10.3.026_A_Dynamic_Programming_Algorithm_FORTRAN_coded_for_Gross_Production_Scheduling 10.3.026 A Dynamic Programming Algorithm FORTRAN Coded For Gross Production Scheduling
10.3.026_A_Dynamic_Programming_Algorithm_FORTRAN_coded_for_Gross_Production_Scheduling 10.3.026_A_Dynamic_Programming_Algorithm_FORTRAN_coded_for_Gross_Production_Scheduling
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1620 GENERAL PROGRAM LIBRARY
A N1amic Programming Algorithm FORTRANCoWd, for Gross Production Scheduling
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A DYNAMIC PROGRAMMING ALGORITHM FORTRAN CODED
FOR GROSS PRODUCTION SCHEDULING
DECK KEY
1. Sample Problem 0, 1, 2
(Refer to Page 17 for Input data listings)
2. Object Deck
3. Source Deck
John W. Burgeson
IBM Corporation
340 South Broadway
Akron, Ohio
Modifications or revisions to this program, as they occur,
will be announced in the appropriate Catalog of Programs
for IBM Data Processing Systems. When such an announcement occurs, users should order a complete new program
from the Program Information Department.
.
~'-\
~1
PROGRAM ABSTRACT
TABLE OF CONTENTS
A Dynamic Programming Algorithm FORTRAN Coded, for
Gros s Production Scheduling.
Title:
Section
John W. Burgeson
IBM 340 South Broadway
Akron a, Ohio
Author:
I/o,
Hardware:
40K, 1620 I Card
Procedure:
Dynamic programming algorithm, described in the body of
the write up.
Execution
Time:
II
hardware divide
Heavily dependent on the size and data of the problem. No
general rule is po s sible to give. A typical problem in vol ving
9 products, 7 levels for each took 4 minutes.
Source
Language:
FORTRAN with FORMAT
Accuracy:
Usual a-digit FORTRAN Accuracy
Limitations:
N less than or equal to 199. M less than or equal to 40.
Page Number
Introduction - The Problem
To solve non-linear production scheduling problems concerning
"Nil products, each product with up to "M" possible production
levels, each level having an associated profit (or cost) figure.
Purpose:
Title
The Solution
III
Description of the Algorithm
IV
Problem Restrictions
v
Running Times and Economics
10
VI
Operation Notes, Data Description
12
VII
Key to Abbreviations, Symbols
13
VIII
Miscellaneous, Key to Decks
14
IX
Typewriter Log of Sample Problem 1
15
x
Typewriter Log of Sample Problem 2
16
Three Sample Problems
17
Listing of the FORTRAN Source Deck
31
XIII
Flow Chart
36
XIV
Listing of the Object deck
37
Partial Distribution List
44
XI
XII
a
Checkout
Checked out completely for N up to 9, M up to 40, Logically
for N up to 199.
~tus:
Comments:
xv
This program. and its documentation were written by an IBM
employee. It was developed for a specific purpose and
submitted for general distribution to interested parties in
the hope that it might prove helpful to other members of the
data processing community. The program and its documentation
are essentially in the author's original form. IBM serves as the
distribution agency in supplying this program. Questions
concerning the use of the program should be directed to the
author's attention.
ABSTRACT
This program has been proven successful in solving production scheduling problems
involving N products, each product with up to M possible production levels, each
level having associated with it a profit (or cost) figure. There is no mathematical
relationship assumed or necessary in any case between production levels and profit
(or cost) figures. Said problem being subject to one constraint-that the total of
all production units be less than or equal to a pre-set "budget."
-i-
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o
()
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o
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Table 1
J. W. Burgeson
IBM Akron, Ohio
INTRODUCTION - THE PROBLEM
This program is one which ha s been profitably employed in situations
where linear programming techniques would have applied except for the
non-linearity of the problem.
As described in this report, the program is shown in the process of
determining an optimum productions schedule of N products each
product with M or less feasible production levels, subject to a constraint
that the totality of all units produced be less than some "budget."
Associated with each production level for each product is some profit
(or cost) figure, there being no particular relationship in any case between
production level and this figure.
..ft0~1 3
Pro_d. 2_
Prod. 1
A DYNAMIC PROGRAMMING ALGORITHM« FORTRAN CODED,
FOR GROSS PRODUCTION SCHEDULING
Xl
VI (Xl)
X2
V2 (X2)
X3
V3 (X3)
0
10
20
30
0.0
1.0
2.0
2.5
10
20
30
40
50
-1.0
0.5
0.8
1.4
1.8
0
5
10
15
20
0.0
0 .. 3
0.9
1.7
1.8
Where ~ (j = 1, 2, 3) is the feasible levels vectcr of_ production for
product j, Vj is the as s ociated profit vector. Xj 1 then is the i th level
of production of product j, Vjiis the associated profit.
I
II
If we have no "budget, /I we can solve the above by inspection for an
optimum solution. Produce 30 of 1, 50 of 2, 20 of 3. No problem.
Suppose, now, we do have a "budget" and that it is less than 1bo units.
THE SOLUTION
Source Language: IBM FORTRAN with FORMAT
Machinery:
Card 40K 1620 with hardware divide
Restrictions:
N less than or equal to 199
M less than or equal to 40
Execution Time: See Section V page 10.
I
What we are looking for is an optimum combination of level selection
from the table. In such a simple problem, we can still solve the problem by inspection, however, not particularly fast ncr easily. The
solution table for all budgets from 100 to 10 (in steps of 10) is:
III
Description of the Algorithm
Table 2
While giving a mathematical description of the algorithm, it is convenient
to describe it also by example. The form of this example is as follows:
(Sample Problem 0)
Consider the manufacture of three products, 1, 2, and 3. We are given data on
these products concerning the possible production levels for each and for each
level an associated profit. In table form:
- 1 -
Budget
. 100
90
80
70
60
50
- 40
30
20
10
Level of 1
Level of 2
Level of 3
50
40
40
20
20
20
20
20
20
10
20
20
20
20
20
10
0
0
0
0
30
30
20
30
20
20
20
10
0
0
-2-
t2!!!
100
90
80
70
60
50
40
30
20
10
The solution proceeds as follqws: There are 3 products (N=8). We are
given Xji and V
ji
jik I we obtain first of all tke corresponding
That is, in calculating any Y
for all produots and Budgets of 100, ~O, 80 •••• , 10~
Vji from the input data. This V
ji
We first set up what is called Tableau *3.
-0-
X
32
-5
>e.ii.
\Ve
nem
subtract from the Sjk of tp.e row we are WQl;'king on, this Xji' obtaining
, Table 3.
X31
corresponds to some
X33
X34
X35
10
15
20
P
3
an argument Sj+ i.m with ~hiCh to find
XB3
a Pj + lin tha
tub,ie of P's of the
precedina tableau.
(831 .. ) 0
In numbers, if we have 40 (=SJk) to assign, we assign 10 (=Xji) we
(S32 .. ) 5
have left ao. Opposite 30 (=8j+ I, -cd in the precedina tableau obtain
(S33 .. ) 10
a P to use in computation.
(8
(8
34
35
.. ) 15
D.
Pjk .. max (Y1ik) (i
11:) 20
E.
XBjk
Where the 8 3k are the amounts of unassigned budget we have left after
no knowledge at this time how much this will be, we must evaluate all
=0
Sa2 = 5
S33 = 10
8
= 15
34
835 = 20
Sal
possibilities. There are 5 of these, the possibility that 0 will be left
(S31)' 5 left (S32)' 10 left (S33)' 15 left (S34)' 20 or more left (Sas).
Define now the elements of the tableau as Yjik • (The element in the
k
til
th
row and the 1 column of the j tableau)
Yjik does not exist for i greater than k, for if we
A.
the Xji where this maximum is found.
.0
.0
.3
.0
.3
.9
.0
.3
.9
1.7
eO
.3
.9
1.7
' 1.8
8S;
XBa
.0
0
.3
5
.9
10
1.7
15
1.8
20
Now, saving the P and XB3 vectors only, Tableau *2:: is generated.
3
Table 5
X21
X22
~3
X24
X25
P2
XB2
have, say, only 5 left of our budget after aSSigning
~oducts
2, ... ,k)
With the above formulae, Tableau *3 is generated (trivial case)
Table 4
X32
X31
X34
P
X33
a
~
the assignment of production levels to Products 1 and 2. Since we have
th
I:
= 1,
1 and 2, we cannot consider the possibility
of producing 10 of product 3.
8 21 = 10
-1.0
S22 = 20
-0.1
0.5
8 23 = 30
0.8
1.4
0.8
= 40
0.8
2.3
1.7
-1.0
10
0.5
20
1.4
20
2.3
20
Define Pn + 1 (any argument) = 0 for an N-Product problem
B.
c.
Yjik .. Vji + Pj + 1 (Sjk - Xji)
fF)
-3-
8 24
()
1.4
(Table 5 continues on the following page.)
-4-
C
?
/
o
0
0
Table 5 (Continued)
X
Y216
= V21 +
Y
=V 22 + P3S = 0.5 +
P3S = -1.0 + 1.8 = 0.8
Z1
X
22
X23
X24
~s
P2
XB
= 50
0.8
2.3
2.6
2.3
L8
2.6
30
Y236=V23+ P35 =0.O+ 1.8=2.6
826 = 60
0.8
2.3
2.6
3.2
2.7
3.2
40
Y246=V24+ P35 =1.4+ 1.8=3.Z
8 27 = 70
0.8
2.3
2.6
3.2
3.6
3.6
50
Y2S6 = V25
8
25
2
226
+ P33
1.8
= Z.3
= 1.8 + 0.9 = 2.7
As an aid to following the mathematics, the calculations necessary are
Y
=V 21 + P3S = -1.0+ 1.8=0.8
217
included as follows:
Y211
to:
V21 + P3l
Y212
=V21 +
= -1.0 +
.0
Y227
= -1.0
= 0.5 +
Y2l3 = V2l + P3S
= -1.0 +
Y247
35
= 0.5 + 1.8 = 2.3
=V24 +
P 3S = 1.4 + 1.8 = 3.2
Y257 = V2S + P3S = 1.8 + 1.8 = 3.6
.0 = 0.5
1.8 = 0.8
P
Y237=V23+ P3S =0.8+ 1.8=2.6
P33 = -1.0 + .9 = -0.1
Y222 = V22 + P31
=V22 +
P21 = max (-1.0)
=
XB 21
-1.0
= 10
Y223=V22+ P33 =0.5+ 0.9=1.4
P 22 = max (-0.1, 0.5) = 0.5
XB22 = 20
Y233=V23+ P3l =0.8+ .0=0.8
P 23 = max (0.8, 1.4, 0.8) :: 1.4
XB23 :: 20
Y224=V 22 + P3S =0.5+ 1.8=2.3
Y23 4:: V23+ P33 =0.8+ .9=1.7
Y244 = V24 + P31 = 1.4 + .0
= 1.4
Y2lS = V21 + P3S = -1.0 + 1.8 = 0.8
Y22S = V22 + P3S = 0.5 + 1.8 = 2.3
=max (0. 8,
=20
P = max (0.8, 2.3, 2.6, 2.3, 1.8) :: 2.6
2S
XB25
= 30
P26 = max (0.8, 2.3, 2.6, 3.2, 2.7) = 3.2
XB 26 :: 40
P27 = max (0.8, 2.3, 2.6, 3.2, 3.6) :: 3.6
XB27
2.3, 1.7, 1.4)
=50
Finally, saving the P2 and XB2 vectors only. Tableau i1 1s generated.
Notice that the 8 vector is growing steadily.
Table 6
Xll
X22
X23
X24
Y23S = V23 + P3S = 0.8 + 1.8 = 2.6
8 11 :: 10
-1.0
Y24S = V24 + P33 = 1.4 + 0.9 = 2.3
812 = 20
0.5
0.0
Y255 =V25 + P31 = 1.8 + .0 = 1.8
8 13 :; 30
1.4
1.5
-5-
= 2.3
XB24
P24
Y214 -V 21 + P3S = -1.0 + 1.8 = 0.8
LO
PI
XB1
-1.0
0
0.5
0
1.5
10
(Table 6 continues on the following page.)
-6-
Table 6 continued
IV. Problem Restrictions
Xl!
X
22
X
23
X
24
!1
XBl
S14 = 40
2.3
2.4
2.5
1.5
2.5
20
grows with arithmetic rapidity. It goes in ,eac!} Tableau from
= 50
2.6
3.3
3.4
2.9
3.4
20
some lower pound ( S0j > to some upper bound ( 3Bj ) in steps
S16 == 60
3.2
3.6
4 .. 3
3.9
4.3
20
of Aj where Aj is defined as the incremental step of production
8 17 == 70
3.6
4'.2
4.6
4.8
4.8
30
level for product j •
S18 = 80
3.6
4.6
5.2
5.1
5.2
20
Two bounds can immediately be put on this Sj vector. There
=90
S110 = 100
3.6
4,6
5.6
5.7
5.7
30
is no gain in allowing SBj to exceed the budget (BUD).
3.6
4.6
5.6
6.1
6.1
30
Similarly, if Qj is defined as the lowest feasible production
S15
8
19
1.
As can be ~een from the description in Part III, the Sj vector
At this point we are completed with Phase 1 of the problem. The P vectors
level of product j, then certainly S0j need never be consi-
are forgotten (although PI does show the actual profits for each possible
dered below:
"budget" from 10 to 100.) The XB data has been put out on intermediate
SUMQ = Qj + Qj+ 1 + ••• + Qn.
cards (or tape). Phase Z of the problem reads this XB data back into the
F. SBj is less than or equal to BUD for all j
machine to determine the actual schedule ....
G.and
Collecting the data fa Phase 2:
2.
Opposite the "budget" in the Slk vector read XBlkl the optimum number of
S0j is greater than or equal to SUM (Ql) (l
=N,
N-1) ••• ,j.
While these formulae help limit the Sj vector, they are not
suffiCient for most ):Ir&c;tical sized problems. Consequently,
Product 1 to be scheduled.
within the program a careful watch is kept on this vector ..
Budget = Budget - XBlk
It 1s never allowed to exceed 100 entries, regardless of
Opposite "budget" in the SZk vector read XB 2k , the optimum number of
formulae F and G. Whenever it threatens to do so, a cal-
Product 2 to be scheduled.
culation is made which locates the
Budget = Budget - XB2k
~
of the Sj vector
at a "most likely position" for use in Phase 2, the reverse
Opposite "budget" in the S3k vector read XB3k' the optimum number of
search. Within the program, this is accomplished by bringing
Product 3 to be scheduled.
in the input datum A2j (average of next three month's demand)
End of Phase 2.
for each product and keeping a sum (SUMA2) of this data.
-7-
o
Therefore:
-8-
o
o
o
o
When the Sj
ve~or
~
gets out of bounds (more than 100 entries),
Once again, experimentally, it appears that th is testrlcUon
the statements:
121
does not affect the final solution to any s1gnificant degree.
K = S0 MIN/A + (SUMA2/BUD) * (SB-S0-100. *A) /A
A
S0=K
S0
l:I
third restriction of sorts has been used in
th~s
model im-
pl1citly all along. This restriction concems possible values
S(2f*A
of the parameter A j • Values of ~ used with this algorithm must
SB:II sQ1 ~ 99.*A
be commensurate with one another. They may all be the same;
are used as a (heuristic) method of keeping the Sj vector
if they differ I the larger Aj must be integer multiples of all
centered around a "most likely" region. You can see the
smaller ~.
results of this action in Section IX.
To an extent, this procedure
threat~ns
Typical values of Aj might be:
to disturb optimality
2, 4, 8, 16, 32, 64, 128,
of the solUtion, Since if we miss the solution point by more
than 50. *~ we will underschedule some product(s) and
or
overschedule others. Experimentally, however, using "live"
In entering data into Phase 1, the products must be sorted
data, it does not appear that we have any problem at this
in order of increasing Aj •
V.
pOint.
Running Times and Economics
A second, somewhat more severe restriction has been built
The question is naturally raised ""Vhy the (arbitrary) restrictions on
into the program. The algorithm, as presented in Section III,
Sj?" The answer to this question lies in the fact that this is not a
calculates all Yjik of the tri-angular array.· As programmed,
speedy algorithm. The running times for the three problems described
not all of these are computed. As the program proceeds, row
in Section X were observed to be: (exclusive of typing)
by row, each time it finds a maximum row entry, it stores this
Prob 0
phase 1 0.6 min.
phase 2 0.3 min/pass
entry in P and the corresponding Xji in XB jk • When starting
jk
Prob 1
phase 1 2.8 min.
phase 2 0.8 min/pass
the next row, it does not start with column 1, but with that
Prob 2
phase 1 36.0 min.
phase 2 0.8 min/pass
column where the maximum was found in the last row. Because
Extending these times analytically to a computer with tape I/O in the
of this, admittedly arbitrary, rule, the machine solution to our
705/7070 class, (and on the basis of observations made on "live"
sample problem 0 (Section X) varies from Table 2 insofar as the
problems on this size machine) it is observed that fairly long machine
budget of 80 is concerned.
-9-
~
25, 50, 100, 200, 400, • • • •
-10-
runs (3-10 hours) are required if the number of products exceeds 1000.
IJmiting Sj to 100 entries instead of 200, S:1y I halves the running time
VI. Operation Notes« Data Description
of such a problem. Using restriction 2 in Part IV again halves the
Input to the progralll cons ists of:
running time, and see~s to be economically sound.
1.
One problelll header card containing according to the Format
This program approach te(!Ufres that profit (or cost) figures be cal-
U4,FIO.0,FI0.0,30H),
culated for each product for each feasible production level. This is,
NUMBR
of course, no trivial job. Meaningful figures must be found for such
BUD
b"ing the No. of products being scheduled
,
"budget",restriction on total units to be scheduled
items as back ordet costs, set-up costs, and inventory carrying costs.
DBUD
Reduce BUD by DBUD for alternate solutions
The cost picture.·fer any product is a complex function of these three
_ 30H
items considered along with such factors as:
2.
up to 30 alphanumeric problem identification
One product header card per product containing according t-o
demand pattern forecast
the FDrmat (20 HIS, IS,F8.0,F8.0 ,F8.0),
quantity on hand
20H
up to 20 alphanumeric product identification
quantity in production
IREeD
Product identifier (stock number?)
facility sharing with other products
M
No. of production levels to be considered
and others.
A
increment size between production levels
Obtaining meaningful figures of this nature is probably the hardest
Q
minimum production
Part of an O. R. man's job if he is to use this or any other s1mllar
A2
average demand next 3 months
algorithm for his scheduling.
3.
Nonetheless, the job can be, and has been, done successfully. It
From 1 to 4 product profit (cost) cards, each containing. up
appears· that, on the basis of many tests with different cost· ,function
to 10 numbers. For 12.M£10, one card will be required, for
c
1l~£20, two cards, etc. Format (lOF? .0).
generators, that as long as all products are computed on the same
Output from the program is in two parts, complete with typed
baSiS, the final schedules do not show much deviation.
instructions. The output from phase 1 is reverse-sorted on
Schedules obtained with this program have been cos ted out against
cc 78-80 and used as input to phase 2. Output from phase 2
actual schedules "made by hand.
is on cards and, with proper sense switch settings, on the
/I
In all cases tested the savings
were very considerable.
typewriter as well. Output is identified by column headings
-11and header mes sages.
c
o
-12-
o
o
o
o
Sense switch settings:
y
i on to type final answers on typev..Titer
2 on to obtain alternate solutions, phase 2.
are the profits(costs) associated with particular S and X
jk
ji
jik
are the max (Y
P
) for i:: 1,2, •••• k
jik
jk
3 on to obtain all messages from the program,off to bypass
are the X where the maximum is found
ji
XB
jk
many of them
4 unused.
Section IX is a typewriter log (sample problem 2) taken with 1 off;
S¢
is the lowest S for any j
jk
SB
is the highest S
VII. Key to Abbreviations« Symbols
1s an index, running from 1 to n
n
is the number of products
Mj
is the number of production levels, j th product
Qj
is the minimum production level
Aj
is the increment between levels
NR
is the number of S rows for any j
jk
VIII
Miscellaneous« Key to Decks
A.
The program is written to accept and use profit data.
This
may be done in two ways:
It is sometimes more convenient to use cost data
1.
2.
are the profits (costs) associated with the levels i = 1,2, ••• , m
fa each product
~i
B.
are the possible levels themselves.
xj1 =0 j
Xj2 = Q j + Aj
~3 =
OJ + Aj + Aj
c.
etc.
BUD
is the "budget" for the total SUM (Xjl)
Sjk
are the possible amounts of unassigned BUD left after aSSigning
-13-
J1
Change the program to scan for a minimum Y
jik
instead of a maximum.
The profit datum associated with the highest production
level of a product should be the highest magnitude of
that profit series. Conversely for cost data. They need
not be in strict ascending magnitude, although frequently
they are.
Key to Decks:
Deck 1: Fortran Source, Numbered DP-OO 1 through
DP-216 in cols. 75-80.
",
products 1, 2, ••• ,j-1.
0
Keep the program as is, add to each cost datum
before input a fictitious profit, for example,
'Y.
k = cost + $10. OO*X··
J1
CAPACj is the maximum level (=OJ + A*(Mj-1)
Vji
for any j
jk
2 on for three passes of phase 2, then off; 3 on.
Deck ~: Object Deck. Listing pages 37-43.
No card numbers
Deck 3: Sample Data, numbered DP-5 0 1
through DP-569 in cols. 75-80.
-14-
1;1'-~j,? - f~ ()
D,YNAM IC PROG MODEL
NO.
3
.-. NO
s0
NO
r'" s0
NO
S0
c---
C
BUDGET
110.
DBUD
10.
.
PHASE 1 COMPLETED
NO.
SAMPLE PROB 0
NAME IRECD
M
3 1940 DESOTO
3
5
20.
=
SB =
2
2 1937 CADILLAC
5
10. S8 =
70.
==
4
1 19lt8 JAGUAR
100.
=
10. S8 ==
INCRE MIN QTY
5.
NR ==
5
10.
10.
NR ==
7
10.
NR = 10
9
CAPAC
20.
AVG OEM
10.
50.
10.
30.
10.
3 ITEMS SCHEDULED
=
110.
':) RERUN INTERMED. CDS. FOR ALT. SOLN.
BEGIN PHASE 2, 8UDGET
==
100.
'-"
RERUN INTERMED. CDS. FOR ALT. SOLN.
BEGIN PHASE 2, BUDGET
=
==
=
==
_~:~ OF JO~
INCRE MIN QTY
CAPAC AVG OEM
25.
14.
125.
25.
NR = 5
8.
25.
50.
NR =
7
14.
50.
300.
NR = 11
NR ... 10
50.
450.
35.
NR ... 19
100.
"600.
50.
35.
NR ... 30
NR = 29
100.
100.
900.
90.
NR ... 24
NR ... ?3
- ._. ·loo(f.- too.
90.
NR = 15
NR = 14
200.
200.
120.
1290.
NR ... 14
NR = 1.3
12-00.
'155.
400.
NR =
8
NR .=
7
9 ITEMS SCHEDULED
BEGIN PHASE 2, BUDGET =
70.
3000.
RERUN INTERMED. CDS. FOR ALT. SOLN.
BEGIN PHASE 2, BUDGET
==
2800.
RERUN INTERMED. CDS. FaR ALT. SOLN.
60.
RERUN INTERMED. CDS. FOR ALT. SOLN.
BEGIN PHASE 2, BUDGET
NAME IRECD
M
WIDGIT
1
5
25. SB =
125.
FRAMIS
2
3
25. SB ==
175.
QuaTl BIT
3
7
SB ...
500.
50. SB ==
500.
GREEB STALL
4
10
50. SB =
950.
GRANCH
5 11
100. SB =
1550.
150. SB =
1550.
GRUNK PITS
6
9
200. SB ...
2500.
300. SB =
2500.
7 ' '6'
ANBER STEM
200. SB ...
3000.
400. SB ...
3000.
RONTER GUY
8
6
400. SB =
3000.
600. SB =
3000.
BINT DUP
4
9
400. SB =
3200.
800. SB =
3200.
saRT aUTPUT IN RVERSE SEQUENCE aN CC 78-80
THEN HIT START TO BEGIN PHASE 2
80.
RERUN INTERMED. CDS. FOR ALT. SOLN.
BEGIN PHASE 2, BUDGET
DBUD
200. PROS. NO.1 FOR D.P.
PHASE 1 COMPLETED
RERUN INTERMED. CDS. FOR ALT. SOLN.
BEGIN PHASE 2, BUDGET
-f1pC"''';~1- I..~ - f~lf"'" 1.
90.
~ RERUN INTERMED. CDS. FOR ALT. SOLN.
BEGIN PHASE 2, BUDGET
BUDGET
3000.
PROD
SO =
PROD 2
so =
PRao a
SO ==
SO ==
PROD 4
SO ..
PROD 5
SO =
SO =
PROD 6
SO =
SO =
PROD 7
SO =
SO =
PRaD 8
SO =
SO =
PROD 9
so =
SO ==
- SORT QUTPUT IN RVERSE SEQUENCE ON CC 78-80
., THEN HIT START TO BEG IN PHASE 2
3 BEGIN PHASE 2, 8UDGET
:II
DYNM11 C PROG tvlODEL
50.
IS
0
BEGIN PHASE
BEGIN PHASE
BEGIN PHASE
BEGIU PHASE
BEGIN PHASE
BEGIN PHASE
END OF JOB
2,
2,
2,
2,
2,
2,
BUDGET
BUDGET
BUDGET
BUDGET
BUDGET
BUDGET
=
==
=
=
=
=
2600.
2400.
2200.
2000.
1800.
1600.
16
0
.0
x
DYNAMIC PROG MODEL
NO.
8
BUDGET
8000.
+-,ff,..,.;l:"" ''1 - I\.ol.l~ 2 0
DBUD
100.
PROBLEM 2 FOR D. P.
NAME fRECD
M
BOLTS U/4 UN NO 3
1 40
so =
100. SB =
2050.
SCREWS NO 18 LONG
2 40
SO =
100. SB =
4000.
LOCOMOTIVE, STEAM
3 40
SO =
150. SB =
5100.
SO =
200. SB =
5150. .
LOCOMOTIVE, DEISEL
4 40
SO =
250. SB =
5200.
EYEGLASS FRAME, BRN
10
5
SO =
300. SB =
5250.
LAMBSKIN TURBAN
6
10
SO =
350. SB =
5300.
1620 COMPUTER
20
7
SO =
500. SB =
750Q.
SO =
600. SB =
7500.
SO =
700. SB =
7500.
HAIRPIN, NO 6 BLACK
8
40
SO =
600. SB =
8000.
SO =
BOO. SB =
8000.
PHASE 1 COMPLETED
INCRE MI N QTY
50.
100.
NR = 40
50.
NR = 79
50.
50.
NR = 100
NR = 100
50.
NR = 100
50.
50.
NR = 100
50.
NR = 100
100.
300.
NR = 71
NR = 70
NR = 69
200.
NR = 3B
NR = 37
CAPAC
2050.
AVG OEM
100.
1950.
200.
2000.
1950.
100.
500.
600.
450.
200.
2200.
350.
7800.
360.
B ITEMS SCHEDULED
SORT OUTPUT IN RVERSE SEQUENCE ON CC 7B-80
THEN HIT START TO BEGIN PHASE 2
=
BOOO.
BEGIN PHASE 2, BUDGET =
7900.
BEGIN PHASE 2, BUDGET =
7800.
=
7700.
BEGIN PHASE 2, BUDGET =
7600.
BEGIN PHASE 2, BUDGET
BEGIN PHASE 2, BUDGET
-.
BEGIN PHASE 2, BUDGET
=
7500.
BEGIN PHASE 2, BUDGET
=
7400.
BEGIN PHASE 2, BUDGET =
7300.
END OF JOB
STOP
17
c
-------_._--_.__ ._---
-
:r'Meu.+
.
3
NO 3
NO 2
-1.
NO 1
110.
10.
1940 DESOTO
.3
.9
1937 CADILLAC
.5
.8
1948 JAGUAR
1.
2.
3
1.7
1.8
1
........... "_" ... ~~w .... _." •• "., ..... ~ _ _ _ _ _ _ ~, ..... _
........ _ _ ~., ...... , ........................ "' ••• .L_ ......... _ _ _
+... 10?
DP
DP
DP
DP
DP
DP
DP
·-10;--· ---rC5;··
1.8
4 10.
-~-.
,j..
SAMPLE PROS 0
5 5.
O.
10.
2- ··5"--10.
1.4
-.---.------.-.-.. ,,--,---.-,- ..
o.
10.
2.5
501
502
503
51)4
505
506
507
. ___.M_
~
~
.~.--
O ...ir·~··~
BEGIN PHASE 2, BUDGET
=
~
Qc)
NO 1 1948 JAGUAR
NO 2 1937 CADILLAC
NO 3 1940 DESOTO
c..
110.
PROD. NO. LEVEL
1
2
3
INCRE
5
6
6
10.
10.
5.
MIN aTY
CAPAC
10.
30.
50.
20.
TOTAL
BEGIN PHASE 2, BUDGET
=
NO 1 1948 JAGUAR
CADILLAC
NO 3 1940 DESOTO
1
2
3
11.10 2 1937
SCHEDULE
30.
50.
20.
100.
100.
MIN aTY
INCRE
PROD. NO. LEVEL
10.
10.
5.
4
5
5
CAPAC
30.
10.
0
50.
20.
TOTAL
SCHEDULE
30.
50.
20.
100.
017
18
19
020···
21
022
023
024
25
026
27
28
29
30
31
032
33
34
035
36
037
038
039
40
041
42
43
44
45
46
I>
.l
~
"I...
---I
'"
0
BEGIN PHASE 2, BUDGET
=
90.
PROD. NO. LEVEL
NO 1 1948 JAGUAR
NO 2 1937 CADILLAC
NO 3 19"40 DESOTO
1
2
3
INCRE
MIN aTY
10.
10.
5.
4
4
5
CAPAC
30.
10.
50.
20.
TOTAL
BEGIN PHASE 2, BUDGET
=
30.
40.
20.
90.
80.
PROD. NO. LEVEL
NO 1 1948 JAGUAR
NO 2 1937 CADILLAC
NO 3 1940 DESOTO
SCHEDULE
1
2
3
INCRE
4
3
5
MIN aTY
CAPAC
10.
30.
50.
20.
10.
10.
5.
TOTAL
SCHEDULE
30.
30.
20.
80.
.....
~
BEGIN PHASE 2, BUDGET
=
70.
PROD. NO. LEVEL
NO 1 1948 JAGUAR
NO 2 1937 CADILLAC
NO 3 1940 DESOTO
1
2
3
4
2
5
INCRE
10.
10.
5.
MIN aTY
CAPAC
10.
30 •
50.
20.
.
TOTAL
t»
---_ .. "'----- -
SCHEDULE
30.
20.
20.
70.
047
48
49
050
51
052
053
054
55
056
57
58
59
60
61
062
63
64
065
66
067
068
069
70
071
72
73
74
75
76
077
78
79
080
81
082
083
084
85
086
87
88
89
90
91
0
T.I_~.t1\
"\
(',
..-.
J_ I.'
BEGIN PHASE 2, BUDGET =
60.
PROD. NO. LEVEL
NO 1 1948 JAGUAR
NO 2 1937 CADILLAC
NO 3 1940 DESOTO
CI
1
2
3
INCRE
3
2
5
MIN
10.
10.
5.
Cly
CAPAC
10.
30.
50.
20.
SCHEDULE
20.
20.
2 o.
TOTAL
BEGIN PHASE 2, BUDGET =
50.
PROD. NO. LEVEL
NO 1 1948 JAGUAR
NO 2 1937 CADILLAC
NO 3 1940 DESOTO
60.
1
2
3
INCRE
MIN OTY
CAPAC
10.
30.
50.
20.
10.
10.
5.
3
2
3
SCHEDULE
20.
20.
10.
50.
TOTAL
N
c:::
BEGIN PHASE 2, BUDGET =
40.
PROD. NO. LEVEL
NO 1 1948 JAGUAR
NO 2 1937 CADILLAC
NO 3 1940 DESOTO
1
2
'3
INCRE
MIN OTY
CAPAC
10.
30.
50.
20.
10.
10.
5.
3
2
1
SCHEDULE
20.
2 O.
40.
TOTAL
OJ
BEGIN PHASE 2, BUDGET
=
30.
PROD. NO. LEVEL
~O 1 1948 JAGUAR
NO 2 1937 CADILLAC
NO 3 1940 DESOTO
1
2
3
INCRE
MIN OTY
CAPAC
10.
,0.
50.
2(1.
.
10.
10.
5.
2
2
1
SCHEDULE
10.
20.
30.
TOTAL
BEGIN PHASE 2, BUDGET
=
20.
PROD. NO. LEVEL
NO 1 1948 JAGUAR
1937 CADILLAC
NO 3 1940 DESOTO
1
2
NO ?
3
INCRE
MIN OTY
CAPAC
10.
30.
50.
20.
10.
10.
5.
1
2
1
20.
2 o.
TOTAL
N
....
BEGIN PHASE 2, BUDGET
=
10.
PROD. NO. LEVEL
0
SCHEDULE
NO 1 1948 JAGUAR
NO 2 1937 CADILLAC
NO 3 1940 DESOTO
1
2
3
INCRE
MIN OTY
CAPAC
10.
30 •
50.
20.
10.
10.
5.
.
SCHEDULE
10.
10.
TOTAL
r.l
S4"f/~
,"0"
I('ta(
0
f.I,
L:
092
93
94
095
96
097
098
099
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
.
--1
~
.1_
So.Yt\t'e 1'...."",.. .1..
I .. p......
9 3000.
200.
PROD 1 WI DGIT
35.
36.
37.
PROD 2 FRAMfs
.75
.88
.62
PROD a QUOTL BIT
5.3
5.2
5.
PROD 4 GREEB STALL
23.
22.
21.
PROD 5 GRANCH
2.
3.
1.
11.01
PROD 6 GRUNK PITS
8.34
8.8
8.17
PROD 7 ANBER STEM
13.1
15.17
11.
PROD 8 RONTER GUY
18.
18.3
-18.
PROD 9 BINT DUP
28.
27.
28.1
1
39.
- ---2
PROBe NO. 1 FOR D.P.
25.
14.
5 25.
39.5
3
5.6
-3 .·-2~-~ ·---6 .----- --~-- 8-;-----
7 50.
o.
5.8
5.81
10
o.
50.
'"
- .-
_--
--- -----DP--5Ti----
5.9
25.6
6
8.99
7
19.22
8
18.33
9
28.5
9 100. 100.
90.
10.21 12.43
9.76
9.12
6 200. o.
90.
26.4
25.8
6 200. 200.
120.
19.04 29.99
4 400. o.
155.
7.
...
_. 14.
4
25.1
5
5.
!i-
-.~--
DP 508
DP 509
DP 510
:35.
27.2
29.1
30.
-1'00;--56.
35.
9.
9.
9.
31.2
35.7
10.1
10.4
15.
512
51:3
514
--"-,,-,,,.---.--
0
515
516
(jp
511-
DP
DP
DP
DP
DP
DP
DP
DP
DP
DP
518
519
520
521
522
523
524
525
526
527
OC4~f""~
BEGIN PHASE 2, BUDGET =
3000.
i ;
PROD. NO. LEVEL
'"
PROD
PROD
PROD
PROD
PROD
PROD
PROD
PROD
PROD
9
8
7
6
5
4
0
2
1
BINT DUP
RONTER GUY
ANBER STEM
GRUNK PITS
GRANCH
GREEB STALL
QUOTl BIT
FRA~lI S
WIDGIT
9
8
7
6
5
4
3
2
1
INCRE
400.
200.
200.
100.
50.
50.
50.
25.
25.
1
6
5
1
6
10
1
1
4
MIN QTY
200.
100.
100.
25.
CAPAC
1200.
1200.
1000.
900.
600.
450.
300.
50.
125.
TOTAL
BEGIN PHASE 2, BUDGET
=
PROD
PROD
PROD
PROD
PROD
PROD
PROD
PROD
PROD
BINT DUP
RONTER GUY
ANBER STEM
GRUNK PITS
GRANCH
GREEB STALL
() QUOTl BIT
2 FRAMIS
1 WIDGIT
9
8
7
9
8
7
6
5
4
6
5
4
3
2
1
INCRE
400.
200.
200.
100.
50.
50.
50.
25.
25.
1
6
4
1
6
10
1
1
4
=
BINT DUP
RONTER GUY
ANBER STEM
GRUNK PITS
GRANCH
GREER STALL
0 QuOTl BIT
2 FRAMIS
1 WIDGIT
9
8
7
6
5
4-
100.
MIN QTY
200.
100.
100.
25.
CAPAC
1200.
1200.
1000.
9(,)0.
600.
450.
30t').
50.
125.
SCHEDULE
1200.
600.
100.
350.
450.
100.
2800.
2600.
PROD. NO. LEVEL
PROD
PROD
PROD
PROD
PROD
PROD
PROD
PROD
PROD
1200.
800.
100.
350.
450.
3000.
TOTAL
BFGIN PHASE 2, BUDGET
SCHEDULE
2800.
PROD. NO. LEVEL
~-
DP
OP
DP
DP
DP
U I~ U C.I
9
8
7
6
5
4
3
2
1
1
2
5
1
11
10
2
4
6
INCRE
400.
200.
200.
100.
50.
50.
50.
25.
25.
MIN QTY
200.
100.
100.
25.
TOTAL
CAPAC
SCHEDULE
1200.
1200.
1000.
900.
600.
450.
300.
50.
125.
400.
800.
100.
600.
450.
50.
50.
125.
2575.
233
234
235
236
237
238
239
240
241
242
243
244245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
0
0
BEGIN PHASE 2, BUDGET
=
2400.
PROD. NO. LEVEL
PROD
PROD
PROD
PROD
PROD
PROD
PROD
PROD
PROD
C
9
8
7
6
5
4
a
2
1
BINT DUP
RONTER GUY
ANBER STfM
GRUNK PITS
GRANCH
GREEB STALL
QUOTL BIT
FRAMIS
WIDGIT
9
8
7
6
5
4
3
2
1
INCRE
MIN aTY
4nO.
200.
200.
100.
50.
50.
50.
25.
25.
1
2
5
1
9
10
1
2
5
200.
100.
100.
25.
CAPAC
1200.
1200.
1000.
900.
600.
450.
300.
50.
125.
TOTAL
BFGIN PHASE 2, RUDGET
,
i\:
.....
=
9
8
7
6
<;
4
0
2
1
400.
800.
100.
500.
450.
25.
125.
240n.
2200.
PROD. NO. LEVEL
PROD
PROD
PROD
PROD
PROD
PROD
PROD
PROD
PROD
SCHEDULE
BINT DUP
RaNTER GUY
ANBER STEM
GRUNK PITS
GRANCH
GREER STALL
QUOTL BIT
FRAMIS
WIDGIT
9
8
7
6
5
4
3
2
INCRE
400.
2nO.
2()O.
100.
50.
50.
50.
25.
25.
1
2
5
1
6
10
1
1
4
1
MIN QTY
200.
10 o.
100.
25.
CAPAC
1200.
1200.
10no.
900.
600.
450.
300.
50.
125.
TOTAL
SCHEDULE
400.
800.
100.
3') C,.
450.
100.
2200.
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
3:B
334
335
336
0
BFGIN PHASE 2, BUDGET
=
2000.
PROD. NO. LEVEL
PROD
PROD
PROD
PROD
PROD
PROD
PROD
PROD
PROD
9
8
7
6
5
4
0
2
1
BINT DUP
RONTER GUY
ANBER STEM
GRUNK PITS
GRANCH
GREEB STALL
QUOTL BIT
FRAMIS
WIDGIT
9
8
7
6
5
4
7
1
INCRE
MIN aTY
4n(').
2no.
2no.
1no.
50.
50.
50.
75.
25.
1
2
4
1
6
10
1
1
4
200.
10 O.
1 (") O.
25.
CAPAC
SCHEDULE
1201") •
1200.
10nn.
90n.
40n.
600.
6()1'1.
4,1).
300.
')0.
I? 5.
TOTAL
lOC.
35(".
450.
Ion.
2000.
337
331:3
339
34n
-'41
34:'
343
344
34')
346
347
348
349
350
'351
?52
~i5 3
354
355
.3S6
357
358
BEGIN PHASE 2, BUDGET
PROD. NO. LEVEL
/~
~
0
1800.
PROD
PROD
PROD
PROD
DROD
PROD
PROD
PROD
PROD
9
8
7
6
5
4
0
2
1
BINT DUP
RONTER GUY
ANBER STEM
GRUNK PITS
GRANCH
GREfB STAll
QUOTL BIT
FRAMIS
WIDGIT
9
8
7
6
5
4
:3
2
1
1
2
3
1
6
10
1
1
4
INCRF
4()0.
200.
200.
InO.
50.
50.
50.
25.
25.
~1l
N QTY
200.
CAPAC
1200.
1200.
1')01).
100.
10 o.
25.
TOTAL
9n('l.
600.
SCHEDULE
4CO.
400.
IN).
4~O.
35C.
4:'C.
300.
50.
125.
10C.
1800.
359
360
361
362
363
364
36:'
366
367
368
369
370
37:
372
":73
374
375
376
377
BEGIN PHASE 2, BUDGET
1600.
PROD. NO. LEVEL
PROD
PROD
PROD
PROD
PROD
PROD
PROD
PROD
PROD
BINT DUP
RONTER GUY
ANBER STEM
GRUNK PITS
GRANCH
GREEB STALL
0 aUOTL BIT
2 FRAMIS
1 WIDGIT
9
8
7
6
5
4
9
8
7
6
5
4
3
2
1
1
2
2
1
6
10
1
1
4
INCRE
MIN QTY
400.
200.
200.
100.
50.
50.
50.
25.
25.
200.
100.
100.
25.
CAPAC
1200.
1200.
1000.
900.
600.
450.
300.
50.
125.
TOTAL
J 4&.Wf l4l fWJ~1 "'"
SCHEDULE
400.
200.
100.
350.
450.
100.
1600.
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
(;)
0
2.
~'14-\-.
....,
""
8000.
100.
8
BOLTS U/4 UN NO 3
2.
3.
1.
12.
13.
11.
22.
23.
21.
32.
33.
31.
NO
!=.CREWS
18 LONG
21.
21.5
211.5
26.
26.5
25.5
,11.5
31.
31.5
36.
36.5
35.5
LOCOMOTIVE t STEAt-1
30.1
30.2
30.
32.
32.1
31.
33.1
33.2
33.
34.
35.
36.
LOCOMOTIVE t DEISEL
20.
20.1
22.88 22.89 22.9
24.
24.4
24.
25.44 25.55 25.66
EYEGLASS FRA~E, RRN
15.3
15.6
15.1
LAMBSKIN TURBAN
30.12 30.44 30.45
1620 COMPUTER
11.56 11.57 11.66
11.94 11.98 12.
HAIRPIN. NO 6 BLACK
1.1
1.12
1.
2.5
2.55
2.
4.
4.22
3.9
5.21
5.31
5.
PROBLEM 2 FOR D. P.
40
50.
100.
100.
4.
6.
5.
7.
8.
14.
15.
.6
17.
18.
24.
25.
26.
27.
28.
38.
34.
35.
37.
39.
40
50.
200.
2
23.5
22.
22.5
23.
24.
27.
27.5
28.
28.5
29.
33.4
34.
32.
32.5
33.
37.
8.
38.
38.5
37.5
50.
50. 300.
40
3
30.4
30.6
30.7
30.3
30.5
32.3
32.4
32.5
32.6
32.3
33.5
33.7
33.3
33.4
33.4
37.4
37.
3701
37.2
37.6
40 50.
100.
4
22.56
22.
22.22 22.23 22.25
22.91 22.92 22.95 22.99 23.
24.5
24.8
24.9
25.
25.11
25.77 25.88 25.99 26.1
26.2
')
50.
50.
600.
10
15.8
16.
16.2
16.2
16.3
50.
2 00.
6
10
30.456 30.458 30.88 31.
32.556
300.
7
20 100.
350.
11.91
11.77 11.88 11.89 11.9
17.5
18.
12.
15.
17.
2(')0.
360.
8
40
1.55
1.123 1.123 1.22
1.235
3.2
2.56
2.58
2.9
3.
4.53
4.76
4.43
4.64
4.33
5.85
5.94
5.64
5.42
5.53
9.
19.
29.
40.
10.
20.
30.
41.
24.5
29.5
34.5
'39.
25.
30.
35.
40.
30.8
32.7
33.8
37.66
30.9
32.8
33.9
37.77
22.75
23.
25.22
26.3
22.78
23.5
25.33
26.9
.88
16.55
33.
34.235
11.92
18.4
11.93
18.5
1.6
3.25
4.87
6.
1.88
3.66
4.87
7.258
DP 528
DP 529
DP 5301
DP 5311
DP 5321
DP 5331
DP 534
DP 5352
DP 5362
DP 5372
DP 5382
DP 539
DP 5403
DP 5413
DP 5423
DP 5433
DP 544
DP 5454
DP 5464
DP 5474
DP 5484
DP 549
DP 5505
DP 551
DP 5526
DP 553
DP 5547
DP 5557
DP 556
DP 5578
DP 5588
DP 5598
DP-5608
0
o ....tel4~
BEGIN PHASE 2, BUDGET
CI
8000.
PROD. NO. LEVEL
HAIRPIN, NO 6 ALACK
1620 COMPUTER
LAMBSKIN TURBAN
EYEGLASS FRAME, BRN
LOCOMOTIVE, DEISEL
LOCOMOTIVE, STEAM
SCREWS NO 18 LONG
BOLTS U/4 UN NO 3
8
7
6
5
4
3
2
1
INCRE
200.
100.
50.
50.
50.
50.
50.
50.
3
21
11
10
40
1
34
15
MIN CTY
300.
50.
50.
100.
CAPAC
SCHEDULE
7800.
2200.
450.
500.
1950.
2000.
1950.
2050.
400.
2200.
450.
500.
1950.
50.
1650.
800.
TOTAL
BEGIN PHASE 2, BUDGET =
""
00
7900.
PROD. NO. LEVEL
HAIRPIN, NO 6 BLACK
1620
CO~PUTER
LAMASKIN TURBAN
~YEGLASS FRAME, BRN
LOCOMOTIVE, DEISEL
LOCOMOTIVE, STEAM
SCREWS NO 18 LONG
BOLTS U/4 UN NO 3
8000.
8
7
6
5
4
3
2
1
INCRE
MIN QTY
2no.
3
20
10
10
37
1
35
15
Ina.
50.
50.
50.
50.
50.
50.
300.
50.
50.
100.
CAPAC
SCHEDULE
7800.
2200.
450.
500.
1950.
2000.
1950.
2050.
400.
2200.
450.
500.
1800.
50.
1700.
800.
7900.
TOTAL
42
43
44
045
46
047
048
049
050
051
052
053
054
55
056
57
58
59
60
61
62
63
64
065
66
067
068
069
070
071
072
073
074
75
076
77
78
79
80
81
0
BfGIN PHASE 2, BUDGET
7800.
PROD. NO. LEVEL
HAIRPIN, NO 6 BLACK
1620 COMPUTER
LAMBSKIN TURBAN
EYEGLASS FRAME, ARN
LOCOMOTIVE, DEISEL
LOCOMOTIVE, STEAM
SCRFWS NO 18 LONG
80LTS lJ/4 UN NO 3
8
7
6
5
4
3
2
1
INCRE
200.
100.
50.
50.
50.
50.
50.
50.
2
21
11
10
40
1
"14
15
MIN aTY
300.
50.
50.
100.
CAPAC
7800.
2200.
450.
500.
1950.
20Q() •
1950.
2050.
SCHEDULE
200.
2200.
450.
500.
1950.
50.
1650.
800.
82
83
84
085
86
087
088
089
090
091
092
093
094
9~
TOTAL
BEGIN PHASE 2, BUDGET
N
<:c
7100.
PROD. NO. LEVEL
HAIRPIN. NO 6 BLACK
1620 COMPUTER
LAMBSKIN TURBAN
EYEGLASS FRAME, BRN
LOCOMOTIVE, DEISEL
LOCOMOTIVE, STEAM
SCREWS NO 18 LONG
BOL TS lJ/4 UN NO 3
B
7
6
5
4
3
2
1
2
20
10
10
37
1
35
15
INCRE
2no.
1(')0.
50.
50.
50.
50.
50.
50.
MIN ()Ty
300.
50.
50.
100.
TOTAL
0
7800.
CAPAC
7800.
22()O.
450.
500.
1950.
2000.
1950.
2050.
SCHEDULE
200.
2200.
450.
500.
1800.
50.
1700.
800.
7700.
096
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _4"·
-----
BEGIN PHASE 2, BUDGET
=
7600.
PROD. NO. LEVEL
HAIRPIN, NO 6 BLACK
1620 COMPUTER
LAMBSKIN TURBAN
EYEGLASS FRAME, BRN
LOCOMOTIVE, DEISEL
L.OCOMoTI VE, STEAM
SCREWS NO 18 LONG
BOLTS U/4 UN NO 3
8
7
6
5
4
3
2
1
INCRE
1
21
200,
100.
50.
50.
50.
50.
50.
50.
11
10
40
1
34
15
MIN QTY
300.
50.
50.
100.
CAPAC
SCHEDULE
7800.
2200.
450.
500.
1950.
2000.
1950.
2050.
2200.
450.
500.
1950.
50.
1650.
TOTAL
BEGIN PHASE 2, BUDGET =
800~
7600.
7500.
C.
•
PROne NO. LEVEL.
HAIRPIN, NO 6 BLACK
1620 COMPUTER
LAMBSKIN TURBAN
EYEGLASS FRAME, RRN
LOCOMOTIVE, DEISEL
LOCOMOTIVE, STEAM
SCREWS NO 18 LONG
BOLTS U/4 UN NO 3
8
7
6
5
4
3
2
1
INCRE
200.
100.
50.
50.
50.
50.
50.
50.
1
20
10
10
37
1
35
15
MIN aTY
300.
50.
50.
100.
CAPAC
SCHEDULE
7800.
2200.
450.
500.
1950.
2000.
1950.
2050.
2200.
450.
500.
1800.
50.
1700.
8(,)0.
TOTAL
7500.
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
-------_.._------
0
~
V
7400.
BEGIN PHASE 2, BUDGET =
PROD. NO. LEVEL
HAIRPIN, NO 6 BLACK
16?0 COMPUTER
LAMBSKIN TURBAN
EYEGLASS FRAME. 8RN
LOCOMOTIvE, DEISEL
LOCOMOTIVE. STEAM
SCREWS NO 18 LONG
BOLTS U/4 UN NO 3
8
7
6
5
4
3
2
1
INCRE
200.
100.
50.
50.
50.
50.
50.
50.
1
20
10
10
35
1
35
15
MIN aTY
300.
50.
50.
100.
CAPAC
SCHEDULE
7800.
2200.
450.
500.
1950.
2000.
1950.
2050.
2200.
450.
500.
1700.
50.
1700.
800.
7400.
TOTAL
BFGIN PHASE 2, BUDGET =
~
7300.
PROD. NO. LEVEL
HAIRPIN, NO 6 BLACK
1620 COMPUTER
LAMBSKIN tURBAN
EYEGLASS FRAME, ARN
LOCOMOTIvE, DEISEL
LOCOMOTIvE, STEAM
SCREWS NO 18 LONG
BOLTS U/4 UN NO 3
8
7
6
5
4
3
2
1
1
20
10
10
33
1
35
15
INCRE
200.
100.
50.
50.
50.
50.
50.
50.
MIN QTY
300.
50.
50.
100.
TOTAL
CAPAC
SCHEDULE
7800.
2200.
450.
500.
1950.
2000.
1950.
2050.
2200.
450.
500.
1600.
50·
1700.
800.
7300.
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
~90
191
192
193
194
195
196
0
c
C
C
C
C
C
C
C
C
C
C
1102
110,
1104
1118
2222
7776
7777
7778
7779
7780
7781
7782
778,
7784
77
C
C
C
C
C
NON-LINEAR PROGRAMMING. A MODEL DESIGNED FOR PRODUCTION SCHEDULING
JOHN W. BURGESON, APPLIED SCIENCE REP. I R M AKRON
CHANGE LEVEL 3/5/62
THIS PROG CAN HANDLE A MAX OF 199 PRODUCTS.
THE LIMIT IS CAUSED BY THE 3 DIGIT SEQUENCE
NUMBER PUT IN CC 78-80 BY THE FORTRAN PUNCH SUBROUTINE.
THE PROG HAS 2 PHASES. OUTPUT FROM 1 IS 5 CARDS PER PRODUCT. THIS
INTERMEDIATE DECK MUST BE SORTED IN REVERSE ORDER FOR INPUT TO
PHASE 2. PHASE 2 MAY BE RUN MANY TIMES WITH THIS DECK, EACH PASS
DEVELOPING A NEW SCHEDULE WITH A (REDUCED) NEW BUDGET.
DIMENSION S(40), V(40), PRECP(100), CURRP(lOO)
FORMAT (1111H )
FORMAT (11111H PHASE 1 COMPLETEDI4,16H ITEMS SCHEDULED)
FORMAT (/11H END OF JOB/)
FORMAT (1118HDYNAMIC PROG MODELII124H NO.
BUDGET
DBUD)
FORMAT(/15X,49HPROD. NO. LEVEL
INCRE MIN OTY
CAPAC SCHEDULE/)
FORMAT (I4,F10.0,F1n.O,30H
)
FORMAT (20H
I5,I5,F8.0,F8.0,F8.0,F8.0,I6)
FORMAT (1/42HSORT OUTPUT IN RVERSE SEQUENCE ON CC 78-80)
FORMAT (/23HBEGIN PHASE 2, BUDGET =F10.0/)
FORMAT (31HTHEN HIT START TO BEGIN PHASE 2)
FORMAT (/35HRERUN INTERMED. CDS. FOR ALT. SOLN.)
FORMAT 1/15X,48HNAME IRECD
M INCRE MIN QTY
CAPAC AVG DEM)
FORMAT 14HSO =FIO.0,6H SB =F10.0,6H NR =14)
FORMAT 1/42X,5HTOTALF15.0)
FORMAT IF7.0,F7.0,F7.0,F7.0,F7.0,F7.0,F7.0,F7.0,F7.0,F7.0)
NUMB
()
TYPE 1118
READ 7776,NUMBR,BUD,DBUD
NUMBR IS THE TOTAL NUMBER OF PRODUCTS TO BE PROCESSED
BUD IS THE BUDGET EXPRESSED IN TOTAL NO. OF UNITS
DBUD IS AN AMOUNT (OPTIONAL) BY WHICH BUD MAY BE REDUCED IN
PHASE 2 TO OBTAIN ALTERNATE SOLUTIONS WITH REDUCED BUDGETS.
TYPE 7776,NUMBR,BUD,DBUD
PLACE = BUD
C;U~~Q=O •
SUMA2=O.
()LDSO=O.
OLDSB=O.
TYPE 1102
PRECP ( 11 =0.
()LDA=O.
NROLD=l
SENS E SWITCH 3 ON PERMITS THIS ADDITIONAL TYPED INFO
IFISENSE SWITCH 3) 79,80
79 TYPE 7782
DP 046
IRECD,M,A,Q,A2
DP 047
IRECD IS PROD IDENTIFIER ISTOCK NO) NOT USED BY PROG
DP 048
M IS NO OF PROD LEVELS CONSIDFRED. MUST BE BETWEEN 1 AND 40
DP 049
A IS INCREMENT SIZF FROM LEVEL TO LFVEL, MUST Bf 25,50,100,ETC
DP 050
Q IS MINIMUM QUANTITY TO BE MADE. MUST gE MULTIPLE OF A
DP 051
A2 IS AVERAGE DEMAND OVER NEXT 3 MONTHS
DP 052
IF(M-40) 85,85,999
DP 053
EM=M-l
DP 054
NOW CALCULATE CAP~C FOR THIS PRODUCT
DP-055
CAPAC = Q + A*E~
DP 056
CAPAC IS THE MAX PROD LEVEL
DP 057
THUS IF X IS A PROD LEVEL WE CAN SAY DP 0,8
X = Q, Q+A. Q+2.*A, • • • , C~PAC
DP 059
DO 81 I=1,~tlO
DP 060
r 2= 1+1
.
DP 061
1"3=1+2
DP 062
14=1+1
DP 063
15=1+4
DP 064
16=1+5
DP 065
17=1+6
DP 066
18=1+7
DP 067
19=1+8
DP 068
10=1+9
DP 069
READ 77,VII),V( I2),VII3) ,VII4),V( I5),VII6),VII7),VI 18),V(I9) .V( 10) DP 070
VII) IS THE PROFIT ASSOCIATED WITH PROD LEVEL I
DP 071
SENSE SWITCH 3 ON PERMITS THIS ADDITIONAL TYPED INFO
DP 072
IF(SEN~E SWITCH 3) 82,83
DP 073
TYPE 7777, IRECD.M,A,Q,(APAC,A2
DP 074
NUMB=NU'"'1B+1
DP 075
SUMQ=SUMQ+Q
DP 076
SUMA2=SUMA2+A2
DP 077
SUMC=OLDSB+CAPAC
DP 078
SO~~IN=OLDSO
DP 079
IFIOLDSO-5UMQ) 114,115,115
DP 080
SOMIN=SUMQ
DP 081
5BMAX=SUMC
DP 082
IFISUMC-BUD) 118,118,117
DP 083
SBMAX =8UD
DP 084
K=SOMIN/A
DP 085
SO=K
DP 086
K=SBMAX/A+.9999
DP 087
SB=K
DP 088
SO=SO*A
DP 089
SB=SB*A
DP 090
80 READ 7777,
C
C
C
C
C
85
C
C
C
(
81
C
C
82
83
o
114
115
117
118
DP-OOI
DP 002
DP 003
DP 004
DP 005
DP 006
DP 007
DP 008
DP 009
DP 010
DP 011
DP 012
DP 013
DP 014
DP 015
DP 016
DP 017
DP 018
DP 019
DP 020
DP 021
DP 022
DP 023
DP 024
DP 025
DP 026
DP 027
DP 028
DP 029
DP 030
DP 031
DP 032
DP 033
DP 034
DP 035
DP 036
DP 037
DP 038
DP 039
DP 040
DP 041
DP 042
DP 043
DP 044
DP 045
NR= (SB-SO) I A+1.
IFINR-1001 135,135,127
127 K=SOMIN/A+ISUMA2/BUD)*ISB-SO-I00.*A)/A
SO=K
SO=SO*A
SB=SO+99.*A
~R=100
~
~
135 DO 136 J = 1,40
136 SIJ) = SO
137 QQ=Q
IFISENSE SWITCH 31 138,139
C
SENSE SWITCH 3 ON PERMITS THIS ADDITIONAL TYPED INFO
138 TYPE 7783,SO,SB,NR
139 IGAG=1
SS=SO
INDEX=l
150 P=-1000000.
X=QQ
IDEXl=IGAG
XB=QQ
CALC OF Y. S WIll CONTAIN FOR EACH X THE HIGHEST S FOUND
171 ARG=SS-X
IFIARG-OlDSBI 185t180~180
180 Y=VIIDEX1) + PRECPINROlD)
GO TO 300
185 T4=ARG-OlDSO
IFIT4) 320,190,190
190 IDEX2 = IARG~OlDSOI/OlDA + 1.5
Y=VIIDEX1)+PRECPIIDEX2)
300 IFIY-P) 320,310,310
310 P=Y
XB=X
00
320
335
340
600
601
602
=
X
IGAG=IDEX1
X=X+A
JDEX1=IDEX1+1
IFIX-SS) 335,335,340
IF IX-CAPAC) 171,171,340
IFIP+IOOOOOO.) 341,600,341
SO=SO+A
IF INR-IOOI 601,602,601
NR=NR-l
GO TO 137
SB=SR+A
GO TO 137
341 CURRPIINDEX)=P
1DEXB=IXB-QI/A +1.5
SIIDEXBI=SS
SS=SS+A
INDEX = INDEX + 1
1FISS-SBI150,150,370
370 DO 372 JK=I,NR
372 PRECPIJK)=CURRPIJK)
OlDSB=SB
OlDSO=SO
OlDA=A
NROlD=NR
DO 378 1=1,41,10
12=1+1
13= 1 +2
14=1+3
15=1+4
16=1+5
17=1+6
T8=1+7
19=1+8
10=1+9
378 PU NCH7 7 , S I 1 ) , S I 12 ) , S I I 3 I ,S I 14 ) , S I I 5 ) , S I I 6 1 ,S I I 7 1 , S I I 8 1 , S ( I 9) ,S I I 0 )
PUNCH 7777, IRECD,M,A,Q,CAPAC,SO,NUMB
IF(NUMB-NU~BR) 80,400,999
400 TYPE 1103,NUMB
TYPE 7778
TYPE 7780
PAUSE
9 TYPE 7779,PlACE
PUNCH 7779, PLACE
IF(SENSE SWITCH 11 3333,3334
TYPE 2222
PUNCH 2222
BE~IN INPUT TO PHASE 2
10 READ 7777, IRECD,M,A,Q,CAPAC,SQ,NUMB
1=41
DO 11 K=l,40tlO
1=1-10
12=1+1
13=1+2
14=1+3
15=1+4
16=1+5
17= I +6
DP
DP
DP
DP
DP
DP
DP
DP
DP
DP
DP
DP
DP
DP
DP
DP
DP
DP
DP
DP
DP
DP
DP
DP
DP
DP
DP
DP
DP
DP
DP
DP
DP
DP
DP
DP
DP
DP
DP
DP
DP
DP
DP
DP
DP
091
092
093
094
09!)
096
097
098
099
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
DP 136
DP 137
DP 138
DP 139
DP 140
DP 141
DP 142
DP 143
DP 144
DP 145
DP 146
DP 147
DP 148
DP 149
DP 150
DP 151
DP 152
DP 153
DP 154
DP 155
DP 156
DP 157
DP 158
DP 159
DP 160
DP 161
DP 162
DP 163
DP 164
DP 165
DP 166
DP 167
DP 168
DP 169
DP-170
DP 171
DP 172
DP 173
DP 174
DP 175
DP 176
DP 177
DP 178
DP 179
DP 180
o
It'
'#' P , M
II
M"
dl
'/
I 'b
It
t, '1'm
11
c
17
18
20
22
23
41
C
C
42
43
C
48
49
51
C
55
52
6999
999
n,!,irj'j"';'k'hWL.".,");
=____________________
.....
t"fM"i'idId!!!:M(jN!jiI"!lJW&itle!f~'i!M!'"fIY"liW¥W'ItW""IIWIWWiIII!iI""""'''_IW!
18=1+7
19=1+8
10=1+9
READ 77.S(IltS(I2hS(I3).S(I4).SII5ltSII6),SII1,.SII8)9S1I9)tSII0)
X = O.
IF(PLACE) 41,41,18
DO 20 I = I.M
IFIPLACE-S(I)) 22.22,20
CONTINUE
X=CAPAC
GO TO 23
EM = I-I
X = Q + A*EM
PLACE = PLACE - X
PUNCH 7777, IRECD,I,~,Q,CAPAC,X
X WILL BE TH[ OPTIMUM NO. OF UNITS TO PRODUCE
IFISENSF SWITCH 1) 42,43
SENSE SWITCH 1 ON TO TYPE ANSWERS AS WELL AS PUNCH THEM
TYPE 7777, IRECD,I,A,Q,CAPAC,X
IF(NUMB-l) 999,48,10
END OF JOB PROCEDURE
TOTAL = BUD - PLACE
PUNCH 7784, TOTAL
IF(SEN~E SWITCH 1) 49,51
TYPE 1784, TOTAL
BUD = BUD - DBUD
PLACE = RUD
SENSE SWITCH 2 ON TO REDUCE BUD BY DBUD AND OBTAIN ALT. SOLN.
PUNCH 1102
IFISENSE SWITCH 2)
55,6999
IF(SENSE SWITCH 3) 52,9
TYPE 1781
GO TO 9
TYPE 1104
~TOP
END
DP
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181
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183
184
185
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188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
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207
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OUT
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~
~
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PARTIAL .DISTRIBUTION LIST
April 1962-March 1963
INDIVIDUAL
IBM OfFICE
DATE
R. Cabell
T. Kallner
R. Smith
W. Sh1mer
R. Evans
J.'Golden
P. McClung
G. Factor
L. Jensen
R.Erwin
L. Smith
G. Wetbal
J. Borches
P. Newman
B. Dzielinsk:
H. Fient
R. Johnson
J. Shevy
W. Allmon
R. Dietz
R. Flood
E. 8r'achett
L. Cannon
M. ltlantan
D. SlmpSCJll
J. Galente
B. Wall.
L. Ruffino
W. Grabe
G. Goodfriend
J. Yellowless
T. Richards
D. Huffinire
R. Reynaert
J. Powers
S. Head
D. Kattwinkel
I. n.bergs
E. Cites
Atlanta, Ed. Center
SBC NYC
Dallas
Galveston
Fort Wayne
Hartford
San Francisco
Seattle Ed Center
Rockford
Flint
WRO
Oslo. Norway
Des Moines
Little Rock
ASDD
Blaricum I Holland
Pittsburgh
Buffalo
Chicago West
Forest Hills
White Plains
Wa shington '
FSD. Washington
ASD Litrary
London. England
ERO
Cambridge
Bethesda
Inglewood
Dist 11
Vancouver
Jacksonville
Elmira
Brussels Belgium
Toledo
Sydney. Australia
West Germany
Montreal
Spain
4/62
4/62
4/62
4/62
Page
I:~'
.4/62
4/62
4/62
4/62
4/62
4/62
4/62
4/62
5/62
5/62
5/62
6/62
6/62
6/62
7/62
7/62
7/62
7/6,2
8/62
8/62
9/62
9/62
9/62
10/62
10/62
10/62
11/62
11/62
12/62
1/63
2/63
2/63
3/63
3/63
3/63
45
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AUJ2lUt. ........._....."-'-___ ................ _ ... ___ ..__ ......
..04310
. . . Rt:lllRN CARRIAyE
04382
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03794 13
lNDXA.INPUT-l
03806 16
JNOXB.INPUT
03818 16
JNDXB,2.10
0383012
J NOXA.2. 10
03842 12
*+21,0.10
03854 16
*+9.1.10,LENGTH 0F THE W0RU BEING W0RKED 0N
03866 11
I Nl)XA ,2
03878 11
' ..... _, .. _ ........ MM
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SM
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AM
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03191 006-2
05806 -6008
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05806 000-2
03875 000-0
03875 000-1
05806
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I"
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INLJXA,INPUT-l
04094 1403791 OOO"-Q
::,.. ')86
16 85806 -60a8
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Q,)334 ':4 Q~8£'" Q~8lJ
01) 346 46 0'J4bb 01200
.0?;31 0
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.__ ~ __• __~_c..Ll1l;.lJik2~._ r~.L_p\.lN(tllti5L-._______ • __ .. -.. _
•
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•
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*
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0'J3(;4 46 O~41tJ DO'ZOO-0';406 ) 1 0') 70b -ooao
. b~'4i 8 i -, oJ?r4 -0000 ...0')430 4r) 0'146& 0006b
0')442 1 7 0'.>706 -0000
6')4,)4 49 0'J4bb 00000
0')466 2~ 0':151"3 0')971
0:'478 2') 0')971 00400
O~ 4'iO 31 0'.>tU8 0')840
0'>')0': 1 L) 0') ')6 'J 00000
0'.> 'J 1'.. 32 O'Jtl3U 00000
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0':>5'>0 33 05916 00000
055()2 49 04~62 00000
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R0IATt TO
*+47,bUFF+132
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10209 00400
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10019 000-0
09940 0994,
09887 00400
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2S 06002 00400
O,7b& 16
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TR
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7.
8.
PART IV - NOI'ES O1i THIS PROGlWol
PART V - INPUl'
A.
Node llumbering
The input to this program contains three types of data cards.
In
III8D;.T
Type
previous programs of this sort the jobs had. to be nU.'llbered
1 and 2 cards may be arranged in a.I\Y desired order.
so that the head of an arrow (J)
"W&S e.b~s
See Appendix A for
greater than the tail (I) of
sample problem input.
that arrow.
In addition input cards had to be in J sequence ,rlthin I
sequence with no missing I values.
TYpe
1 - Heading or description cards
These restrictions allowed checking
~se
arrow diagram logic
are identified by some character in column 1, other than a
by a sequence check of I values and a test of I against
blank or numeric ered
noae
and for 60,000
is 999.
For
20,000 digits the max:llIaa mmiber of Jobs may be less than 1400 for the
b
3 - EDd of the pro.lect
This is the last card in the input deck and should be blank.
reason stated in Part VI - C.
C.
Blanks in
the
total. number of nodes, so it is scaet1mes necessar,y to use the smallest
numbers ava:1l.able for I and J.
type 2
However, the restrictions on max1mum project
Machiiie
Regu1rements
1620
Data Process1Qg
1622
Card Bead
S¥stem
Punch
110 other special features
1623 Additional Core
Memory is optional.
13
14
b~o
9·
10.
the last .Job and halts.
To work the next project press START.
PARr VI - OPERATTIlG INSTRUCTIONS
~ - f.fore than one "last" node
A.
Pl'O@'!! Deck
of sc;xne arrow) bas been found.
!III SPS 118t1Jtg of this program is in Appendix C.
(8 node which is not the tail
Typevr1ter prints the numbers of all but
The condensed
the first "last" node found and halts.
To find the first "last" node
progre cleek (Uat1Ds in AppeDdi.x D) consists of 70 cards numbered
00 through
69
in colUIIIDS
79-80.
Column 1 of card number
62
type out locations 3247-49.
To vork the next project INSERT 16 01095
00016
contains
49 00402, RELEASE, START.
a digit s1gn:l.f'yiJlg the core memol")" size of the computer being used.
Error 3 - M:>re than one "first" node (a node which is not the head of
"2
20,000 Posi tiona
1;:
40,000 Positions
b
60,000 Positions
same arrow) has been found.
Typevriter prints the numbers of all but the
first "first" node found and halts.
out location 3244-146.
B.
f!'S!II!
~ - A loop has been found in the arrow diagram.
Switch
STOP
I,J,D, COST for the first job where the error
I/O
Switch
STOP
earliest start far this Job exceeds the sum. of all JOb times.)
PJ:csNa
Switches
DOt used
Deed DOt be on the loop itself', but DI8l' be on a chain of Jobs which PIUUIes
o FUM
tbrougb ODe of the nodes on the loop.
DePft8S RESBT, place prqp."Ia deck in read bopper,
To read final prcgram c81"d, dePftss REA1lBR ~.
p1"08:l'8
UDdetected as such.
is loaded.
To re. the tiDal c1ata ca:rd, aeprees
locat1oaa
mwa S'.I!ARr.
eJ'l'Ql'S WN cUecovezed,
hopper aDd .blaDk c8Z'ds in paDCb bCJ.ppe~.
.
and cClll,Vllter S'l!ART.
C.
be detected. (i.e. '!'he
This Job
To work the next project press START.
During data pass I a temporary table is set up in
Itooo - 6oOJ.
lltoo Jobs ar
CClIIIP1Iter does errar ~1s aDd either halts ar pr.lDta aD errar _sease·
Data Pass II - If DO
IIIIq"
'l'Jpewr1ter prlit,ts
There 1s a vel")" remote possibility that a type 1 error could go
CCIIIpUter
Data Pus I - Place 4ata declt in read hopper, press B1WJER S'1'ARf aDd
,
For example 'a
series of jObs (1,2), (2,3), and (3,1) would be a loop.
Switch
halts wheJ1
cCllplter ST.AB!f.
00016
STOP
PABITI
Deck -
depress LOAD.
~
To work the next project INSERT 16 01095
49 00402, REIEASE, START.
Procedure
Load
To find the first "first" node type
IIIQl'e
&1.'e
several. tJpe2 aDd
3
to be used to find "first" aDd "last" nodes.
read, this table
IIIIq"
be destroyed.
If
This will cause
error messager however.
place data declt in l'ead
Press BEAlBR fJlA'Br, IUICH STABT,
To read the final cJata ca:rd, depress RBADBR STAJiI!.
Error Me8",S !1!4 Actl.
!!:!::2!:.J: -
AvaUable starase bas been e2lOeeded.
Tbe number of the
,~
highest JMII)ered arrow plus the number of jObs is greater than 1612
(for 20,000 positions of storage).
o
TJpewriter' priJrts I,J,D.COsT for
J5
o
16
o
o
n-
o
12.
11.
PART VIII - SUGGESTIONS
PART VII - ot1l'Pt11'
A deck ot cards s1a1l.ar to the pass II data deck is produced.
type 1 output carda are uncbaDged.
The
trom the data deck in the second data pass.
80.
reports- on
ODe
Prepare a transter card with
56-60
Earliest t1n1sb date
it on top ot the pass 2 deck.
61 - 65
Lt.test start date
second pass.
66-70
Lt.test tin1sb date
B
11-15
Total tloat time
16 - SO
Free tloat time
15
CaDta1na
*
01'T98 0000 in coltDllDs 1 - 32, and place
Press RESET and LOAD to execute another
Least Cost Estimating
Repeated applications of this program will give an idea ot how project
First schedule the project with nonlal.
job time and normal. costs, then caapress the schedule along the er1t1cBJ. path,
it this is a
vh1ch abortens the over-all project time at the expense ot inCreasingSODle
Job costs.
Tbe last output
card 18 a tJpe 1 card COIlta1n1D& project cost and Cecie.l. Output
The second pass of data controls the amount ot output.
The tn>e 2 output cards are identi cal
to iDput in columna 1 - 50, and eonta1n the following calcul.ated
quant1ties in columna 51 -
A
-
autaaat1~ by
of a specialized parametric linear progr&Dlll1ng algorithm.
In either
case a series of project durations are obtained as a f'unction ot direct
Job costa.
By caaibin1ng these with the indirect costs
penalties, etc., the least cost B8¥ be estimated.
J7
18
tor overhead,
13.
14.
PART IX BIBLIOGRAPHY
Arrow
m.-
Pl.aDniDg.
PART X - APPENDIX A
Du Pont - Petrol.eum Chemical.s Division.
"Better Plans CelIe From Study of ADatc:qr of an Engineering Job, "
Busine88 Week, March 21, 1959.
FreeIIIm, R. J., "A GeDer&1.1zed Network Approach to Project A.ctivity Sequencing,"
IRE
'rraDaact1Cl1l8 011
EDgI,neer1Dg MaDageaent I September 1960.
Harting, L. P. and Morgan, J. E.,
PflI.fJ!/FBP
A. D;rDaa1c Project Control
Method, IlI4 Federal Systems Division, Space Guidance Center, OWego, Nev York.
Kelley, J. E., Jr. I "Cr1tical-Path Plam:a1:Dg aDd Sebedul1.D&."
1959 Proceed1ngs
of the Eastern Joint 0c!gPuter Oontereoce.
Kelley, J. E., Jr., "Critical-Path PlaDD.1.Dg aDd Scbeduling
case
Histories,"
Paper presented at ORSA. Natiooal Meeting, Detroit, October, 1960.
Martino, R. L., "Bow
t
Cr1 tical.-Path· Scheduling Works, ..
CIIDad181l Q1emic&l
Proce8.1!s, FebruatT. 1960·
Matye. Tea T. aDd Rieb, Gl.erm K.,
Joumal
at Macb1De.
"PI!lfr/Y1:P
Account1Jlg, ~,
"Rev Tool ror Job ~,"
Pl.aIm1Dg and ~ on BAM,"
1961.
Bnrrfft"!1.!!i
JIen-Becarcl, J8DIIU'Y
26, 1961.
PearbBl, J., "BDglDeer1.ng Progrea PlaI:m1Dg IIIDd Coatrol. 'l'brougb the Use
or PERT," IRE Trlm8acti011S
Serer,
~,
"Space-Age Scheduling
c
!D§1.!leer1Dg !!IIII!tp!!lt I DeCEllber, 1960.
J. S., Kel.le7, J. E., Jr., IIIDd V&llter, M. B., "Critical. Path
Scbedl1l1uB,"
"
OlD.
Juq,
~960.
.Arr:l.Te8
in CPl," aa-tcal. Week, October 15, 1960.
19
~\-\
~_;I
7/19/61.
em
2H
r -':
\.
!
o
o
APPENDIX A -
;:>RO~LEi""l
SAMPLE
SAMPLE PROBLEM ~CHEOl.lLE
-----_._--. ---'-:;:'f':j '-'0
~
10
,
~B._.
'It
~o
~
4
4
5
6
,
300
ERECT
4
7
~o
~50
p~on'~~
2
300
1
25
_. ______J__ 4 .. t_.l.00
_ _ _ _ _ _ _ _ _...-..::I4~A
5
6
,
Inn
6
FF
TF
PI PF
10
6
11 1'-
-------~1.;-1· 1~
1
100
4 -- 300--"INSU[ATt
._ _ _ _ _ _---'1....2...........,,1:...=:~_
I? 14
1, 14
1
50
1
1
J GO
100
ff·--} . ·f06
14 15
LF
nFArTJVATF LJNF
.. __
.
REMOVE OLD PIPE
-1:;-l=----.:2~-:1~t)~O~··WEU,_
.,'
·LS
VALVf-~.
PRFFAR SECTIONS
"PLACt VALVFS---'
800
PLACE NEW PIPE
·----··e
----------:-10-=-.9
EF
S(AF~OLn
6
400
5 1200
E5
DEVELOP MATFQJ AL LIST
9
9
1
J()RC\
MA!..f.-ASS l.§ti~ENr.s. __ ..
_.!..L~!!.Q_~R.~CU~E
. _____ ._ _ _ ._____ .6.... __~ ___ .. __ __
FIGURE 1
LEAl) TIM~
rJME AVAILARLE
MEASURE AND SKETCH
1
1
2
_ _ _ _. ___ .. ..2-2£t
Flr'UT
APi PE '- I NE
REPL·ACEMENT OF
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