries
of size D (in miles per truckload).
Phe time- and
tunction
mileage proportional
of a variable
delivery
T (D)
(2.2)
cost per
gallon
as a
size D is:
M ()
+
TC
distribution
T (DR)
MC
M (DR)
DIS
The remaining
task is to formulate
the
functions
dlescribe the
dependence of the time spent and the mileage driven to
T(D) and
(D), which
distribute one truckload of oil on the delivery size.
Only part
of the time of a
truck tour
is dependenton deliverysizes.
'imes which are independent of the delivery size are:
(a)
Pumping
times at the oil supplier.
(h) Transportation times from the supply-point to the distribut ion a rea.
(c)
Pumping times at customer locations.
OIL DISTRIBUTION COST
'rimes which (lo depend on the delivery
size are:
(a) Se.t-up times at customer locations.
The st-up
time pr customer is the time between getting the truck off
and back onlto the road minus the actual
pumping time.
percustomer is independent of the delivery
time per
truck tour
therefore, on
size. The total set-up
the number
depends on
the delivery size.
The set-up time
of stops
The set-up
per tour
time per truck
and,
tour is
computed from.
(2.3)
Truck Capacity
Set-up time per consumer
*Delivery Size
(b)
Driving times (and distances) between customer locations.
The consumption
of each
consumer does not
a given clientele.
a result
of a
the number of truck tours necessary
change in delivery size, nor does
to serve
change as
We can
is served through one truck tour.
think of a geographical
area
which
The size of this area
depends on
the consumption per customer and time unit,
on how close the consumers
live together
insofar as he
and on the
dealer's
exactly the day of reaching the
ep1ivory diate. The
ize.
policy
decides
how
safety level .should coincide with the
size of the area
does not depend on
the delivery
01T, .DISTRIB[JTION
COST
9
which changes with
The quantity
the delivery size is the
number of
:;tops pr truck tour, which is roughly:
Truck Capacity
(2.14)
Number of Stops
=
Delivery Size
the distance travelled per truck tour as a function of the number of customers visited, a simple model of the distriIn order to express
customers is
hution area is constructed: A large number of residential
assumed to be evenly distributed
random
one of Figure 2. We select
tions within
sample
on the
,i specific
within a square area
samples
of
5,
the area and compute an efficient
assumption
10,
similar to the
loca-
20 customer
round-trip
for each
enters and leaves the area at
that the truck
location.
Figure 3 gives the
average distance
travelled
per
truck tour
as a
function of the numberof stops. The distance unit is the side length
of the square shaped distribution area of figure 2.
The curve of Figure
3 can be approximated
q7
(2.5)
a
=
1,0236.
where 'a' denotes
by:
.
b'
the number of distance units travelled
notes the nmber of stops per tour.
and 'b' de-
Figure
2:
RouAndTrip Computed
Del ivery
di
for
Simplified
Area
s tnce
tin i t
a rea
entrance
Figture
3:
ftlumber of
Distance
units travelled per
Truck Tour
no. of
distance
tin i ts
trave
1 e I1
A
k
i
i
LO
i
hzo
number of stops per tour
OIL DIS;TiBrITI'ON
How will this
s tops
COST
11
function be used?
per tour and
ur distributor
a 2 mile distance
hy an increase of the number of stops
Vellfd per
delivery
trip
averages 15 customer
etween.stops.
We estimate
from 15 to 25 the distance
would increase
that
tra-
from 2 x 15 = 30 miles per
t:Otirto:
30
-15
38 (miles per tour)
30...
-3.8
And the average distance between two customers would decrease to:
38
_--
1.5
(miles)
25
:;ome
ad(lditionial notation is used to write expressions for
,;pent
nd the mileage driven to distribute
tuc+tion of the delivery
?T =
the time
one truck load of oil as a
size:
Time per tour which is invariant
(time to
drive from the
of the.number of stops
supply point to
the delivery
area plus pumping times).
PM =
Mileaygepr
tour which is
stops (distance
the distribution
PTR =
invariant
of the
number of
from the supply point to the edge of
area).
Set-u[) time at each stop.
12
OTI, rISTRIBUTION
miles between
=
MSR
(in miles
two stops for
the fixed delivery
COST
size DR
per stop).
Drivinq speed between stops (in miles per minute)
Truck capacity (i
C'AP =
gallons per truck).
-; ince
CAP
D)
is the number of stops per truck
tour, the mileage driven within
distribution
equation 2.5):
area would be (sing
CAP
Ca
CAP
D
DR
CAP
(2.6) MSR---.
the
CAP
= MSR--- --
-
D:R
DR
Th, time total
variable times
for the whole truck
tour is equal to
'(set-up tine and travel time within
area):
CAP
(2.7)
T(D)
= FT + PTR --D
CAP
+
1
SR ..
DR
SR
fix.d times and
the distribution
OIL DSTRIBUTION
13
COST
rhe mileaqe total. within the area is equal to:
CAP
(2.8)
M(D)
=
FM
MSR
-D
rho
xpresions
2.7 and 2 .
1) R
are used in euation
2.2.
COST OF INVESTMENT IN TANK AND OIL
I14
3.
Cost
of Investment
The costs
in Tank and
of the investment
il
in tank and oil are:
of the tank.
a.
Depreciation
1.
Interest
on the money tied in the tank investment.
c.
Interest
on the money tied in
the average amount of oil
stored in the tank.
rhe depreciation
of the tank is calculated
from:
Tank Price
(3.1) ----_
Dpreciation Period
on the money tied
The interest
in the tank
investment
is calculated
from:
(3.2)
x
Price of Tank
x
Interest.
ate
Sased on a constant consumption rate the interest
on the money tied in
the stored oil is:
(3.3)
Interest
rate x Price of
il x
afetyLevel +
Delivery Size
2
15
COST OF INVESTMENT IN TANK AND)OIL
The costs (3.1, 3.2 and 3.3) - in $
er
eating season - depend on all
three decision variables: tank capacity, dlivery
01. In addition
different
a given tank capacity can consist
tank sizes
lives a few cost
(with different
examples.
cost
size and safety levof combinations of
implications). Figure 4
Figure 4:
Cost of Investment into Tank Capacity
(in $ per season)
Tank si ze
(In
allons)
rate (in
Interest
0
3
7.5
o~?per
270
12.2
15.1
19.2
26. 2.
1000
23.3
28.6
76.5
49.6
Cost of Investment into
Heating
season)
15
Oil1 (in
per
Season)
a
I
Interest rate (in
De ivery
;'
per season)
Si 7.e
0
3
7.5
15
I -
100n
0
1.0
2.1;
1; . 8
ii
200
1.9
4..8
!v
I
0 O
in0
0
600
0
0
800
3.8
5.8
9.6
9.6
9.6
19.2
1 .
19.2
28. 8
38 . t
.it, r;
Price of tank, (2.,70gallons)
"
"
nepreciat
Oil1 price
0
(n1000gallons)
ion period
$ 185
$ 350
15 years
$
. I;
The safety level is kept at 30° of the del ivery size.
TrHECOST OF OIL
4.
17
The Cost of Oil
Tf the
oil price changes during a year,
heating season) depends on the quantities
different
prices.
is the fraction
lower price.
(a)
the cost
of oil that are
The largoer the available
of the consumption
pr
of oil (in
$ per
stored at
tank capacity, the larger
season
that can
e bought
at a
This aspect is considered by assuming that:
The oil price does not include
the portion of oil distribu-
tion cost which depends on the delivery size.
(b)
It is the first delivery
of
boughtat a lower price.
All following deliveries
purchased at a higher price.
TPable 5 gives
a few cost
examples.
the heating season
which can be
have to be
Figujre
5:
Cost
Price of oil
at
f i rst
del ivery
of
Oil
(In
Dollars
Del ivery size at
gal lons)
400
200
per
f i rst
ieating
del ivery
(in
800
(in V/gallon)
. Il
00
4 00
lo00
.38
39(3
392
38 1
.36
392
384l
368
wihe re:
consumpt ion 1000 gallons per heating season
price of oil for
suhsequent del iveries
$ . I
Season)
19
' ESULT S
:u1. i:t;
5
This section reports on costs (in
$ per heating season) that are vari-
able for various inventory situations. According to the assumed situation lI cost criteria
are distinguished:
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.·.
1.
A large tank size
is
already
available.
The price of oil is
stable. Thecost criterion is the sum of oil distribution
cost and the cost of investment into stored oil.
2.
The tank
capacity must still be
stable.
The cost criterion is the sum of oil distribution
bought. The price of oil is
cost and the cost of investment into oil and into tank ca-
pacity.
3.
A large tank size is already available.
the first delivery
The price
during the heating season
cf oil
for
is lower than
for later deliveries. The cost criterion is the sumof oil
distribution cost, the cost of investment into oil and the
cost of oil.
4.
The tank capacity
the first delivery
must still
be bought. The price of oil for
during the heating season
for later deliveries.
The cost criterion
distribution cost, the cost of
tank capacity,
is lower than
is the sum of oil
investment into oil and into
and the cost of oil.
20
.RESULTS
Tablps
1 and 2 assume a consumption of 100.0 gallons
-on.
per heating
ol..
In Table
1 an
existing,
large tank capacity
t,r¢st. rate the savings in distribution
erysize. At higher interest
At a low in-
costs call for a large deliv-
rates the cost of investment
to a reduction of
:;toredoil has more weight and leads
lelivery
is assumed.
sea-
into the
the
rofitable
size.
In Table 2 it is assumed that
the tank capacity
has to be purchased in form of one
of tank capacity
does not exist,but
or more.270 gallon tanks.
The cost
becomes the prominent cost item. Only 1 tank should
he bought.
Tables 3 and 4 assume a consumption of 2000 gallons per heating season
and in all other respects the
situation
of
Tables
1 and
2.
The larger
consumption causes no major change of results.
Tables 5 and
6 consider
.70 gallon tanks can
the cost of
the effect
and the
he
7 assumes that the first oil
boughlt t
assumed
that
so far, but that
price of oil have
increased
by
There is no major change of the results.
rTabhles
7 to 9 assume a consumption
Tabl
It is
be bought at the price assumed
oil distribution
50% in later years.
of inflation.
a price
which is
of 1000 gallons
per season.
delivery of the heating season can
2 cent
below the
price per
gallon
1 ) CI'Tl,'RIUlJM 1:
GALLONSPER SEASON
1000
NOUUMZIP0NON
DELIVERY
-
INTEREST RATE
0.0
.0
7.5
100
31.90
150
2g.00
32. 6
27 . it
31. 30
29 . 60
200
22.80
24 .72
27. 60
X3 2.
0
300
19 .10
0
17.50
X26,.60
33.
;00
22.28
500
16,30
600
1
SIZE
800
1000
2)
CRITERIUM
3)
TANKS
DELIVERY
SIZE
2
270
2
270
3
3
270
270
4
270
5
270
CRITERIUM
21.
36.70
8
23.20
28.30
2 .80
't0.30
33.50
52.70
It1I.
37.60
20
61. 60
GALLONS PER SEASON
NO SIZE
270
270
270
14.30
, 13 . 60
33.20
27.10
X 21.10
21.16
10
.
3 6.70
2:
CONSUMPTION ON'1000
1
1
1
21.311
15
INTEREST RATE
0.o
.
53.57
42.55
4 8 .87
5.13
/39.83
3
I;i
3
11]4t.07
X lq6.87
65.14
52.50
2.17
5.
5 3.30
2.i40"
6 3.63
7 5.27
1000
7,5
8.33
150
k,,'
3.0
I47.97
100
.200
300
400
500
600
800
,
'1.23
It,
51.56
65. 64
66.Li2
86.11
66.48
87. 61
82.41
98.74
110.58
133.95
15.0
62.91
59.41
'
5
. 61
86.22
89.12
118.92
122.82
157.53
192.64
1
CONSUMPTION ON 2000 GALLONS PER SEASON
TANKS
NO SIZE
INTEREST RATE
DELIVERY
0.0
1STZ
-
3.0
6J4.7 6
150
63.80
52.00
53. 4114
200
I 5. 60
47.52
38.80
300
35.00
on00
32.60
30.80
500
600
800
1000
28. 60
/2
7 . 20
II
7.5
15.0
66, 20
55.60
50 .O
59.20
4t1.68
46.00
38 .84
37.40
44. 60
/, 4t). 60
36.56
/ 36.28
15 .20
147.80
36.80
51.20
68. 60
55.20
X 53.20
54 .20
56.60
59. 60
67. 00
75.20
4)
CIITERTUM
2:
CONS'UMPTIONON 2000 GALLONS PER SEASON
TANKS
NO SIZE
DELIVERY
SIZE
1
270
1
270
150
1
270
200
/ 57.93
270
300
2
100
INTEREST RATE
0.()
3.0
2 27000
o00
7)6.13
611t.33
9t.n.
6.55
74.87
69.67
63..47
71.90
l .5lt
r)59.67
69.06
270
3
270
600
4
270
n0o0
5
270
8.87
5) CRITERIUM
15.0
A5.117
,62.6 3
3
1000
7.5
79.87
69. 60
3.
I
85.11
Y 81.41I
105. 62
106.
62
2.72
102.itl
135.22
G7.O
01 ,80
103.01
138.22
77.93
96.71
124.88
171.83
112.34
147.55
206.24L
2:
CONSUMPTION 1000 GALLONS PER SEASON
50 PER CENT INCREASE IN TRUCK COST AND OIL PRICE
AS
ABOVE
0.0
3.0
7.5
100
150
60.10
51.33
6q. 0
56.27
70.72
63.67
200
l46.53
52.19
60. 67
74 .1
300
400
53.77
50.92
63.64
62.23
78.44
79.19
103.12
107.47
102.51
14'1.92
127.33
183.88
152.75
223.L44L
500
600
61.45
60.10
800
70.78
1000
02.07
76.98
77.06
93.40
110.34
100.26
15.0
81.26
76.01
139.07
. 6) CRITERIUM 2:
CONSUMPTION 2000 GALLONS PER SEASON
50 PER CENT INCREASE IN TRUCK COST OIL PRICE
7,5
15.0
100
108.03
0.0
112.25
110.57
129.11
150
90.33
95.27
102.67
115.01
AS
200
80.73
8 6.39
911.87
ABOVE
300
02.87
92.74
107.541
132.22
400
77.17
88.48
105.44
133.72
500
600
85i.90
8 3.20
101.43
100.16
124.71
125.61
163.52
168.02
114.85
130.7It
148.78
173.15
205.33
243.84
oo0
1000
92.23
102. 7
3.0
109.01
,'f
2
2.3
- T. T S
and that a large tank capacity is
charged for the remaining deliveries
The table suggests that the wholeconsumptionof
,ilr:aly available.
the lower price unless the as-
t-he hialting sfason should be stored at
;umed interest
rate is high.
,elivhry
be 400 gallons
hould
,al.lons
(See T'abl
rables
hotight
and
rate of 154 the first
At a interest
deliveries should
and subsequent
1)
9 cove(r the case
in form of 270 gallon
must still
where the tank capacity
A 2 cent
tanks.
(Tahle
8) and
he
even a 4
delivery are insufficant
cfn (Table 9) price decrease for the first
to invest into more than 1 270 gallon tank.
incentives
rables 10 to 12 show results equivalent
to Table
7 to 9 for a consump-
tionof 2000 gallon per heating season.
There is no
the results reported for the 1000 gallon
user.
'.ahbls 13 an(d 14
assume a constant
,unnt into 1
gallon
iestm:elltinto
t he 2090
be 200
100
1 270
allon
tank
oil price
(row 1
gallon tank
(row
user the investment
and
ajor change from
compare the invest-
to 3 of the table)
with the in-
4). For both the 1000
into
the 270 gallon
gallon
tank
and
is ad-
vanteqeo us.
:'ables 15 and
16
compare
the investment
case that the oil priceof the first
:lallon.
hl .
into both
ank
sizes for the
delivery is reduced
by 4 cent per
Only for the 2000 gallon user the largetank becomes profita-
7) CRITERIUMA 3:
CONSUMPTION 10 00 GALLONS PER SEASON
OIL PRICE AT FIRST DELIVERY .38 DOLLARS PER GALLON
INTEREST RATE
DELIVERY
SIZE
100
150
0.0
't29.90
23.00
3.0
3 .0
5
7.
1
. 8 6
1 24 . 3
420.70
5 . 0
'132 . 29
1311. 68
2 6. 57
1123.55
' 28.30
'130.15
200
300
1413.410
41
00
409 .50
500
'106.30
'413 . 2 6
410.98
417 15
600
1403.140
408.9 6
'11 6.09
800
1000
398.30
X(393.60
t2 6. 62
0 5 .5 0
)(X115. 35
131 .10
139. 20
4
t
. 0
3
st
G. 2 4
X402 .72
1120 .11 9
14118. 61
41 6.40
1 26G. 60
25.7
X
4
't25.75
8) CRITERIUM4:
CONSUMPTION
1000
GALLONS PER SEASON
OIL PRICE AT FIRST DELIVERY .38 DOLLARS PER GALLON
TANK
NO SIZE
1
270
1
270
1 '270
2
270
2
270
3
270
3
270
DELIIVERY
SI27E
100
150
200
300
INTEREST
O..
.00
11;2.23
435.33
X'431.13.
438.07
400
500
134 .17
44 3.30
600
t01o . 110
4
270
800
5
270
1000
1447.63
4155.27
RATE
3.0
3.
t15
.
7.5
9 6
439.54
451 .5 6
Li1 5 . 84
15
. 0
1460 . 88
415 6.35
459.03
x 45It.51
1 79.02
'78 .15
;5 6.30
474 . 9 6
501 .37
1511.29
4173. 90
5 05
It 65.93
1192.44
512.754
535. 94
' 35 . 1
L1
. Li 5
44L1 6
6.4
'1;1 3 .11F8
478.2
6
X4 2. 82
457.15
5 12 .7 5
.
2 Li
570.24
9) CRITERIUM 4:
CONSUMPTION 1000 GALLONS PER SEASON
OIL PRICE AT FIRST DELIVERY .36 DOLLARS PER GALLON
0.
100
150
200
AS
300
ABOVE
'o00
'44O. 23
I32.33
i 27.13
132 . 07
X '1 6.17
3.,0
LL13.9
7 . 5
6
'43 6. 53
'. 1131.79
It 0 . 4 1
' 35 . 0
4 Li 2
. 55
.66
.8
.82
77
X Li38 I..77
1 52
.93
.96
500
'433.30
It' 6.18
.600
28.410
'4'42. 12
4t 8 . 9 6
l16'1 * 66
;t 61il .11 7
'57.78
It 91
800
1000
nnn
1 nn
1 31. 63
'435.27
Itt9. .62
75
67
.55
15.0
-
'1 5 8 . 8 6
'453.30
X 1 50. 12
4 72 .80
I1 69.77
119 3 . 7 7
'193.77
'192.38
51
.11 0
5147.8 4
10) CRITRTUM 3:
OO0UR2Y5 70-2o000 GALLON,' i'?:I? SAS.'ON
.38 DOLLARS PER GALLON
OIL PRICE AT FIRST DELIVERY
INTEREST RATE
DELI VERY
0.0
SIZE
100
150
3.0
7.
850.43
852 . 59
200
8i 9.00
841 .60
813 .51
835.66
84 G,38
300
832.80
827,00 0
822.60
500
600
800
818, 80
812. 60
X80o7.20
·1000
.830.80
8 2 7 . 34
824.47
820.13
,X816.30
1
.0
-
862.7
4~00
6
5
8 61 . 80
86
8 66. 59
85 6.17
. 9
851.15
847.09
839,95
8.3 6.50
8415.21
84 3 . 75
842. 69
834.45
832.56
829.50
'/827.30
X 841
.95
843 .00
11 ) CRITERIUM4:
CObUMPTON 2000 GALLONSPER SEASON
OIL PRICE AT FIRST DELIVERY .38 DOLLARS PER GALLON
TANK
NO SIZE
DELIVERY
SIZE
1
270
1
270
100
150
1
270
200
2
270
300
2
270
1100
3
270
500
3
270
600
4
5
270
270
INTEREST RATE
0.0
Z
874. 13
87 7 .87
8 61.33
8 6!5. 54
853.93
857.147
A' 851
. 67
859. 60
855.80
800
1000
3.0
X 85 3. 62
6!5 . 88
1.02
87 2.66
8 6:
8 6 9.80
7.5
15 . 0
883 . 6
892 . 80
871.86
X 8 65.
878.
65
t 9
882. 38
X 877.36
899. 51
897. 62
875.05
892.26
922 . 37
890.38
92 1 . 31
Oi 6.79
974. 04l
8 61.93
a88 0. 5 6
906.58
8 68.87
89 1 . 84
923. 65
.12) CRITERIUM 4:
CONSUMPTION 2000 GALLONS PER SEASON
OIL PRICE AT FIRST DELIVERY .36 DOLLARS PER GALLON
00
.
100
AS
ABOVE
15 o
872.13
858.33
200
300
849.93
851 . 7
'100
'500
*I
6000
800
1000
/
3.0
875.86
8 62 . 54
85z~.
fi1
84 3. 67
859.85
X11852.
98
849. 60
8 62. 60
843.80
857.71
84 5 .93
86
848 . 87
871. 60
t 1
7 .5
15 . 0
881.4 6
8 68.84
890.78
X. 8 f1 . G62
87 2 . I 3
866. 95
882.11
878.
1 6
890. 20
903 05
81379.35
.
8373.31
9 3 .1 0
8 n 9.
3
912.07
908.88
930.02
952.84
9 1 2 .. 03
0 2.
7
93
952 . Bt
13) CRIITRIUM 2:
CONSUMPTION 1000
GALLONS PLERSEASON
TANK
DELIVERY
NO SIZE
SIZE
INTEREST RATE
0.0
!
3.0
50.86
7.5
63
1000
300O
I 2 .73
1
1
1
1000
1000
270
500
800
39. 63
3.17.63
49. 68
6.7
5
69.
200
35.13
39.83
46.87
3,0
70.26
7 . 26
7 5
82.
6
65 .98
81.06
8 6
84 . 2 6
0
. 56
83.38
06
i
.
15.0
-
89.88
6
102.28
9 6
58.61
14 ) CRITERIUM 2:
CONSUMPTION 2000 GALLONS PER SEASON
0,0
300
500
AS
ABOTVE
800
62.13
55.93
51.93
64.
1 5 .0
102.78
106.18
116.58
15) CRITERIUM 4:
CONSUMPETIRON1000
GALLONS PER SEASON
OIL PRICE AT FIRST DELIVERY
_'
AS
ABOVE
30
3 00
500
.36 DOLLARS PER GALLON
0.0
r3-0,
1430. 73
4f19. 63
8000 405.63
16)
_
3.0
438.78
4t29.
t4
417 .77
7 .-5_
.
_
_
_
15,0
450.84;
4t 69 . 97
f41; 331
I 6
435. 0l
4 63.15
-
. 73
CRITERIUM 4:
CONSUMPTIOTN 2000 GALLONS PER SEASON
OIL PRICE AT FIRST DELIVERY .36 DOLLARS PER GALLON
AS
ABOVE
00
.
300
500
850.13
835.93
800
819
93
3.0
858.22
845
.
8 6
833.23
7.5
870. 35
861.81
850.41
15.0
892.27
884.53
875.97
17 ) CRITERIUM 4:
CONSUMPTION 1000 GALLONS PER SEASON
OIL PRICE AT FIRST DELIVERY .36 DOLLARS PER GALLON
TAN/,
1/270+
1/1000
1/270
0.0
3.0
300
500
Iti 3.07
f 53.89
7.5
47011
It7n0
I
4 31.97
It t
4 62.58
4l 90.94
1000
4~09. 27
t 25
450.93
442.82
4192.59
454.51
DELIV.
200
431.13
.. 5 5
93
435.81
15.0
49
1 6.18
. 1
18) CRITERIUM
4:
CONSUMFPTION2000 GALLONS PER SEASON
OIL PRICE AT FIRST DELIVERY .36 DOLLARS PER GALLON
TANKS
1/270+
1/1000
.j
, "
"
0.0
DELIV.
300
5 00n
1)(00
862.It7
&
Ail
. 27
81322. /
.
3.0
7.5
15.0
87:.33
889 . 62
918.48
8 (0.
7
I1i). 31
881.0 l
8 63.13
910.71;
13 59
ESQTT.TS
'abh1
-27
17 and 18
ind. compares the
assume a consumer
who already owns
investment alternatives
1 270 gallon tank
of an additional
270 gallon
)r 1000 gallon tank. Only for the 2000 gallon user the investment into
l 100) g(allon ta[nkis profitable.
CONCLUSION
28
6.
Conclusion
Although the cost
reductions which could result
sizes are substantial
for the oil
from larger delivery
distributor,
even the complete
transfer of the
reductions to the consumer does not
cient incentive
for the
purchase of additional
provide a suffi-
tank capacity.
For
e xa mp.(e:
An increase in the delivery size from 200 to 400 gallons reduces delivery
cost
;sum?d per
by
season
creas(d delivery
tank
and
'Tables
of the
1
ant
size
1).
In
the consumer has
A contlsum.r
to invest into
this in-
an additional
2)
(stuch as a low
interest
the realization of oil
tronq incentive
jallon tnk.
order to realize
cost of $ 17 per season (compare
variables that could increase
tion) only
needs a
(compare Figure
or by $ 5 if 1000 gallons are con-
a larqer oil inventory at a
tank capacity
<-intly
.5 cent per gallon
the attractiveness
rate, a large
of
a larger
annual consump-
price differences can be
to buy tank capacity in addition
a suffi-
to one 270
For xamnple:
of
1000
gallons
rice reduction
per
season
who owns
of 10% (from 40 to 36 cant
a 270
gallon tank
for the first
de-
livery throughout the depreciation period for thp tank) to profit from
additional1 tank capacity.
CO NCT li S I(O)N
29
A future
consum:r who doe s not own tank capacity
t:o save
oney from te
purchase of
has
a better
a tank size larger
than 270 gal-
1lons. A 5'Acost reduction for the first delivery is sufficient
rant
a 1000 gallIon
Ion 'i; l
r
;vds
fl
tank for a consumer
with a consumption
chance
to war-
of 2000 gal-
30
APPENDIX:
truck
variable
.i]r-a(q
cost
TC = 18400
FIGURE
$ per year and truck.
truck cost MC= 2800$ per year and truck.
Averagemileagepertour,
which is invariant
of the number of stops FM
= 20 miles per tour.
*
verag e time per tour whiich is invariant
of
the numker of stops FT
98 minutes per toiur.
)et-up time at each stop PTR = 5 minutes
.veratge number
of miles
bf tween
.rving peed between stops
D~ri~vin g kspeed3 bet~wee~n stop~s
T'ruck capacity
Avera.qe delivery
two
size
per
SRt = 15 miles
DR = 200 gl
stop.
MSR = 1.5 miles per stop.
stops
SP = 15 miles per
CAP = 3200 gallons
of yallons distributed
.hiumb,hr
peryt r..
1
1
A~pendix: Data Used to.Compute Figur
rime? variable
DATA 'IIUSFD TO CO.PtlTE
pert
hour. .
per truck.
per delivery
per truck
and customer.
and year DIS = 930000 gallons