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

------

- - -

---~---

44

. 0 A

N1amic

Programming Algorithm

FORTRAN-

'00

W

>-..

1620

GENERAL

PROGRAM

LIBRARY

CoWd, for

Gross

Production Scheduling 10.

-:

26

'.

4~

+ + + + + + + + + +

+'

:

~~+++++++++++

.

;+++++++++++++

'

+++**********

.

+**·********el~

* * * * * * + * * * *

II,

+ + + * + * * * * * *

*~ft

+ * * + + * * + + * * *

Jft:l_

+ * * + * * * + + * +

*b+~

~\

o

A DYNAMIC PROGRAMMING ALGORITHM

FORTRAN

CODED

FOR GROSS PRODUCTION SCHEDULING

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 announce-

ment

occurs,

users

should

order

a complete new

program

from

the

Program

Information

Department.

.

0-""

()

DECK KEY

1. Sample

Problem

0,

1,

2

(Refer

to

Page

17

for

Input

data

listings)

2.

Object Deck

3. Source Deck

------~------------~)

~1

Title:

Author:

Purpose:

Hardware:

Procedure:

Execution

Time:

Source

Language:

Accuracy:

Limitations:

Checkout

~tus:

Comments:

()

PROGRAM

ABSTRACT

A

Dynamic

Programming

Algorithm

FORTRAN

Coded,

for

Gros

s

Production

Scheduling.

John

W.

Burgeson

IBM

340

South

Broadway

Akron

a,

Ohio

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.

40K,

1620

I

Card

I/o,

hardware

divide

Dynamic

programming

algorithm,

described

in

the

body

of

the

write

up.

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.

FORTRAN

with

FORMAT

Usual

a-digit

FORTRAN

Accuracy

N

less

than

or

equal

to

199.

M

less

than

or

equal

to

40.

Checked

out

completely

for

N

up

to

9,

M

up

to

40,

Logically

for

N

up

to

199.

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.

o

~'-\

TABLE

OF

CONTENTS

Section

Title

Page

Number

Introduction

-

The

Problem

II

The

Solution

III

Description

of

the

Algorithm

IV

Problem

Restrictions

a

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

XI

Three

Sample

Problems

17

XII

Listing

of

the

FORTRAN

Source

Deck

31

XIII

Flow

Chart

36

XIV

Listing

of

the

Object

deck

37

xv

Partial

Distribution

List

44

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-

()

II

o

A DYNAMIC PROGRAMMING ALGORITHM«

FORTRAN

CODED,

FOR

GROSS PRODUCTION SCHEDULING

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

I

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.

THE

SOLUTION

Source

Language:

Machinery:

Restrictions:

Execution

Time:

IBM

FORTRAN

with

FORMAT

Card

40K 1620

with

hardware

divide

N

less

than

or

equal

to

199

M

less

than

or

equal

to

40

See

Section

V I

page

10.

III

Description

of

the

Algorithm

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 -

o

~

Table

1

Prod.

1 Pro_d.

2_

..ft0~1

3

Xl

VI (Xl) X2 V2

(X2)

X3

V3

(X3)

0

0.0

10

-1.0

0

0.0

10

1.0

20

0.5

5 0

..

3

20

2.0

30

0.8

10

0.9

30

2.5

40

1.4

15

1.7

50

1.8

20

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.

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.

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

pro-

blem

by

inspection,

however,

not

particularly

fast

ncr

easily.

The

solution

table

for

all

budgets

from 100

to

10

(in

steps

of

10)

is:

Table

2

Budget

Level

of

1

Level

of

2

Level

of

3

t2!!!

. 100 30 50 20

100

90

30

40 20

90

80 20 40 20 80

70

30

20 20 70

60 20 20 20 60

50 20 20 10 50

-40 20 20 0 40

30 10 20 0

30

20 0 20 0 20

10 0 10 0 10

-2-

The

solution

proceeds

as

follqws:

There

are

3

products

(N=8).

We

are

given

Xji

and

V

ji

for

all

produots

and

Budgets

of

100,

~O,

80

••••

,

10~

We

first

set

up

what

is

called

Tableau

*3.

(831

..

) 0

(S32

..

) 5

(S33

..

) 10

(8

34

..

) 15

(8

35

11:)

20

X

31

-0-

X32

-5

,

Table

3.

X33

10

X

34

15

X35

20

P3

XB3

Where

the

8

3k

are

the

amounts

of

unassigned

budget

we

have

left

after

the

assignment

of

production

levels

to

Products

1

and

2.

Since

we

have

no

knowledge

at

this

time

how

much

this

will

be,

we

must

evaluate

all

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

Y

jik

• (The

element

in

the

th

til

th

k

row

and

the

1

column

of

the

j

tableau)

A.

B.

c.

fF)

Y

jik

does

not

exist

for i

greater

than

k,

for

if

we

have,

say,

only

5

left

of

our

budget

after

aSSigning

~oducts

1

and

2,

we

cannot

consider

the

possibility

of

producing

10

of

product

3.

Define

P n + 1

(any

argument)

= 0

for

an

N-Product

problem

Y

jik

..

V

ji

+ Pj+ 1 (Sjk -Xji)

-3-

()

That

is,

in

calculating

any

Y

jik

I

we

obtain

first

of

all

tke

corresponding

V

ji

from

the

input

data.

This

V

ji

corresponds

to

some

>e.ii.

\Ve

nem

subtract

from

the

Sjk

of

tp.e

row

we

are

WQl;'king

on,

this

Xji'

obtaining

an

argument

Sj+

i.m

with

~hiCh

to

find

a Pj+

lin

tha

tub,ie

of

P's

of

the

precedina

tableau.

In

numbers,

if

we

have

40 (=SJk)

to

assign,

we

assign

10

(=X

ji

)

we

have

left

ao.

Opposite

30 (=8j+

I,

-cd

in

the

precedina

tableau

obtain

a P

to

use

in

computation.

D.

Pjk

..

max

(Y1ik)

(i

=

1,

2,

...

,k)

E. XBjk

I:

the

Xji

where

this

maximum

is

found.

With

the

above

formulae,

Tableau

*3

is

generated

(trivial

case)

8S;

Table

4

X

31

X32

X33

X

34

~

Pa

XBa

Sal

= 0

.0

0

Sa2

= 5

.0

.3

5

S33 = 10

.0 .3

.9

10

8

34

= 15

.0

.3

.9

1.7

15

835

= 20

eO

.3

.9

1.7

'

1.8 1.8

20

Now,

saving

the

P3

and

XB3

vectors

only,

Tableau

*2::

is

generated.

Table

5

X21 X22

~3

X24 X25 P2

XB2

821 = 10

-1.0

10

S22 =

20

-0.1

0.5 0.5

20

823 = 30

0.8

1.4

0.8

1.4

20

8

24

= 40

0.8

2.3

1.7 1.4

2.3

20

(Table 5

continues

on

the

following

page.)

-4-

C /

?

0

Table 5 (Continued)

X

Z1

X22 X23 X24

~s

P2

XB

2

825 = 50

0.8

2.3

2.6

2.3

L8

2.6

30

826

=

60

0.8

2.3

2.6

3.2

2.7

3.2

40

827 =

70

0.8

2.3

2.6

3.2

3.6 3.6

50

As

an

aid

to

following

the

mathematics,

the

calculations

necessary

are

included

as

follows:

Y211

to:

V21 + P

3l

=

-1.0

+

.0

=

-1.0

Y212 =

V21

+ P33 =

-1.0

+

.9

=

-0.1

Y222 = V22 + P31 =

0.5

+

.0

=

0.5

Y

2l3

= V

2l

+ P

3S

=

-1.0

+

1.8

=

0.8

Y223=V22+

P33

=0.5+

0.9=1.4

Y233=V23+

P

3l

=0.8+

.0=0.8

Y214

-V

21 + P3S =

-1.0

+

1.8

=

0.8

Y224=V

22 + P3S

=0.5+

1.8=2.3

Y23

4::

V

23+

P33

=0.8+

.9=1.7

Y

244

= V

24

+ P

31

=

1.4

+

.0

=

1.4

Y2lS

=

V21

+ P3S =

-1.0

+

1.8

=

0.8

Y22S =

V22

+ P3S =

0.5

+

1.8

=

2.3

Y23S =

V23

+ P

3S

=

0.8

+

1.8

=

2.6

Y24S = V24 + P33 =

1.4

+

0.9

=

2.3

Y255

=V25

+ P31 =

1.8

+

.0

=

1.8

-5-

0 o

Y216 = V21 + P

3S

=

-1.0

+

1.8

=

0.8

Y226 = V

22

+ P

3S

=

0.5

+

1.8

=

Z.3

Y236=V23+

P35

=0.O+

1.8=2.6

Y246=V24+

P35

=1.4+

1.8=3.Z

Y2S6 = V25 + P33 =

1.8

+

0.9

=

2.7

Y217

=V

21 + P

3S

=

-1.0+

1.8=0.8

Y227 = V22 + P35 =

0.5

+

1.8

=

2.3

Y237=V23+

P

3S

=0.8+

1.8=2.6

Y247 = V24 + P

3S

=

1.4

+

1.8

=

3.2

Y257 = V

2S

+ P

3S

=

1.8

+

1.8

=

3.6

P21 =

max

(-1.0)

=

-1.0

P22 =

max

(-0.1,

0.5)

=

0.5

P23 =

max

(0.8,

1.4,

0.8)

::

1.4

P 24 = max

(0.

8,

2.3,

1.7,

1.4)

=

2.3

XB

21 = 10

XB22

= 20

XB23

:: 20

XB24

= 20

P

2S

=

max

(0.8,

2.3, 2.6, 2.3,

1.8)

::

2.6

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

= 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 PI

XB1

811 ::

10

-1.0

0

812

= 20

0.5

0.0 0.5

0

813 :; 30

1.4

1.5

LO

1.5

10

(Table

6

continues

on

the

following

page.)

-6-

Table

6

continued

Xl!

X22 X23 X24

!1

XBl

S14 = 40

2.3

2.4

2.5

1.5

2.5

20

S15 = 50

2.6

3.3

3.4

2.9

3.4

20

S16

==

60

3.2

3.6

4

..

3

3.9

4.3

20

817

==

70

3.6

4'.2

4.6

4.8

30

S18 =

80

3.6

4.6

5.2

5.1

5.2

20

819 = 90

3.6

4,6

5.6

5.7

30

S110 = 100

3.6

4.6

5.6

6.1

30

At

this

point

we

are

completed

with

Phase

1

of

the

problem.

The P

vectors

are

forgotten

(although

PI

does

show

the

actual

profits

for

each

possible

"budget"

from 10

to

100.)

The

XB

data

has

been

put

out

on

intermediate

cards

(or

tape).

Phase

Z

of

the

problem

reads

this

XB

data

back

into

the

machine

to

determine

the

actual

schedule

....

Collecting

the

data

fa

Phase

2:

Opposite

the

"budget"

in

the

Slk

vector

read

XBlkl

the

optimum number

of

Product

1

to

be

scheduled.

Budget = Budget -

XBlk

Opposite

"budget"

in

the

SZk

vector

read

XB

2k,

the

optimum number

of

Product 2

to

be

scheduled.

Budget = Budget -

XB2k

Opposite

"budget"

in

the

S3k

vector

read

XB3k'

the

optimum number

of

Product 3

to

be

scheduled.

End

of

Phase

2.

-7-

o o

IV. Problem

Restrictions

1.

As

can

be

~een

from

the

description

in

Part

III,

the

Sj

vector

grows

with

arithmetic

rapidity.

It

goes

in

,eac!}

Tableau

from

some

lower

pound (

S0

j>

to

some

upper

bound (

3B

j)

in

steps

2.

of

Aj

where

Aj

is

defined

as

the

incremental

step

of

production

level

for

product

j •

Two

bounds

can

immediately

be

put

on

this

S j

vector.

There

is

no

gain

in

allowing

SB

j

to

exceed

the

budget

(BUD).

Similarly,

if

Qj

is

defined

as

the

lowest

feasible

production

level

of

product

j,

then

certainly

S0

j

need

never

be

consi-

dered

below:

SUMQ = Qj + Qj+ 1 +

•••

+

Qn.

Therefore:

F.

SB

j

is

less

than

or

equal

to

BUD

for

all

j

G.and

S0

j

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,

within

the

program a

careful

watch

is

kept

on

this

vector

..

It

1s

never

allowed

to

exceed

100

entries,

regardless

of

formulae F

and

G.

Whenever

it

threatens

to

do

so,

a

cal-

culation

is

made

which

locates

the

~

of

the

Sj

vector

at

a

"most

likely

position"

for

use

in

Phase

2,

the

reverse

search.

Within

the

program,

this

is

accomplished

by

bringing

in

the

input

datum

A2j

(average

of

month's

demand)

for

each

product

and

keeping

a sum

(SUMA2)

of

this

data.

-8-

o

~

o

When

the

Sj

ve~or

gets

out

of

bounds

(more

than

100

entries),

the

statements:

121 K =

S0

MIN/A + (SUMA2/BUD) *

(SB-S0-100.

*A)

/A

S0=K

S0

l:I

S(2f*A

SB:II

sQ1

~

99.*A

are

used

as

a

(heuristic)

method

of

keeping

the

Sj

vector

centered

around a

"most

likely"

region.

You

can

see

the

results

of

this

action

in

Section

IX.

To

an

extent,

this

procedure

threat~ns

to

disturb

optimality

of

the

solUtion,

Since

if

we

miss

the

solution

point

by more

than

50.

*~

we

will

underschedule

some

product(s)

and

overschedule

others.

Experimentally,

however,

using

"live"

data,

it

does

not

appear

that

we

have

any

problem

at

this

pOint.

A

second,

somewhat

more

severe

restriction

has

been

built

into

the

program.

The

algorithm,

as

presented

in

Section

III,

calculates

all

Y

jik

of

the

tri-angular

array.·

As

programmed,

not

all

of

these

are

computed.

As

the

program

proceeds,

row

by

row,

each

time

it

finds

a maximum

row

entry,

it

stores

this

entry

in

P

jk

and

the

corresponding

X

ji

in

XB

jk

•

When

starting

the

it

does

not

start

with

column

1,

but

with

that

column where

the

maximum

was

found

in

the

last

row.

Because

of

this,

admittedly

arbitrary,

rule,

the

machine

solution

to

our

sample

problem 0

(Section

X)

varies

from Table 2

insofar

as

the

budget

of

80

is

concerned.

-9-

o

~

Once

again,

experimentally,

it

appears

that

th

is

testrlcUon

does

not

affect

the

final

solution

to

any

s1gnificant

degree.

A

third

restriction

of

sorts

has

been

used

in

th~s

model

im-

pl1citly

all

along.

This

restriction

concems

possible

values

of

the

parameter

Aj• Values

of

~

used

with

this

algorithm

must

be commensurate

with

one

another.

They may

all

be

the

same;

if

they

differ I

the

larger

Aj

must

be

integer

multiples

of

all

smaller

~.

Typical

values

of Aj might

be:

2,

4,

8,

16,

32,

64,

128,

or

25,

50,

100,

200,

400,

••••

In

entering

data

into

Phase

1,

the

products

must

be

sorted

in

order

of

increasing

Aj•

V. Running Times

and

Economics

The

question

is

naturally

raised

""Vhy

the

(arbitrary)

restrictions

on

Sj?"

The

answer

to

this

question

lies

in

the

fact

that

this

is

not

a

speedy

algorithm.

The

running

times

for

the

three

problems

described

in

Section

X were

observed

to

be:

(exclusive

of

typing)

Prob 0

phase

1

0.6

min.

phase

2

0.3

min/pass

Prob 1

phase

1

2.8

min.

phase

2

0.8

min/pass

Prob 2

phase

1

36.0

min.

phase

2

0.8

min/pass

Extending

these

times

analytically

to

a computer

with

tape

I/O

in

the

705/7070

class,

(and on

the

basis

of

observations

made on

"live"

problems on

this

size

machine)

it

is

observed

that

fairly

long

machine

-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

of

such

a

problem.

Using

restriction

2

in

Part

IV

again

halves

the

running

time,

and

see~s

to

be

economically

sound.

This

program

approach

te(!Ufres

that

profit

(or

cost)

figures

be

cal-

culated

for

each

product

for

each

feasible

production

level.

This

is,

of

course,

no

trivial

job.

Meaningful

figures

must

be

found for

such

items

as

back

ordet

costs,

set-up

costs,

and

inventory

carrying

costs.

The

cost

picture.·fer

any

product

is

a

complex

function

of

these

three

items

considered

along

with

such

factors

as:

demand

pattern

forecast

quantity

on

hand

quantity

in

production

facility

sharing

with

other

products

and

others.

Obtaining

meaningful

figures

of

this

nature

is

probably

the

hardest

Part

of

an

O.

R.

man's

job

if

he

is

to

use

this

or

any

other

s1mllar

algorithm

for

his

scheduling.

Nonetheless,

the

job

can

be,

and

has

been,

done

successfully.

It

appears·

that,

on

the

basis

of

many

tests

with

different

cost·

,function

generators,

that

as

long

as

all

products

are

computed

on

the

same

baSiS,

the

final

schedules

do

not

show

much

deviation.

Schedules

obtained

with

this

program

have

been

cos

ted

out

against

actual

schedules

"made

by

hand.

/I

In

all

cases

tested

the

savings

were

very

considerable.

-11-

c o

VI.

Operation

Notes«

Data

Description

Input

to

the

progralll

cons

ists

of:

1.

2.

3.

One problelll

header

card

containing

according

to

the

Format

U4,FIO.0,FI0.0,30H),

NUMBR

b"ing

the

No.

of

products

being

scheduled

,

BUD

"budget",restriction

on

total

units

to

be

scheduled

DBUD

Reduce

BUD

by

DBUD

for

alternate

solutions

_ 30H up

to

30

alphanumeric

problem

identification

One

product

header

card

per

product

containing

according

t-o

the

FDrmat (20

HIS,

IS,F8.0,F8.0

,F8.0),

20H up

to

20

alphanumeric

product

identification

IREeD Product

identifier

(stock

number?)

M

No.

of

production

levels

to

be

considered

A

increment

size

between

production

levels

Q minimum

production

A2

average

demand

From 1

to

4

product

profit

(cost)

cards,

each

containing.

up

to

10

numbers.

For

12.

M

£10,

one

card

will

be

required,

for

c

1l~£20,

two

cards,

etc.

Format (lOF?

.0).

Output from

the

program

is

in

two

parts,

complete

with

typed

instructions.

The

output

from

phase

1

is

reverse-sorted

on

cc

78-80

and

used

as

input

to

phase

2.

Output from

phase

2

is

on

cards

and,

with

proper

sense

switch

settings,

on

the

typewriter

as

well.

Output

is

identified

by

column

headings

and

header

mes

sages.

-12-

o

Sense

switch

settings:

i on

to

type

final

answers

on

typev..Titer

2

on

to

obtain

alternate

solutions,

phase

2.

3

on

to

obtain

all

messages

from

the

program,off

to

bypass

many of

them

4

unused.

Section

IX

is

a

typewriter

log

(sample problem

2)

taken

with

1 off;

2

on

for

three

passes

of

phase

2,

then

off; 3

on.

VII. Key

to

Abbreviations« Symbols

1s

an

index,

running

from 1

to

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

CAPACj

is

the

maximum

level

(=OJ

+ A*(Mj-1)

V

ji

~i

BUD

Sjk

are

the

profits

(costs)

associated

with

the

levels

i =

1,2,

•••

, m

fa

each

product

are

the

possible

levels

themselves.

x

=0

j1

j

X

j2

= Qj + Aj

~

3 =

OJ

+

Aj

+

Aj

etc.

is

the

"budget"

for

the

total

SUM

(Xjl)

are

the

possible

amounts

of

unassigned

BUD

left

after

aSSigning

products

1,

2,

•••

,j-1.

-13-

o

y

jik

P

jk

XB

jk

S¢

SB

NR

o

are

the

profits(costs)

associated

with

particular

S

and

X

are

the

max

(Y

)

for

i::

1,2,

••••

k

jik

are

the

X

where

the

maximum

is

found

ji

is

the

lowest

S

for

any

j

jk

is

the

highest

S for

any

j

jk

is

the

number

of

S

rows

for

any

j

jk

ji

VIII

Miscellaneous«

Key

to

Decks

A.

B.

c.

",

The

program

is

written

to

accept

and

use

profit

data.

It

is

sometimes

more

convenient

to

use

cost

data

0

This

may

be

done

in

two

ways:

1.

Keep

the

program

as

is,

add

to

each

cost

datum

before

input

a

fictitious

profit,

for

example,

'Y.

k =

cost

+

$10.

OO*X··

J1 J1

2.

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.

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-

D,YNAM

I C

PROG

MODEL

1;1'-~j,?

-

f~

()

NO.

3

BUDGET

110.

DBUD

10.

SAMPLE

PROB

0

NAME

IRECD

M

INCRE

MIN

QTY

.-.

NO

3 1940

DESOTO

3 5

5.

s0

= .

SB

= 20.

NR

==

5

NO

2 1937

CADILLAC

2 5 10. 10.

r'"

s0

==

10.

S8

= 70.

NR

==

7

NO

1

19lt8

JAGUAR

4 10.

S0

=

10.

S8

==

100.

NR

=

10

c---

C

PHASE

1

COMPLETED

3

ITEMS

SCHEDULED

-

SORT

QUTPUT

IN

RVERSE

SEQUENCE

ON

CC

78-80

.,

THEN

HIT

START

TO

BEG

I N

PHASE

2

3

BEGIN

PHASE

2,

8UDGET

= 110.

':)

RERUN

INTERMED.

CDS.

FOR

ALT.

SOLN.

BEGIN

PHASE

2,

8UDGET

==

100.

'-"

RERUN

INTERMED.

CDS.

FOR

ALT.

SOLN.

BEGIN

PHASE

2,

BUDGET

= 90.

~

RERUN

INTERMED.

CDS.

FOR

ALT.

SOLN.

BEGIN

PHASE

2,

BUDGET

==

80.

RERUN

INTERMED.

CDS.

FOR

ALT.

SOLN.

BEGIN

PHASE

2,

BUDGET

= 70.

RERUN

INTERMED.

CDS.

FOR

ALT.

SOLN.

BEGIN

PHASE

2,

BUDGET

==

60.

RERUN

INTERMED.

CDS.

FOR

ALT.

SOLN.

BEGIN

PHASE

2,

BUDGET

50.

_~:~

OF

JO~

IS

CAPAC

AVG

OEM

20. 10.

50. 10.

30. 10.

0

DYNM11

C

PROG

tvlODEL

:II

-f1pC"''';~1-

I

..

~

-

f~lf"'"

1.

NO.

9

DBUD

BUDGET

3000. 200.

PROS.

NO.1

FOR

D.P.

NAME

IRECD

M

INCRE

PROD

WIDGIT

1 5 25.

SO

= 25.

SB

= 125.

NR

=

PROD

2

FRAMIS

2 3 25.

so

= 25.

SB

==

175.

NR

=

PRao

a

QuaTl

BIT

3 7

50.

SO

==

SB

...

500.

NR

=

SO

==

50.

SB

==

500.

NR

...

PROD

4

GREEB

STALL

4

10

50.

SO

..

50.

SB

= 950.

NR

...

PROD

5

GRANCH

5

11

50.

SO

= 100.

SB

= 1550.

NR

...

SO

= 150.

SB

= 1550.

NR

=

PROD

6

GRUNK

PITS

6 9 100.

SO

= 200.

SB

...

2500.

NR

...

SO

= 300.

SB

= 2500.

NR

...

PROD

7

ANBER

STEM

7 ' '6' too.

SO

= 200.

SB

...

3000.

NR

=

SO

= 400.

SB

...

3000.

NR

=

PRaD

8

RONTER

GUY

8 6 200.

SO

= 400.

SB

= 3000.

NR

...

SO

= 600.

SB

= 3000.

NR

=

PROD

9

BINT

DUP

9 4 400.

so = 400.

SB

= 3200.

NR

=

SO

==

800.

SB

= 3200.

NR

.=

PHASE

1

COMPLETED

9

ITEMS

SCHEDULED

MIN

QTY

CAPAC

25. 125.

5 50.

7 300.

11

10

450.

19

100.

"600.

30

29

100. 900.

24

?3

-

._.

·loo(f.- -

15

14

200. 1290.

14

1.3

12-00.

8

7

saRT

aUTPUT

IN

RVERSE

SEQUENCE

aN

CC

78-80

THEN

HIT

START

TO

BEGIN

PHASE

2

BEGIN

PHASE

2,

BUDGET

= 3000.

RERUN

INTERMED.

CDS.

FOR

ALT.

SOLN.

BEGIN

PHASE

2,

BUDGET

==

2800.

RERUN

INTERMED.

CDS.

FaR

ALT.

SOLN.

BEGIN

PHASE

2,

BUDGET

= 2600.

BEGIN

PHASE

2,

BUDGET

==

2400.

BEGIN

PHASE

2,

BUDGET

= 2200.

BEGIU

PHASE

2,

BUDGET

= 2000.

BEGIN

PHASE

2,

BUDGET

= 1800.

BEGIN

PHASE

2,

BUDGET

= 1600.

END

OF

JOB

16 0

AVG

OEM

14.

8.

14.

35.

90.

120.

'155.

.0

DYNAMIC

PROG

MODEL

x

+-,ff,..,.;l:""

''1 -

I\.ol.l~

2 0

NO.

8

BUDGET

8000.

DBUD

100.

PROBLEM

2

FOR

D.

P.

NAME

fRECD

M

INCRE

MI

N

QTY

BOLTS

U/4

UN

NO

3 1

40

50.

so

= 100.

SB

= 2050.

NR

=

40

SCREWS

NO

18

LONG

2

40

50.

SO

= 100.

SB

= 4000.

NR

=

79

LOCOMOTIVE,

STEAM

3

40

50.

SO

= 150.

SB

= 5100.

NR

=

100

SO

= 200.

SB

= 5150. .

NR

= 100

LOCOMOTIVE,

DEISEL

4

40

50.

SO

= 250.

SB

= 5200.

NR

=

100

EYEGLASS

FRAME,

BRN

5

10

50.

SO

= 300.

SB

= 5250.

NR

=

100

LAMBSKIN

TURBAN

6

10

50.

SO

=

350.

SB

= 5300.

NR

= 100

1620

COMPUTER

7

20

100.

SO

=

500.

SB

= 750Q.

NR

=

71

SO

= 600.

SB

= 7500.

NR

=

70

SO

= 700.

SB

= 7500.

NR

=

69

HAIRPIN,

NO

6

BLACK

8

40

200.

SO

= 600.

SB

= 8000.

NR

=

3B

SO

=

BOO.

SB

= 8000.

NR

=

37

PHASE

1

COMPLETED

B

ITEMS

SCHEDULED

SORT

OUTPUT

IN

RVERSE

SEQUENCE

ON

CC

7B-80

THEN

HIT

START

TO

BEGIN

PHASE

2

BEGIN

PHASE

2,

BUDGET

=

BEGIN

PHASE

2,

BUDGET

=

BEGIN

PHASE

2,

BUDGET

=

BEGIN

PHASE

2,

BUDGET

=

BEGIN

PHASE

2,

BUDGET

=

-.

BEGIN

PHASE

2,

BUDGET

=

BEGIN

PHASE

2,

BUDGET

=

BEGIN

PHASE

2,

BUDGET

=

END

OF

JOB

STOP

BOOO.

7900.

7800.

7700.

7600.

7500.

7400.

7300.

100.

50.

300.

CAPAC

AVG

OEM

2050. 100.

1950. 200.

2000.

1950. 100.

500. 600.

450. 200.

2200. 350.

7800. 360.

17

c

-------_._--_.

__

._---

-

-.---.------.-.-

..

,,--,---.-,-

..

-~-.

...........

"_"

...

~~w

....

_."

••

".,

.....

~

______

~,

.....

_

........

__

~.,

......

,

........................

"'

•••

.L_

.........

___

:r'Meu.+

,j

..

+...

10?

3

110.

10.

SAMPLE

PROS

0

DP

501

NO

3

1940

DESOTO

3 5

5.

O.

10.

DP

502

..

___

.M_

.

.3

.9

1.7

1.8

DP

503

NO

2

1937

CADILLAC

2-

··5"--10.

·-10;--·

---rC5;··

DP

51)4

-1.

.5 .8

1.4

1.8

DP

505

NO

1

1948

JAGUAR

1 4

10.

o.

10.

DP

506

~

0

1.

2.

2.5

DP

507

~

O ...

ir·~··~

.~.--

c..

BEGIN

PHASE

2,

BUDGET

=

110.

017

I>

18

.l

19

PROD.

NO.

LEVEL

INCRE

MIN

aTY

CAPAC

SCHEDULE

020···

~

21

Qc)

NO

1

1948

JAGUAR

1 5

10.

30. 30.

022

"

NO

2

1937

CADILLAC

2 6

10.

50.

023

NO

3

1940

DESOTO

3 6

5.

20.

024

I

25

...

TOTAL

100.

026

-

27

--

28

I

29

'"

30

31

BEGIN

PHASE

2,

BUDGET

=

100.

032

33

34

PROD.

NO.

LEVEL

INCRE

MIN

aTY

CAPAC

SCHEDULE

035

36

NO

1

1948

JAGUAR

1 4

10.

30.

037

11.10

2

1937

CADILLAC

2 5

10.

50. 50.

038

NO

3

1940

DESOTO

3 5

5.

20. 20.

039

40

TOTAL

100.

041

42

43

44

45

46

0

BEGIN

PHASE

2,

BUDGET

=

90.

047

48

49

PROD.

NO.

LEVEL

INCRE

MIN

aTY

CAPAC

SCHEDULE

050

51

NO

1

1948

JAGUAR

1 4

10.

30.

052

NO

2

1937

CADILLAC

2 4

10.

50.

40.

053

NO

3

19"40

DESOTO

3 5

5.

20.

054

55

TOTAL

90.

056

57

58

59

60

61

BEGIN

PHASE

2,

BUDGET

=

80.

062

63

64

PROD.

NO.

LEVEL

INCRE

MIN

aTY

CAPAC

SCHEDULE

065

66

NO

1

1948

JAGUAR

1 4

10.

30.

067

NO

2

1937

CADILLAC

2 3

10.

50.

30.

068

NO

3

1940

DESOTO

3 5

5.

20.

069

70

TOTAL

80.

071

72

73

74

.....

75

~

76

BEGIN

PHASE

2,

BUDGET

=

70.

077

78

79

PROD.

NO.

LEVEL

INCRE

MIN

aTY

CAPAC

SCHEDULE

080

81

NO

1

1948

JAGUAR

1 4

10.

.

30

•

30.

082

NO

2

1937

CADILLAC

2 2

10.

50.

20.

083

0

NO

3

1940

DESOTO

3 5

5.

20.

084

85

TOTAL

70.

086

87

88

89

90

91

---_

..

"'----- -

t»

T.I_~.t1\

"\

(',

..-.

J_

I.' f.I,

L:

BEGIN

PHASE

2,

BUDGET

=

60.

092

93

94

PROD. NO.

LEVEL

INCRE

MIN

Cly

CAPAC

SCHEDULE

095

96

CI

NO

1

1948

JAGUAR

1 3

10.

30.

20.

097

NO

2

1937

CADILLAC 2 2

10.

50.

20.

098

NO

3

1940

DESOTO

3 5

5.

20.

2 o.

099

100

TOTAL

60.

101

102

103

104

105

106

BEGIN

PHASE

2,

BUDGET

=

50.

107

108

109

PROD. NO.

LEVEL

INCRE

MIN

OTY

CAPAC

SCHEDULE

110

111

NO

1

1948

JAGUAR

1 3

10.

30.

20.

112

NO

2

1937

CADILLAC 2 2

10.

50.

20.

113

NO

3

1940

DESOTO

3 3

5.

20.

10.

114

115

TOTAL

50.

116

117

N

118

119

c:::

120

121

BEGIN

PHASE

2,

BUDGET

=

40.

122

123

124

PROD. NO.

LEVEL

INCRE

MIN

OTY

CAPAC

SCHEDULE

125

126

NO

1

1948

JAGUAR

1 3

10.

30.

20.

127

NO

2

1937

CADILLAC 2 2

10. 10.

50.

2 O.

128

NO

3

1940

DESOTO

'3

1

5.

20.

129

130

TOTAL

40.

131

132

133

134

135

136

OJ

BEGIN

PHASE

2,

BUDGET

=

30.

137

138

139

PROD. NO.

LEVEL

INCRE

MIN

OTY

CAPAC

SCHEDULE

140

141

~O

1

1948

JAGUAR

1 2

10.

.

,0.

10.

142

NO

2

1937

CADILLAC 2 2

10. 10.

50.

20.

143

NO

3

1940

DESOTO

3 1

5.

2(1.

144

145

TOTAL

30.

146

147

148

149

150

151

BEGIN

PHASE

2,

BUDGET

=

20.

152

153

154

PROD. NO.

LEVEL

INCRE

MIN

OTY

CAPAC

SCHEDULE

155

156

NO

1

1948

JAGUAR

1 1

10.

30.

157

NO

?

1937

CADILLAC 2 2

10. 10.

50.

20.

158

NO

3

1940

DESOTO

3 1

5.

20.

159

160

TOTAL

2 o.

161

N

162

....

163

164

165

166

BEGIN

PHASE

2,

BUDGET

=

10.

167

168

169

PROD.

NO.

LEVEL

INCRE

MIN

OTY

CAPAC

SCHEDULE

170

171

NO

1

1948

JAGUAR

1

10.

.

30

•

172

0

NO

2

1937

CADILLAC 2

10.

50.

10.

173

NO

3

1940

DESOTO

3

5.

20.

174

175

TOTAL

10.

176

r.l

S4"f/~

,"0"

I('ta(

0 .

--1

I

..

p

......

So.Yt\t'e

1'

....

"",..

.1..

.1_

U

I~

U

C.I

9

3000.

200.

PROBe

NO. 1

FOR

D.P.

DP

508

PROD

1

WI

DGIT 1 5

25. 25.

14.

DP

509

35.

36.

37.

39.

39.5

DP

510

0

PROD

2 FRAMfs -

---2

-3

.

·-2~-~

·---6

.-----

--~--

8-;-----

'" -

.-

-.~--

...

_--

---

-----DP--5Ti----

--"-,,-,,,.---.--

.62

.75

.88

DP

512

PROD

a

QUOTL

BIT 3 7

50.

o.

_.

14.

OP

51:3

5.

5.2 5.3

5.6

5.8

5.81

5.9

DP

514

PROD

4

GREEB

STALL 4 10

50.

o.

:35.

DP

515

21. 22.

23.

25.1

25.6

27.2

29.1

30.

31.2

35.7

DP

516

PROD

5

GRANCH

5

!i-

56. -1'00;---

35.

(jp

511-

1.

2.

3.

5.

7.

9.

10.1

10.4

DP

518

11.01

DP

519

PROD

6

GRUNK

PITS

6 9

100. 100.

90.

DP

520

8.17

8.34

8.8

8.99

9.12 9.76

10.21

12.43

15.

DP

521

PROD

7

ANBER

STEM

7 6

200.

o.

90.

DP

522

11.

13.1

15.17

19.22

26.4

25.8

DP

523

PROD

8

RONTER

GUY

8 6

200. 200.

120.

DP

524

-18.

18.

18.3

18.33

19.04

29.99

DP

525

PROD

9 BINT

DUP

9 4

400.

o.

155.

DP

526

28.1

28.

27.

28.5

DP

527

~

OC4~f""~

BEGIN

PHASE

2,

BUDGET

=

3000.

233

234

i ;

235

'"

PROD.

NO.

LEVEL

INCRE

MIN

QTY

CAPAC

SCHEDULE

236

237

PROD

9 BINT

DUP

9 1

400.

1200.

238

PROD

8

RONTER

GUY

8 6

200.

1200.

239

PROD

7

ANBER

STEM

7 5

200.

1000.

800.

240

PROD

6

GRUNK

PITS

6 1

100.

900.

100.

241

PROD

5

GRANCH

5 6

50.

100.

600.

350.

242

PROD

4

GREEB

STALL

4

10

50.

450.

243

PROD

0 QUOTl BIT 3 1

50.

300.

244-

PROD

2

FRA~lI

S 2 1

25.

50.

245

PROD

1 WIDGIT 1 4

25. 25.

125.

100.

246

247

TOTAL

3000.

248

249

250

0

251

252

253

BEGIN

PHASE

2,

BUDGET

=

2800.

254

255

256

PROD.

NO.

LEVEL

INCRE

MIN

QTY

CAPAC

SCHEDULE

257

258

PROD

9 BINT

DUP

9 1

400.

1200.

259

PROD

8

RONTER

GUY

8 6

200.

1200.

260

PROD

7

ANBER

STEM

7 4

200.

1000.

600.

261

PROD

6

GRUNK

PITS

6 1

100. 100.

9(,)0.

100.

262

PROD

5

GRANCH

5 6

50.

100.

600.

350.

263

PROD

4

GREEB

STALL 4

10

50.

450. 450.

264

PROD

()

QUOTl BIT 3 1

50.

30t').

265

PROD

2 FRAMIS 2 1

25.

50.

266

PROD

1 WIDGIT 1 4

25. 25.

125. 100.

267

268

TOTAL

2800.

269

270

271

272

~-

273

274

BFGIN

PHASE

2,

BUDGET

=

2600.

275

276

277

PROD.

NO.

LEVEL

INCRE

MIN

QTY

CAPAC

SCHEDULE

278

279

PROD

9 BINT

DUP

9 1

400.

1200.

280

PROD

8

RONTER

GUY

8 2

200.

1200.

400.

281

PROD

7

ANBER

STEM

7 5

200.

1000.

800.

282

PROD

6

GRUNK

PITS

6 1

100.

900.

100.

283

PROD

5

GRANCH

5 11

50.

100.

600.

284

PROD

4-

GREER

STALL

4

10

50.

450.

285

PROD

0 QuOTl BIT 3 2

50.

300.

50.

286

PROD

2 FRAMIS 2 4

25.

50.

287

0

PROD

1 WIDGIT 1 6

25. 25.

125.

288

289

TOTAL

2575.

290

291

292

293

294

295

BEGIN

PHASE

2,

BUDGET

=

2400.

296

297

298

PROD.

NO.

LEVEL

INCRE

MIN

aTY

CAPAC

SCHEDULE

299

300

PROD

9

BINT

DUP

9 1

4nO.

1200.

301

C

PROD

8

RONTER

GUY

8 2

200.

1200.

400.

302

PROD

7

ANBER

STfM

7 5

200.

1000.

800.

303

PROD

6

GRUNK

PITS

6 1

100. 100.

900.

100.

304

PROD

5

GRANCH

5 9

50.

100.

600.

500.

305

PROD

4

GREEB

STALL

4

10

50.

450.

306

PROD

a

QUOTL

BIT 3 1

50.

300.

307

PROD

2

FRAMIS

2 2

25.

50.

25.

308

PROD

1

WIDGIT

1 5

25. 25.

125.

309

310

TOTAL

240n.

311

312

313

314

315

316

BFGIN

PHASE

2,

RUDGET

=

2200.

317

318

319

PROD.

NO.

LEVEL

INCRE

MIN

QTY

CAPAC

SCHEDULE

320

i\:

321

.....

,

PROD

9

BINT

DUP

9 1

400.

1200.

322

PROD

8

RaNTER

GUY

8 2

2nO.

200.

1200.

400.

323

PROD

7

ANBER

STEM

7 5 2()O.

10no.

800.

324

PROD

6

GRUNK

PITS

6 1

100.

10

o.

900.

100.

325

PROD

<;

GRANCH

5 6

50.

100.

600.

3') C,.

326

PROD

4

GREER

STALL

4

10

50.

450.

327

PROD

0

QUOTL

BIT 3 1

50.

300.

328

PROD

2

FRAMIS

2 1

25.

50.

329

PROD

1

WIDGIT

1 4

25.

125.

100.

330

331

TOTAL

2200.

332

3:B

334

335

336

0

337

BFGIN

PHASE

2,

BUDGET

=

2000.

331:3

339

34n

PROD.

NO.

LEVEL

INCRE

MIN

aTY

CAPAC

SCHEDULE

-'41

34:'

PROD

9

BINT

DUP

9 1 4n(').

1201")

•

343

PROD

8

RONTER

GUY

8 2

2no. 200.

1200.

40n.

344

PROD

7

ANBER

STEM

7 4

2no.

10nn.

600.

34')

PROD

6

GRUNK

PITS 6 1

1no.

10

O.

90n.

lOC.

346

PROD

5

GRANCH

5 6

50.

1

(")

O. 6()1'1.

35(".

347

PROD

4

GREEB

STALL

4

10

50.

4,1).

450.

348

PROD

0

QUOTL

BIT 1

50.

300.

349

PROD

2

FRAMIS

7 1

75.

')0.

350

PROD

1

WIDGIT

1 4

25.

I?

5.

Ion.

'351

?52

TOTAL

2000.

~i5

3

354

355

.3S6

357

358

BEGIN

PHASE

2,

BUDGET

1800.

359

360

361

/~

PROD.

NO.

LEVEL

INCRF

~1l

N

QTY

CAPAC

SCHEDULE

362

~

363

PROD

9

BINT

DUP

9 1

4()0.

1200.

364

PROD

8

RONTER

GUY

8 2

200. 200.

1200.

4CO.

36:'

PROD

7

ANBER

STEM

7 3

200.

1')01).

400.

366

PROD

6

GRUNK

PITS

6 1

InO.

100.

9n('l.

IN).

367

DROD

5

GRANCH

5 6

50.

10

o.

600.

35C.

368

PROD

4

GREfB

STAll 4

10

50.

4~O.

4:'C.

369

PROD

0

QUOTL

BIT

:3

1

50.

300.

370

PROD

2

FRAMIS

2 1

25.

50.

37:

PROD

1

WIDGIT

1 4

25.

125.

10C.

372

":73

0

TOTAL

1800.

374

375

376

377

378

(;)

379

BEGIN PHASE

2,

BUDGET

1600.

380

381

382

PROD.

NO.

LEVEL INCRE

MIN

QTY

CAPAC

SCHEDULE

383

384

PROD

9 BINT

DUP

9 1

400.

1200.

385

PROD

8

RONTER

GUY

8 2

200. 200.

1200.

400.

386

PROD

7

ANBER

STEM

7 2

200.

1000.

200.

387

PROD

6

GRUNK

PITS

6 1

100.

900.

100.

388

PROD

5

GRANCH

5 6

50.

100.

600.

350.

389

PROD

4

GREEB

STALL 4

10

50.

450.

390

PROD

0 aUOTL

BIT

3 1

50.

300.

391

PROD

2 FRAMIS 2 1

25.

50.

392

PROD

1 WIDGIT 1 4

25. 25.

125.

100.

393

394

TOTAL

1600.

395

0

J

4&.

Wf

l4l

fWJ~1

"'"

2.

~'14-\-.

8

8000.

100.

PROBLEM

2

FOR

D.

P.

DP

528

BOLTS

U/4

UN

NO

3

40

50.

100.

DP

529

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

DP

5301

11.

12. 13.

14.

15.

.6

17. 18.

19.

20.

DP

5311

21. 22.

23.

24.

25.

26.

27.

28.

29.

30.

DP

5321

31. 32.

33.

34.

35.

37.

38.

39.

40. 41.

DP

5331

!=.CREWS

NO

18

LONG

2

40

50.

200.

DP

534

211.5

21.

21.5

22.

22.5

23.

23.5

24.

24.5

25.

DP

5352

25.5

26.

26.5

27.

27.5

28.

28.5

29.

29.5

30.

DP

5362

,11.5

31.

31.5

32.

32.5

33.

33.4

34.

34.5

35.

DP

5372

35.5

36.

36.5

37.

37.5

8.

38.

38.5

'39.

40.

DP

5382

LOCOMOTIVE t

STEAt-1

3

40

50.

300.

DP

539

30.

30.1

30.2

30.3

30.4

30.5

30.6

30.7

30.8

30.9

DP

5403

31.

32.

32.1

32.3

32.3 32.4

32.5

32.6 32.7

32.8

DP

5413

33.

33.1

33.2 33.3

33.4

33.5

33.7

33.8

33.9

DP

5423

34.

35. 36.

37.

3701

37.2

37.4

37.6

37.66

37.77

DP

5433

LOCOMOTIVE t

DEISEL

4

40

50.

100.

DP

544

20.

20.1

22.

22.22

22.23

22.25

22.56

22.75

22.78

DP

5454

22.88 22.89

22.9

22.91

22.92

22.95

22.99

23.

23.5

DP

5464

""

24.

24.4

24.5

24.8 24.9

25.

25.11

25.22

25.33

DP

5474

....,

25.44

25.55

25.66 25.77 25.88 25.99

26.1

26.2

26.3

26.9

DP

5484

EYEGLASS

FRA~E,

RRN

')

10

50. 50.

600.

DP

549

15.1

15.3 15.6

15.8

16.

16.2

16.2 16.3

.88

16.55

DP

5505

LAMBSKIN

TURBAN

6

10

50.

2

00.

DP

551

30.12

30.44

30.45

30.456

30.458

30.88

31.

32.556

33.

34.235

DP

5526

1620

COMPUTER

7

20

100.

300.

350.

DP

553

11.56

11.57

11.66

11.77

11.88

11.89

11.9

11.91

11.92

11.93

DP

5547

11.94

11.98

12.

15.

17.

17.5

18.

18.4

18.5

DP

5557

HAIRPIN.

NO

6

BLACK

8

40

2(')0.

360.

DP

556

1.

1.1

1.12

1.123 1.123

1.22

1.235

1.55

1.6

1.88

DP

5578

2.

2.5

2.55

2.56

2.58

2.9

3.

3.2

3.25

3.66

DP

5588

0

3.9

4.

4.22 4.33

4.43

4.53

4.64

4.76

4.87

DP

5598

5.

5.21

5.31 5.42

5.53 5.64

5.85

5.94

6.

7.258

DP-5608

o

....

tel4~

BEGIN

PHASE

2,

BUDGET

8000.

42

43

CI

44

PROD.

NO.

LEVEL

INCRE

MIN

CTY

CAPAC

SCHEDULE

045

46

HAIRPIN,

NO

6

ALACK

8 3

200.

7800.

400.

047

1620

COMPUTER

7 21

100.

300.

2200.

048

LAMBSKIN

TURBAN

6 11

50.

450.

049

EYEGLASS

FRAME,

BRN

5

10

50.

500. 500.

050

LOCOMOTIVE,

DEISEL 4

40

50.

1950.

051

LOCOMOTIVE,

STEAM

3 1

50.

2000.

50.

052

SCREWS

NO

18

LONG

2

34

50.

1950. 1650.

053

BOLTS

U/4

UN

NO

3 1 15

50.

100.

2050.

800.

054

55

TOTAL

8000.

056

57

58

59

60

61

BEGIN

PHASE

2,

BUDGET

=

7900.

62

63

64

PROD.

NO.

LEVEL

INCRE

MIN

QTY

CAPAC

SCHEDULE

065

""

66

00

HAIRPIN,

NO

6

BLACK

8 3

2no.

7800.

400.

067

1620

CO~PUTER

7

20

Ina.

300.

2200.

068

LAMASKIN

TURBAN

6

10

50.

450. 450.

069

~YEGLASS

FRAME,

BRN

5

10

50. 50.

500.

070

LOCOMOTIVE,

DEISEL 4

37

50.

1950.

1800.

071

LOCOMOTIVE,

STEAM

3 1

50. 50.

2000.

50.

072

SCREWS

NO

18

LONG

2 35

50.

1950. 1700.

073

BOLTS

U/4

UN

NO

3 1

15

50.

100.

2050.

800.

074

75

TOTAL

7900.

076

77

78

79

80

81

0

BfGIN

PHASE

2,

BUDGET

7800.

82

83

84

PROD.

NO.

LEVEL

INCRE

MIN

aTY

CAPAC

SCHEDULE

085

86

HAIRPIN,

NO

6

BLACK

8 2

200.

7800.

200.

087

1620

COMPUTER

7 21

100.

300.

2200.

088

LAMBSKIN

TURBAN

6 11

50.

450.

089

EYEGLASS

FRAME,

ARN

5

10

50. 50.

500. 500.

090

LOCOMOTIVE,

DEISEL 4

40

50.

1950.

091

LOCOMOTIVE,

STEAM

3 1

50. 50.

20Q() •

50.

092

SCRFWS

NO

18

LONG

2

"14

50.

1950.

1650.

093

80LTS

lJ/4

UN

NO

3 1 15

50.

100.

2050.

800.

094

9~

TOTAL

7800.

096

97

98

99

100

101

BEGIN

PHASE

2,

BUDGET

7100.

102

103

N

104

<:c

PROD.

NO.

LEVEL

INCRE

MIN

()Ty

CAPAC

SCHEDULE

105

106

HAIRPIN.

NO

6

BLACK

B 2

2no.

7800.

200.

107

1620

COMPUTER

7

20

1(')0.

300.

22()O.

2200.

108

LAMBSKIN

TURBAN

6

10

50.

450.

109

EYEGLASS

FRAME,

BRN

5

10

50. 50.

500.

110

LOCOMOTIVE,

DEISEL 4

37

50.

1950. 1800.

111

LOCOMOTIVE,

STEAM

3 1

50.

2000.

50.

112

SCREWS

NO

18

LONG

2 35

50.

1950.

1700.

113

BOL

TS

lJ/4

UN

NO

3 1

15

50.

100.

2050.

800.

114

115

TOTAL

7700.

116

0

117

118

119

120

121

___________________________________________________

4"·

-----

-------_

..

_------

BEGIN

PHASE

2,

BUDGET

=

7600.

122

123

0

124

PROD.

NO.

LEVEL

INCRE

MIN

QTY

CAPAC

SCHEDULE

125

126

HAIRPIN,

NO

6

BLACK

8 1

200,

7800.

127

1620

COMPUTER

7

21

100.

300.

2200. 2200.

128

LAMBSKIN

TURBAN

6

11

50.

450.

129

EYEGLASS

FRAME,

BRN

5

10

50.

500.

130

LOCOMOTIVE, DEISEL 4

40

50.

1950.

131

L.OCOMoTI

VE,

STEAM

3 1

50.

2000.

50.

132

SCREWS

NO

18

LONG

2

34

50.

1950.

1650.

133

BOLTS

U/4

UN

NO

3 1

15

50.

100.

2050.

800~

134

135

TOTAL

7600.

136

137

138

139

140

141

BEGIN

PHASE

2,

BUDGET

=

7500.

142

143

C.

144

• PROne

NO.

LEVEL.

INCRE

MIN

aTY

CAPAC

SCHEDULE

145

146

HAIRPIN,

NO

6

BLACK

8 1

200.

7800.

147

1620

COMPUTER

7

20

100.

300.

2200.

148

LAMBSKIN

TURBAN

6

10

50.

450.

149

EYEGLASS

FRAME,

RRN

5

10

50.

500. 500.

150

LOCOMOTIVE, DEISEL 4

37

50.

1950.

1800.

151

LOCOMOTIVE,

STEAM

3 1

50.

2000.

50.

152

SCREWS

NO

18

LONG

2 35

50.

1950.

1700.

153

BOLTS

U/4

UN

NO

3 1 15

50.

100.

2050.

8(,)0.

154

155

TOTAL

7500.

156

157

158

159

160

161

~

V

BEGIN

PHASE

2,

BUDGET

=

7400.

162

163

164

PROD.

NO.

LEVEL

INCRE

MIN

aTY

CAPAC

SCHEDULE

165

166

HAIRPIN,

NO

6

BLACK

8 1

200.

7800.

167

16?0

COMPUTER

7

20

100.

300.

2200.

168

LAMBSKIN

TURBAN

6

10

50.

450.

169

EYEGLASS

FRAME.

8RN

5

10

50.

500.

170

LOCOMOTIvE, DEISEL 4 35

50.

1950.

1700.

171

LOCOMOTIVE.

STEAM

3 1

50. 50.

2000.

50.

172

SCREWS

NO

18

LONG

2 35

50.

1950. 1700.

173

BOLTS

U/4

UN

NO

3 1 15

50.

100.

2050.

800.

174

175

TOTAL

7400.

176

177

178

179

180

181

BFGIN

PHASE

2,

BUDGET

=

7300.

182

183

184

~

PROD.

NO.

LEVEL

INCRE

MIN

QTY

CAPAC

SCHEDULE

185

186

HAIRPIN,

NO

6

BLACK

8 1

200.

7800.

187

1620

COMPUTER

7

20

100.

300.

2200.

188

LAMBSKIN

tURBAN

6

10

50.

450. 450.

189

EYEGLASS

FRAME,

ARN

5

10

50. 50.

500.

~90

LOCOMOTIvE, DEISEL 4

33

50.

1950.

1600.

191

LOCOMOTIvE,

STEAM

3 1

50. 50.

2000.

50·

192

SCREWS

NO

18

LONG

2 35

50.

1950.

1700.

193

BOLTS

U/4

UN

NO

3 1 15

50.

100.

2050.

800.

194

195

TOTAL

7300.

196

0

c

o

C NON-LINEAR

PROGRAMMING.

A

MODEL

DESIGNED

FOR

PRODUCTION

SCHEDULING

C

JOHN

W.

BURGESON,

APPLIED SCIENCE REP. I R M

AKRON

C

CHANGE

LEVEL

3/5/62

C THIS

PROG

CAN

HANDLE

A

MAX

OF

199

PRODUCTS.

C

THE

LIMIT

IS

CAUSED

BY

THE

3 DIGIT

SEQUENCE

C

NUMBER

PUT

IN

CC

78-80

BY

THE

FORTRAN

PUNCH

SUBROUTINE.

C

THE

PROG

HAS

2 PHASES.

OUTPUT

FROM

1

IS

5

CARDS

PER

PRODUCT. THIS

C

INTERMEDIATE

DECK

MUST

BE

SORTED

IN

REVERSE

ORDER

FOR

INPUT

TO

C

PHASE

2.

PHASE

2

MAY

BE

RUN

MANY

TIMES

WITH

THIS DECK,

EACH

PASS

C

DEVELOPING

A

NEW

SCHEDULE

WITH

A (REDUCED)

NEW

BUDGET.

DIMENSION

S(40),

V(40),

PRECP(100),

CURRP(lOO)

1102

FORMAT

(1111H

)

110,

FORMAT

(11111H

PHASE

1 COMPLETEDI4,16H

ITEMS

SCHEDULED)

1104

FORMAT

(/11H

END

OF

JOB/)

1118

FORMAT

(1118HDYNAMIC

PROG

MODELII124H

NO.

BUDGET

DBUD)

2222

FORMAT(/15X,49HPROD.

NO.

LEVEL

INCRE

MIN

OTY

CAPAC

SCHEDULE/)

7776

FORMAT

(I4,F10.0,F1n.O,30H

)

7777

FORMAT

(20H

I5,I5,F8.0,F8.0,F8.0,F8.0,I6)

7778

FORMAT

(1/42HSORT

OUTPUT

IN

RVERSE

SEQUENCE

ON

CC

78-80)

7779

FORMAT

(/23HBEGIN

PHASE

2,

BUDGET

=F10.0/)

7780

FORMAT

(31HTHEN HIT

START

TO

BEGIN

PHASE

2)

7781

FORMAT

(/35HRERUN INTERMED. CDS.

FOR

ALT. SOLN.)

7782

FORMAT

1/15X,48HNAME

IRECD

M

INCRE

MIN

QTY

CAPAC

AVG

DEM)

778,

FORMAT

14HSO

=FIO.0,6H

SB

=F10.0,6H

NR

=14)

7784

FORMAT

1/42X,5HTOTALF15.0)

77

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

C

NUMBR

IS

THE

TOTAL

NUMBER

OF

PRODUCTS

TO

BE

PROCESSED

C

BUD

IS

THE

BUDGET

EXPRESSED

IN

TOTAL

NO.

OF

UNITS

C

DBUD

IS

AN

AMOUNT

(OPTIONAL)

BY

WHICH

BUD

MAY

BE

REDUCED

IN

C

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

C

SENS

E

SWITCH

3

ON

PERMITS THIS ADDITIONAL

TYPED

INFO

IFISENSE

SWITCH

3)

79,80

79

TYPE

7782

80

READ

7777,

IRECD,M,A,Q,A2

C

IRECD

IS

PROD

IDENTIFIER

ISTOCK

NO)

NOT

USED

BY

PROG

C M

IS

NO

OF

PROD

LEVELS

CONSIDFRED.

MUST

BE

BETWEEN

1

AND

40

C A

IS

INCREMENT

SIZF

FROM

LEVEL

TO

LFVEL,

MUST

Bf

25,50,100,ETC

C Q

IS

MINIMUM

QUANTITY

TO

BE

MADE.

MUST

gE MULTIPLE

OF

A

C

A2

IS

AVERAGE

DEMAND

OVER

MONTHS

IF(M-40)

85,85,999

85

EM=M-l

C

NOW

CALCULATE

CAP~C

FOR

THIS

PRODUCT

CAPAC

= Q +

A*E~

C

CAPAC

IS

THE

MAX

PROD

LEVEL

C

THUS

IF X

IS

A

PROD

LEVEL

WE

CAN

SAY

-

( X =

Q,

Q+A.

Q+2.*A,

•••

,

C~PAC

DO

81

I=1,~tlO

r 2= 1+1 .

1"3=1+2

14=1+1

15=1+4

16=1+5

17=1+6

18=1+7

19=1+8

10=1+9

81

READ

77,VII),V(

I2),VII3)

,VII4),V(

I5),VII6),VII7),VI

18),V(I9)

.V(

10)

C

VII)

IS

THE

PROFIT ASSOCIATED

WITH

PROD

LEVEL

I

C

SENSE

SWITCH

3

ON

PERMITS THIS ADDITIONAL

TYPED

INFO

IF(SEN~E

SWITCH

3)

82,83

82

TYPE

7777,

IRECD.M,A,Q,(APAC,A2

83

NUMB=NU'"'1B+1

SUMQ=SUMQ+Q

SUMA2=SUMA2+A2

SUMC=OLDSB+CAPAC

SO~~IN=OLDSO

IFIOLDSO-5UMQ)

114,115,115

114

SOMIN=SUMQ

115

5BMAX=SUMC

IFISUMC-BUD)

118,118,117

117

SBMAX

=8UD

118

K=SOMIN/A

SO=K

K=SBMAX/A+.9999

SB=K

SO=SO*A

SB=SB*A

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

DP

046

DP

047

DP

048

DP

049

DP

050

DP

051

DP

052

DP

053

DP

054

DP-055

DP

056

DP

057

DP

0,8

DP

059

DP

060

DP

061

DP

062

DP

063

DP

064

DP

065

DP

066

DP

067

DP

068

DP

069

DP

070

DP

071

DP

072

DP

073

DP

074

DP

075

DP

076

DP

077

DP

078

DP

079

DP

080

DP

081

DP

082

DP

083

DP

084

DP

085

DP

086

DP

087

DP

088

DP

089

DP

090

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

= X

IGAG=IDEX1

320

X=X+A

JDEX1=IDEX1+1

IFIX-SS)

335,335,340

335 IF IX-CAPAC)

171,171,340

340 IFIP+IOOOOOO.)

341,600,341

600

SO=SO+A

IF INR-IOOI

601,602,601

601 NR=NR-l

GO

TO

137

602

SB=SR+A

341

370

372

378

400

GO

TO

137

CURRPIINDEX)=P

1DEXB=IXB-QI/A

+1.5

SIIDEXBI=SS

SS=SS+A

INDEX

=

INDEX

+ 1

1FISS-SBI150,150,370

DO

372 JK=I,NR

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

PU

N C H 7 7 , S I 1 ) , S I

12

) , S I I 3 I

,S

I 1 4 ) , 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

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

091

DP

092

DP

093

DP

094

DP

09!)

DP

096

DP

097

DP

098

DP

099

DP

100

DP

101

DP

102

DP

103

DP

104

DP

105

DP

106

DP

107

DP

108

DP

109

DP

110

DP

111

DP

112

DP

113

DP

114

DP

115

DP

116

DP

117

DP

118

DP

119

DP

120

DP

121

DP

122

DP

123

DP

124

DP

125

DP

126

DP

127

DP

128

DP

129

DP

130

DP

131

DP

132

DP

133

DP

134

DP

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

'/

c

C

,~

,I

o

I

'b

It

t,

'1'm

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

DP

181

19=1+8

DP

182

10=1+9

DP

183

11

READ

77.S(IltS(I2hS(I3).S(I4).SII5ltSII6),SII1,.SII8)9S1I9)tSII0)

DP

184

X =

O.

DP

185

17 IF(PLACE)

41,41,18

DP

186

18

DO

20 I = I.M

DP

187

IFIPLACE-S(I))

22.22,20

DP

188

20

CONTINUE

DP

189

X=CAPAC

DP

190

GO

TO

23

DP

191

22

EM

=

I-I

DP

192

X = Q +

A*EM

DP

193

23

PLACE

=

PLACE

-X

DP

194

41

PUNCH

7777,

IRECD,I,~,Q,CAPAC,X

DP

195

C X

WILL

BE

TH[

OPTIMUM

NO.

OF

UNITS

TO

PRODUCE

DP

196

IFISENSF

SWITCH

1)

42,43

DP

197

C

SENSE

SWITCH

1

ON

TO

TYPE

ANSWERS

AS

WELL

AS

PUNCH

THEM

DP

198

42

TYPE

7777,

IRECD,I,A,Q,CAPAC,X

DP

199

43 IF(NUMB-l)

999,48,10

DP

200

C

END

OF

JOB

PROCEDURE

DP

201

48

TOTAL

=

BUD

-

PLACE

DP

202

PUNCH

7784,

TOTAL

DP

203

IF(SEN~E

SWITCH

1)

49,51

DP

204

49

TYPE

1784,

TOTAL

DP

205

51

BUD

=

BUD

-

DBUD

DP

206

PLACE

=

RUD

DP

207

C

SENSE

SWITCH

2

ON

TO

REDUCE

BUD

BY

DBUD

AND

OBTAIN

ALT.

SOLN.

DP

208

PUNCH

1102

DP

209

IFISENSE

SWITCH

2)

55,6999

DP

210

55 IF(SENSE

SWITCH

3)

52,9

DP

211

52

TYPE

1781

DP

212

GO

TO

9

DP

213

6999

TYPE

1104

DP

214

999

~TOP

DP

215

END

DP

216

COMPUTER

TECHNOLOr.~Y

aLi

IN

I

Flow

Chart

of

the

Algorithm

S(:r:)=Scj

:t

=1,

'10

~

Q~

==G.

IJ37

.r---------~)I

z6ltG

=,

SS-:=S~

%NDEX

=1

p=

-00

"~

)(;G.Gl.

%DExr:IGA6~kr-

__________________

__

X8=QCil

OUT

37

rJ

:¥fiT'

~/itl';'

of

fl..

o~j

.c.i

~~clc

4}0000000500360008C0050036001600050036002400050036003200050016100000000026199991

26099961999926199951

0000260999219999261998110oo0260998019999261«19011Oooo2'""T7:...---+----

9481999926199151

0000260986419999261977910000260

964419999261942310000260906.,;8.;.1~9

...

9;-99.;....-~

__

---t~_

261849110000

2607560

1999926160511000026036I212875330966~OOOOO'33cr04~OOO~'

6004600336007004600348009004600360014004600372016004600384017003600000005004900

3200500000002639999199992620500010003

320000000003

300500000004900312000'0000000000

---'-._-

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PARTIAL

. DISTRIBUTION LIST

April

1962-March

1963

INDIVIDUAL

IBM

OfFICE

DATE

R.

Cabell

Atlanta,

Ed.

Center

4/62

T.

Kallner

SBC

NYC

4/62

R.

Smith

Dallas

4/62

W.

Sh1mer

Galveston

4/62

R.

Evans

Fort

Wayne

.4/62

J.'Golden

Hartford

4/62

P.

McClung

San

Francisco

4/62

G.

Factor

Seattle

Ed

Center

4/62

L.

Jensen

Rockford

4/62

R.Erwin

Flint

4/62

L.

Smith

WRO

4/62

G.

Wetbal

Oslo.

Norway

4/62

J.

Borches

Des

Moines

5/62

P.

Newman

Little

Rock

5/62

B.

Dzielinsk:

ASDD

5/62

H.

Fient

Blaricum I

Holland

6/62

R.

Johnson

Pittsburgh

6/62

J.

Shevy

Buffalo

6/62

W.

Allmon

Chicago

West

7/62

R.

Dietz

Forest

Hills

7/62

R.

Flood

White

Plains

7/62

E.

8r'achett

Wa

shington

' 7/6,2

L.

Cannon

FSD.

Washington

8/62

M.

ltlantan

ASD

Litrary

8/62

D.

SlmpSCJll

London.

England

9/62

J.

Galente

ERO

9/62

B.

Wall.

Cambridge

9/62

L.

Ruffino

Bethesda

10/62

W.

Grabe

Inglewood

10/62

G.

Goodfriend

Dist

11

10/62

J.

Yellowless

Vancouver

11/62

T.

Richards

Jacksonville

11/62

D.

Huffinire Elmira

12/62

R.

Reynaert

Brussels

Belgium

1/63

J.

Powers

Toledo

2/63

S.

Head

Sydney.

Australia

2/63

D.

Kattwinkel

West

Germany

3/63

I.

n.bergs

Montreal

3/63

E.

Cites

Spain

3/63

Page

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.....

INI.>XC2

os

5 -

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._

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09

b

09

q

02..0

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....

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.

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.

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...

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402.

o

7.

PART

IV

-

NOI'ES

O1i

THIS

PROGlWol

A.

Node

llumbering

In

III8D;.T

of

this

sort

the

jobs

had.

to

be

nU.'llbered

so

that

the

head

of

an

arrow

(J)

"W&S

e.b~s

greater

than

the

tail

(I)

of

that

arrow.

In

addition

input

cards

had

to

be

in

J

sequence

,rlthin

I

sequence

with

no

missing

I

values.

These

restrictions

allowed

checking

arrow

diagram

logic

by

a

sequence

check

of

I

values

and a

test

of

I

against

J.

In

this

program

another

method

is

used

for

checking

logic

that

removes

these

restrictions.

As laDS

as

none

or

the

restrictions

of

Part

n

are

violated,

I

and

J

may

be

a1V"

three

digit

numbers. However,

the

restrictions

on

max1mum

project

size

are

in

terms

of

the

highest

numbered node

and

not

in

terms

or

the

total.

number

of

nodes,

so

it

is

scaet1mes

necessar,y

to

use

the

smallest

numbers ava:1l.able

for

I

and

J.

There

1s

also

a

slight

speed

advantage

in

putting

the

jobs

in

approximately

the

same

order

as

the

required.

B.

Program

capacity

For

a 20,000

digit

core

memory machine,

the

sum

or

the

number

of

the

highest

numbered node

and

the

nUDber

or

Jobs

must

be

1672

or

less.

FClr

40,000

digits

or

storage

this

restricticm

is

3672

and

for

60,000

digits

it

is

5672. The

bigbest

possible

DIIIi>ered

noae

is

999.

For

20,000

digits

the

max:llIaa mmiber

of

Jobs

may

be

less

than

1400

for

the

reason

stated

in

Part

VI -C.

C.

Machiiie

Regu1rements

1620

Data

Process1Qg

S¥stem

1622

Card

Bead

Punch

110

other

special

features

1623

Additional

Core Memory

is

optional.

13

o o

PART

V - INPUl'

The

input

to

this

program

contains

three

types

of

data

cards.

Type

1

and

2

cards

may

be

arranged

in

a.I\Y

desired

order.

See Appendix A

for

sample

problem

input.

TYpe

1 - Heading

or

description

cards

~se

are

identified

by

some

character

in

column

1,

other

than

a

blank

or

numeric

<tigit.

The

remainder

of

the

card

ma.v

be

plDlched

with

a.I\Y

information

desired.

The

identif'ying

character

in

column 1

ma;y

be

dif'ferent

for

each

type

1

card.

type 20

-Job

description

cards

There

is

one

of

these

for

every

job

in

the

project.

Blanks

in

numeric

fields

are

taken

as

zeros,

except

that

a

zero

I

field

must

b~o

punched

zero

in

the

1.mi

ts

position

(column

3).

0

~

1 - 3

4 - 6

Tail.

c£

the

job

arrow -I

Head

or

the

job

arrow

- J

T -

10

Time

duration

of

the

job

-D

(I,J)

11

-15

Cost

of

the

job

16 -50

Description

of

the

job

and

miscellaneous

data

51 -80 Not

used

-

mt1¥

contain

aD¥thing

b 3 -

EDd

of

the

pro.lect

This

is

the

last

card

in

the

input

deck

and

should

be

blank.

14

8.

,

.

PARr VI -

OPERATTIlG

INSTRUCTIONS

A. Pl'O@'!!

Deck

!III

SPS

118t1Jtg

of

this

program

is

in

Appendix

C. The

condensed

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

contains

a

digit

s1gn:l.f'yiJlg

the

core

memol")"

size

of

the

computer

being

used.

"2

20,000

Posi

tiona

1;:

40,000

Positions

b

60,000

Positions

B.

Procedure

PABITI

Switch

STOP

o

FUM

Switch

STOP

I/O

Switch

STOP

PJ:csNa

Switches

DOt

used

9·

Load

f!'S!II!

Deck

-

DePft8S

RESBT,

place

prqp."Ia

deck

in

read

bopper,

depress

LOAD.

To

read

final

prcgram

c81"d,

dePftss

REA1lBR

~.

CCIIIpUter

~

halts

wheJ1

p1"08:l'8

is

loaded.

Data

Pus

I -

Place

4ata

declt

in

read

hopper,

press

B1WJER

S'1'ARf

aDd

cCllplter

ST.AB!f.

To

re.

the

tiDal

c1ata ca:rd, aeprees

mwa

S'.I!ARr.

CClIIIP1Iter

does

errar

~1s

aDd

either

halts

ar

pr.lDta

aD

errar

_sease·

Data

Pass

II

-

If

DO

eJ'l'Ql'S

WN

cUecovezed,

place

data

declt

in

l'ead

hopper

aDd

.blaDk

c8Z'ds

in

paDCb

bCJ.ppe~.

Press

BEAlBR fJlA'Br,

IUICH

STABT,

and cClll,Vllter

S'l!ART.

To

read

the

final

cJata

ca:rd,

depress

RBADBR

STAJiI!.

C.

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).

TJpewriter'

priJrts

I,J,D.COsT

for

o J 5 o

10.

the

last

.Job

and

halts.

To

work

the

press

START.

~

-f.fore

than

one

"last"

node

(8

node

which

is

not

the

tail

of

sc;xne

arrow)

bas

been

found.

Typevr1ter

prints

the

numbers

of

all

but

the

first

"last"

node

found

and

halts.

To

find

the

first

"last"

node

type

out

locations

3247-49. To vork

the

INSERT

16

01095

00016

49

00402,

RELEASE,

START.

Error

3 -

M:>re

than

one

"first"

node

(a

node

which

is

not

the

head

of

same

arrow)

has

been

found.

Typevriter

prints

the

numbers

of

all

but

the

first

"first"

node

found

and

halts.

To

find

the

first

"first"

node

type

out

location

3244-146.

To

work

the

INSERT

16

01095

00016

49

00402,

REIEASE,

START.

~

- A

loop

has

been

found

in

the

arrow

diagram.

For

example

'a

series

of

jObs

(1,2),

(2,3),

and

(3,1)

would

be

a

loop.

'l'Jpewr1ter

prlit,ts

I,J,D,

COST

for

the

first

job

where

the

error

IIIIq"

be

detected.

(i.e.

'!'he

earliest

start

far

this

Job

exceeds

the

sum.

of

all

JOb

times.)

This

Job

Deed DOt

be

on

the

loop

itself',

but

DI8l'

be

on

a

chain

of

Jobs

which

PIUUIes

tbrougb

ODe

of

the

nodes

on

the

loop.

To

work

the

press

START.

There

1s

a vel")"

remote

possibility

that

a

type

1

error

could

go

UDdetected

as

such.

During

data

pass

I a

temporary

table

is

set

up

in

locat1oaa

Itooo

-

6oOJ.

to

be

used

to

find

"first"

aDd

"last"

nodes.

If

lltoo

Jobs

ar

IIIQl'e

&1.'e

read,

this

table

IIIIq"

be

destroyed.

This

will

cause

several.

tJpe2

aDd 3

error

messager

however.

,~

16 o

o

PART

VII

-

ot1l'Pt11'

A

deck

ot

cards

s1a1l.ar

to

the

pass

II

data

deck

is

produced.

The

type

1

output

carda

are

uncbaDged. 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

-

80.

Co1U111D8

51

-55

Earliest

start

date

56-60

Earliest

t1n1sb

date

61

-

65

Lt.test

start

date

66-70

Lt.test

tin1sb

date

11-15

Total

tloat

time

16

-

SO

Free

tloat

time

15

CaDta1na *

it

this

is

a

er1t1cal

job

There

are

no

tJpe

3

carda

in

the

output

deck.

Tbe

last

output

11.

card

18

a

tJpe

1

card

COIlta1n1D&

project

cost

and

C<IIIp1etlon

date.

By

letting

the

first

coJJ.D

ot

the

output

card8

bea

pr1nter

tomat

control,

8D;Y

desired

llsting

.,

be

deYel.oped.

J 7

o

n-

A

PART

VIII

-

SUGGESTIONS

Add!

tlonal

or

S1>ecie.l.

Output

12.

The

second

pass

of

data

controls

the

amount

ot

output.

For

example

if'

you

do

not

wish

to

include

d.uDIIv

jobs

in

the

printed

report,

aD1t

them

trom

the

data

deck

in

the

second

data

pass.

If

you

wish

to

prepare

several

reports-

on

ODe

project,

it

is

possible

to

make

several

second

passes.

Prepare a

transter

card

with

49

01'T98

0000

in

coltDllDs 1 -

32,

and

place

it

on

top

ot

the

pass

2

deck.

Press

RESET

and

LOAD

to

execute

another

second

pass.

B

Least

Cost

Estimating

Repeated

applications

of

this

program

will

give

an

idea

ot

how

project

cc.p1etion

time

varies

with

cost.

First

schedule

the

project

with

nonlal.

job

time

and

normal.

costs,

then

caapress

the

schedule

along

the

er1t1cBJ.

path,

vh1ch

abortens

the

over-all

project

time

at

the

expense

ot

inCreasingSODle

Job

costs.

Running

the

schedule

aga1n

will

show

the

new

project

time

and

cost

and

the

new

critical.

path.

It

the

assumpt10n

is

made

that

cost

ot

a

Job

varies

1iDear~

with

completion

time

between

the

llmits

of

normal.

job

tiJle

and

crash

time,

this

estimating

IIIBiY'

be

done

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

tor

overhead,

penalties,

etc.,

the

least

cost

B8¥

be

estimated.

18

"

c

PART

IX

BIBLIOGRAPHY

Arrow m.-Pl.aDniDg.

Du

Pont

-

Petrol.eum

Chemical.s

Division.

"Better

Plans

CelIe

From

Study

of

ADatc:qr

of

an

Engineering

Job,

"

Busine88

Week, March

21,

1959.

13.

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

"Cr1

tical-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.,

"PI!lfr/Y1:P

Pl.aIm1Dg

and

~

on

BAM,"

Joumal

at

Macb1De.

Account1Jlg,

~,

1961.

"Rev

Tool

ror

Job

~,"

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

OlD.

!D§1.!leer1Dg

!!IIII!tp!!lt

I DeCEllber, 1960.

Serer,

J.

S.,

Kel.le7,

J.

E.,

Jr.,

IIIDd

V&llter,

M.

B.,

"Critical.

Path

Scbed

l1l1u

B,"

~,

Juq,

~960.

"Space-Age

Scheduling

.Arr:l.Te8

in

CPl,"

aa-tcal.

Week,

October

15, 1960.

19

~\-\

~_;I

14.

PART X - APPENDIX A

7/19/61.

em

2H

r

-':

\.

!

o o

APPENDIX

A - SAMPLE

;:>RO~LEi""l

Flr'UT

SAMPLE PROBLEM -

FIGURE

1

~CHEOl.lLE

REPL·ACEMENT

OF

APi

PE

'-

I

NE

-----_._--.

---'-:;:'f':j

'-'0

COSTDESCRtPTTON

(JF'

J()RC\

1

~

10

1 ,

~B._.

2 'It 2

300

____

.

___

..

..2-2£t 1

25

~o

~

LEAl)

TIM~

rJME

AVAILARLE

MEASURE

AND

SKETCH

MA!..f.-ASS

l.§ti~ENr.s.

__

..

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______ J

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4

..

t_.l.00

DEVELOP

MATFQJ AL

LIST

4 5

4 6 ,

300

ERECT

S(AF~OLn

4 7

~o

~50

p~on'~~

PI

PF

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...-..::I4~A

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5 6 ,

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nFArTJVATF LJNF

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_____

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6 9 6

400

REMOVE

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PRFFAR

SECTIONS

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.

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o

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800

PLACE

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PRES~URE

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ET

t

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~------------------------------------------------------.

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________

t.E.5..'L

PROBLEM

-SEE

fIGURE

L

__

~

__

_

.

..

I

i I J

"COST

DESCRIPTION OF

JOBS

...,...

1 ,

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.,

1 , 9

2.

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251

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4 5

456

.----_._---

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----------.....,r-----------.,--------------------~-

. J 6 .....

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:_13L::·,'

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r

SA~PL~

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-

FIGURE

1

5CHFDULE REPLACFMFNT

OF

A

PIPE

LINE

...

-1

J o

COST

DESCRIPTION

OF

JO~S

ES

EF LS

LF

TF

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1 2 10 LEAD TIt-1E

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28

T [ME AVA

ILARLE

is

16

44

16

2 3 2

30U

~lEASURE

AND

SK'ETCH

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12

.10

12

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20

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..

MAKE

ASSIGNMENTS

10

11

12..

1

20

3

11 11

1;::

17

1 1

3 4 1

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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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