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.
Production Allocation Remodeling System:
Optimizing for Competitive Advantage
in a Mature Manufacturing Industry
by
D. Bonaquist*, R. Brown**, T. Hanson*,
J. Shapiro***, V. Singhal**
OR 155-87
*
**
***
January 1987
Linde, Union Carbide, Tonawanda, NY
Resource Management Systems, Cambridge, MA
Massachusetts Institute of Technology, Cambridge, MA
page 1
PAMS O.R. PAPER, draft l(rwb), 21 January 1987
I. INTRODUCTION
production
Setting
manufacturing
sites
manufacturing
companies.
conceals
is
location
of
extreme,
between
large
and
manufacturing
set
also
may
as
for
for
a
cost
of
level
lower
scheduling
production
and
targets largely determine
for manufacturing
call
the
as service levels.
stage
More generally,
of utilization
targets
the
such
decisions,
affects
as well
to customers,
inventory management.
the level
in
a routine decision, yet it
clearly
production
targets
manufacturing
problem
decision
is
This
dispersed
geographically
have a direct effect on corporate performance.
distributing products
Production
common
a
tradeoffs
important
distribution that
The
for
targets
site
sites.
to
be
At the most
shut
down or
mothballed.
This
paper
describes
work
we
have
allocation modeling system (PAMS) for the
Union Carbide
Corporation.
done on a production
Linde Division
of the
The system has been in use for more
than a year in the company's Eastern region, and installations in
other regions
are underway.
PAMS to a national
Work is also in progress to elevate
model encompassing
all of
Linde's important
sites and customers.
Linde
is
a
major
producer
of
industrial gases (oxygen,
nitrogen, argon, hydrogen), with numerous manufacturing sites and
customers throughout the United States.
PAMS
is
to
minimize
combined
The immediate purpose of
regional
manufacturing
and
page 2
PAMS O.R. PAPER, draft l(rwb), 21 January 1987
distribution costs over a planning period of approximately thirty
days.
More generally,
individual
customer
production sites.
sites
in
corporate
demands
PAMS also
keeping
planners
to
use
it
to allocate
geographically
optimally
allocates
dispersed
idle
time to
with complex relationships between production
costs and capabilities.
Beyond the immediate
general
interest
application,
because
it
we
believe
PAMS
the
demonstrates
is of
value
of
optimization in a mature industry where conventional wisdom might
lead
one
limited.
can
be
to
expect
opportunities
for
cost
reduction
to be
In particular, it demonstrates how an integrating model
used
to
bring
the
production and engineering
company's
to
bear
on
technical
the
expertise in
strategic
goal of
lowering costs to enhance competitive position.
The
PAMS
project
also
illustrates
how
a
application evolve together over the course of a
an
interplay
between
considerations.
model
and an
project through
practical, computational, and theoretical
In this case the model became
both more correct
and simpler -- a happy but perhaps fortuitous outcome which is by
no means the rule with complex modeling applications.
The model development in PAMS is novel in that mixed integer
programming (MIP) constructs for describing electricity contracts
(see Bender et al (1981), Bender et al (1985) for
of construct
other examples
analysis) are combined with manufacturing submodels
and a distribution network.
Moreover, the implementation
PAMS O.R. PAPER, draft l(rwb), 21 January 1987
successfully linked
a chemical
page 3
process optimization
model to a
mathematical programming model for tactical planning.
II. INDUSTRY BACKGROUND
Production
of
quintessential
industrial
mature
gases
is
manufacturing
in
many
industry.
ways
the
The process of
cryogenic distillation by which air is separated into gaseous and
liquid elemental
fractions has been known for over eighty years.
Competing producers now
similar
intrinsic
operate
capital
thermodynamic
intensive
efficiencies;
plants with
few
radical
breakthroughs in production technology are to be expected.
the sole
raw material,
quality.
Nor is there much
except
for
special
Air,
is free and does not vary appreciably in
scope for
product differentiation--
applications
where
extreme
purity
is
essential, all liquid oxygen is very much the same.
Despite this uniformity on
the
supply
side,
however, the
markets for industrial gases are changing, largely in response to
structural changes in the national and world economy.
Demand for
liquid and gaseous oxygen was for many years the driving force of
the industry.
demand
has
In recent
been
declining,
such as steelmaking shift
for liquid
years
nitrogen is
the
low
temperature
offshore.
increasing for
and
of
increase
in this
as the centers of basic industries
enhanced oil recovery, and other
very
rate
areas
chemical
On the
other hand, demand
use in food preparation,
where
a
inertness
combination of
is
essential.
PAMS O.R. PAPER, draft l(rwb), 21 January 1987
(Figure 1
shows this
shift in
page 4
demand over the last two decades
for the industry as a whole.)
These changes have also led to
demand, away
from the
near the
proportion of
industry's
by gas
customer's
in the
location of
older midwestern industrial centers.
years, the bulk of the
large customers
a shift
production
pipeline, from
facility.
was
For
delivered to
production sites located
Now,
a
large
and increasing
demand is for liquid products, which are delivered
in insulated trucks
or
railcars
to
a
larger
number
of more
geographically dispersed customers.
The result has been to alter accepted premises and operating
procedures.
stable larger
were.
The company is no
industries, and
longer principally
an adjunct of
cannot afford to operate as if it
This shift in the conditions underlying competition in the
industry
stability.
raises
It
hazards
also
where
opens
up
for
decades
new
opportunities
there
companies that can been adapt to the new conditions.
had
for
been
those
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page 5
PAMS O.R. PAPER, draft l(rwb), 21 January 1987
III.
PROJECT BACKGROUND
The PAMS
of
Linde's
project originated in a general desire on the part
upper
to
management
bolster
competitive position
through better operation of the Linde production and distribution
system.
Delivered cost
competitive advantage
service.)
control
over
costs are
have
of the
primary determinants of
in this industry (the other being customer
The two primary elements of cost
production.
cost.
is one
the
short
and
The latter
still quite
subject to
term are distribution and
medium
are generally
larger, but distribution
significant -- typically 30% of delivered
It was therefore
focused
that are
that
natural
at -first
on
independently of the other,
Linde's
reducing
particularly
attention should
each
of
since
these
such
costs
an effort
meshed with the current division of functional responsibilities.
For
the
purposes
Linde groups its
large regions
customers
and
-- East, South,
any site can serve
demanded by
of production and distribution planning,
demands
planning
cycle.
are
provided it
Within
assigned
These
sites
Central, and so on.
any customer,
the customer.
customer
production
demands
to
into several
In principle,
makes the product
a region, known or predicted
a
site
through
a monthly
can
then
be aggregated into
production targets for each product at each site.
In practice, planners in the distribution
function assigned
customers to sites, since it was they who managed the shipment of
PAMS O.R. PAPER, draft l(rwb), 21 January 1987
product to
customers.
made heavy use of
developed to
an
In making
elaborate
page 6
this decision, these planners
network
minimize distribution
model
costs.
which
had been
This tended to favor
assignment of customers to the nearest site, without taking fully
into account
the cost of production at the site.
process
its
and
represented well
economics
were
rates
too
complex
to
be
in such a model, and found no other exponent in
production allocation process.
production
simply
The production
through
Instead,
an
region
informal
attempted to reconcile forecasted
management set
heuristic process which
product demand,
relative site
production costs, inventory levels, and distribution costs.
Linde
also
had
in
place
a
improve the localized efficiency
element
of
this
program
was
quite
successful program to
of production
a set
(including
should
minimizing
Although
be
the
it
random
The
search) to
instantaneous performance of individual sites.
SOM had been developed for use at each site to
site
the authors.
of data gathering procedures and software based on
nonlinear optimization techniques
optimize the
A major
the Site Optimization Map (SOM),
which was developed and implemented by two of
SOM is
sites.
has
operated
rate
been
of
to
determine how the
meet given production rates while
energy
and
The
consumption
still
localized optimization, it could
is
not
very
in
(power
demand).
successful at this
itself
determine what
those rates should be.
As we
reviewed Linde's procedures and tools it became clear
that cost reductions in production and
distribution would
be at
PAMS O.R. PAPER, draft l(rwb), 21 January 1987
best
haphazard,
concert.
if
not
page 7
illusory, unless they were achieved in
Conspicuous by its absence was the ability to plan both
production
and
distribution
comprehensive framework
to
activities
achieve
the
within
greatest
a
single,
overall cost
reductions.
This kind
of coordinated planning looked to be a relatively
untapped area in which
company from
it would
be possible
to distinguish the
its competitors, which generally have smaller, less
complex production and distribution systems
than
Linde.
In a
competitive industry such as Linde's, cost reductions of even one
or two percent can be extremely important.
IV. MODEL DEFINITION
Air
separation
fractions.
sites
produce
gaseous
and
air
Gases (oxygen, nitrogen) are distributed by pipeline
to customers located near the site.
Liquids
(oxygen, nitrogen,
argon) are distributed by truck or railroad tanker.
joint deliveries; in fact, each vehicle is dedicated
product.
liquid
There are no
to a single
This means that the distribution system -- and costs--
for each product are linked only through joint
production at the
sites.
The distribution
simple network
of arcs
component of PAMS is thus represented as a
linking production
(or external supply)
points to
customers.
customer.
Unit transportation cost between a site and a customer
reflects
the
distance
In general,
between
any site
can deliver to any
the two points, and perhaps the
page 8
PAMS O.R. PAPER, draft l(rwb), 30 December 1986
intervening geography.
historical
data
and
costs used in PAMS are derived from
The
were
already
in
use
for
distribution
planning.
Most
of
the
structure
of
the
representation of the production sites.
representation
them
joint
from
stems
production,
model
lies
in
the
of this
The complexity
variety of related factors, among
a
electricity
contracts,
and
shut-down
operation.
A. Joint Production
A site
process -- up to
produced at
jointly from
produces products
five
any rate,
products
at
the same production
once.
A
product
can be
within upper and lower limits that depend
upon the site, the product, and the rates at which other products
are being produced.
P1
P2
Figure 2
The
(instantaneous)
increasing function
strong cross
power
of production
demand
(KW)
rates for
of the site is an
all products, with
terms, particularly for liquid products.
There are
page 9
PAMS O.R. PAPER, draft l(rwb), 21 January 1987
strong
theoretical
and
surface is convex.
empirical
In fact,
definitive quadratic
reasons
to believe that the
multiple regression
form gives
a good fit.
to a positive
No closed form for
the function KW=f(P1,...Pn) is known.
KW
production rate, product P2
-
Figure 3
For
modeling
purposes,
all
our
knowledge
about
the KW
surface for a site is obtained from the SOM, which was originally
developed to
help site
most efficiently.
production managers
Given
operate their sites
desired production
rates for a set of
products, the SOM will determine the minimum power demand for the
site
to
produce
at
methods to find this
chemical
engineering,
those
minimum.
where
rates.
This
Wang (1978)).
is
standard
practice in
the complexity and nonlinearity of
the underlying production processes
difficult to
The SOM uses random search
makes gradient
methods very
implement and cumbersome to use (see Martin (1982),
Random
search
methods
also
make
it
configure the SOM to the characteristics of each site.
easier to
page 10
PAMS O.R. PAPER, draft l(rwb), 21 January 1987
B. Electricity Contracts
Virtually the
only variable cost is the cost of electricity
used to run compressors and liquefiers,
is very
so that
production cost
closely tied to the site's power demand.
assign a
therefore
customer
for,
implicitly
say,
alters
L02
(liquid
the
nitrogen) at that site, and hence
A decision to
oxygen)
to
site A
cost of producing LN2 (liquid
the economics
of assigning an
LN2 customer to site A.
But production
cost at
thermodynamic efficiency.
that
are
often
a site
It
quite
is not strictly a matter of
is governed
complex
and
by contractual terms
that
differ,
sometimes
radically, from site to site.
One typical contractual feature is that the site
is charged
both for energy (KWH) consumption and for maximum (instantaneous)
power draw (KW) during
called "billing
some contract
demand".
billing period
These costs
are roughly
-- the soof the same
magnitude, though energy costs tend to be higher.
Under
most
discontinuously by
contracts
time of day.
which the day is divided
hours.
Energy
the
into
charges
are
unit
cost
of
energy
Figure 4 depicts a situation in
on-peak,
mid-peak,
The
relative
and off-peak
highest during the on-peak hours,
lowest during off-peak, and take on an intermediate
mid-peak.
varies
proportion
of
value during
on, off, and mid peak
periods in
a
different.
Any period type may be absent from any day type.
weekday,
weekend
day,
and
holiday
may
all be
PAMS O.R. PAPER, draft l(rwb), 21 January 1987
page 11
$ /KWH
0 ---- hour in day ----- 24
Figure 4
Time of Day Energy Pricing
The charge on billing demand ($/KW) may also be different in
on, off, and mid-peak
energy charges.
periods,
Often
although
not
in
proportion to
billing demand charges are only incurred
during certain periods.
Under such contractual terms, there is a strong incentive to
produce at
higher rates during off-peak periods, when energy and
power are cheaper, and to
throttle
back
during
more expensive
(i.e. on-peak) periods.
C. Shut-down Operation
Linde
has
excess
production
Gaseous products cannot be
for liquids
is limited.
capacity
inventoried,
and
in
some
regions.
inventory capacity
Therefore, it is often necessary to put
a site into standby mode for some part of the month.
If left to itself, an LP model would choose to
down during
expensive.
on-peak hours,
when energy
shut a plant
and power are both most
In practice, such a solution would be impractical for
page 12
PAMS O.R. PAPER, draft l(rwb), 21 January 1987
operational
reasons.
While
the
purpose
of
PAMS was not to
schedule site production day by day or hour by hour, it was vital
that the
solutions be
operationally feasible.
It was therefore
necessary to impose a kind of loose parity between the
length of
time the site would be shut down during on, off, and mid-peak.
D. Slates: Discretizing the Decision Space
Both energy
both are
and power costs can be very significant.
directly related
important
to
represent
One approach might have
to power
demand (KW)
Since
it was clearly
these relationships with fair accuracy.
been
to
use
quadratic
programming to
describe energy costs, but this was rejected for several reasons.
First, there are no commercial grade QP codes capable of handling
MIP constructs.
Also, we had at best only an empirically derived
quadratic KW function, based on regression.
Instead, we chose
number of
to
discretize
production slates.
production rate for each
associated
with
A
the
The basic decision of the model,
space
into
a large
slate is a vector containing a
product, and
operating
the
the minimum
power demand
site to produce at those rates.
therefore, is
to determine how
long to operate each potential slate.
This itself would have presented little problem, since LP is
quite able
cost
of
to represent
power
(so
a convex
called
demand
cost function.
However, the
charge) is based on billing
demand, that is, the maximum instantaneous power demand
entire period.
over the
Thus, this cost would be incurred only by the set
PAMS O.R. PAPER, draft l(rwb), 21 January 1987
of production
rates used
during the period that resulted in the
greatest power demand, regardless
operated.
page 13
of
how
long
that
slate was
page 14
PAMS O.R. PAPER, draft 1(rwb), 21 January 1987
V. MODEL FORMULATION
We present here the original MIP formulation upon which PAMS
based.
was
formulation, both
planning
simplifications.
of this section.
MIP
models
drawn
from
this
prior to and after their application to actual
led
problems,
approach for
with
Experience
a
to
the
modifications
and
discussed briefly at the conclusion
These are
In
of
number
following
implementing the
section,
we
discuss our
system based on these models, and
experience with the system.
Indices
i: 1 to I
index for plants
j: 0 to J
index for slates at each plant (slate 0 is
plant shut-down)
k: 1 to K
index for products
m: 1 to M
index for customers
Parameters
Pij
=
power draw for jth slate at plant i
e i = electric energy charge at plant i
(KW)
($ per KWH)
E i = electric power demand charge at plant i
($ per KW)
Cik m = cost of transporting one unit of product k from plant i to
customer m
($ per cubic foot)
aijk = instantaneous production rate of product k by jth slate at
plant i
(cubic feet per hour)
dkm = demand for product k by customer m
(cubic feet)
R = minimum run time for any slate at any plant
T = length of planning horizon
(hours)
(hours)
PAMS O.R. PAPER, draft l(rwb), 21 January 1987
page 15
Variables
tij = length of time plant i uses jth slate
W i = maximal power demand at plant i
(hours)
(KW)
1 if jth slate at plant i is used at a positive level
xij
0 otherwise
Yikm
=
quantity of product k shipped from plant i to customer m
(cubic feet)
Production Allocation Model (PAM)
I
J
I
minimize z
eiPijtij
i=S
+
EiW
K
+
i
j=u
(1)
ikmikm
i=b k=l
Subject to:
For i = 1,...,I
J
j=1
M
-
aijktij
>
Yikm
0
for k = 1 ,...,
K
(2)
m=l
J
r
tij
=
T
(3)
j=0
tij
- Rxij
>
0
tij
-
<
0
Txij
Wi
(4a)
for j = 1,..., J
Ž Pijxij
(4b)
(4c)
For m= 1,...,M
I
Yikm
tij
0,
W i > 0,
=
dm
for k = 1,..., K
Xij = 0 or 1,
Yikm
0
(5)
(
(6)
page 16
PAMS O.R. PAPER, draft l(rwb), 21 January 1987
The
objective
function
(1)
in
this
energy costs, energy power demand costs,
Note
that
energy
and
power
for use
at each
with that
with
furthermore, each
operating characteristics.
and distribution costs.
costs differ from plant to plant.
This is because the contracts
location, and
model is the sum of
Note
electric
utilities
vary by
plant has its unique design and
also that
the slates available
plant, and their costs, are uniquely associated
plant.
We have
chosen the
fixed number
J of trial
slates for each plant simply for expositional convenience.
The constraints
(2) state
that the
total quantity shipped
from each plant cannot exceed the total production.
the inequality
was extended
to account
for small quantities of
beginning and allowable ending inventories.
state that
In practice,
The constraints (3)
the entire planning horizon is consumed at each plant
by production time and down time
plant shut-down slate).
(recall
that
slate
0
is the
The constraints (4a) and (4b) state that
the time tij that the jth slate is used at plant i, if it is used
at
all,
must
lie
between
maximal allowable time T.
is redundant
the
conditional
The upper bounding
minimum R and the
constraint in (4b)
in the light of constraint (3); we have included it
for expositional purposes. Constraint (4c) ensures that the power
demand W i upon which the power charge is based equals the maximum
of the power demand draws among slates selected by the
plant i.
The constraints
shipments from the plants.
(5) state
We
that demand
note that
model for
must be met by
most customers demand
PAMS O.R. PAPER, draft l(rwb), 21 January 1987
only one
product.
page 17
Thus, the total number of constraints (6) is
far fewer than KM.
The specific models generated by PAMS turned out
complex than
(PAM) for
extended
distinguish
to
operations when
several reasons.
among
peak,
First,
mid-peak
to be more
the model was
and
off-peak
the electricity rates vary significantly.
Plant
shut-downs were modeled more extensively to ensure that shut-down
periods
occur
contiguously.
Moreover,
contracts
with
the
electric utility may be more complicated, involving, for example,
terms
relating
off-peak
to
differences
periods.
These
in power draws between peak and
complications
were
modeled
by
straightforward extensions of the modeling techniques used above.
Finally, for complex manufacturing sites involving several interconnected
plants,
the
models
were extended so that they would
choose the plant configurations as well as the
slates
for each
plant.
Even without
these extensions,
model of the fixed charge
demand charges
variety.
In
a large scale MIP
particular,
the power
associated with the W i behave in a manner similar
to fixed charges.
Tricks involving
objective functions
relatively
(PAM) is
derived from
effective
solutions quickly.
in
A
causing
cutting planes
an optimal
the
charges Ei relative to the
energy
charges
branch and bound to work more efficiently.
the MIP optimization with the best
LP solution proved
models
uniform reduction
on the plant
to
in size
ei
produce good
of the demand
also
caused the
A second pass through
solution from
this heuristic
page 18
PAMS O.R. PAPER, draft l(rwb), 21 January 1987
as incumbent required far less CPU time than that required from a
cold start without an incumbent.
Feedback from
users
at
the
simplification that
allowed the
optimized. For
purposes
running the
the
plant prefer
plants
to
an important
models to be still more rapidly
of
monthly
to employ
period (peak, mid-peak, off-peak).
optimal solution
led
planning,
the people
one slate for each contract
The
slate suggested
from an
to (PAM) for each contract period is the convex
combination of the slates where the weights are
the time that a slate is used.
slate function for the
the fractions of
Since the surface of the cost vs.
plants studied
thus far
has empirically
proven to be convex, we have been able to relax the corresponding
MIP constructs in optimizing the model.
However,
MIP constructs
are still required to properly model shut-downs.
VI. IMPLEMENTATION AND RESULTS
PAMS was implemented for an IBM mainframe computer using the
LOGS model generation language (see Brown
et al
(1986)) and the
IBM optimization package MIP/370.
It is
important to emphasize that the LOGS model generation
in PAMS produces a family of models.
a
model
for
a
specific
region
depends on the data passed to
whether a
certain contractural
it.
The precise
consisting
of several plants
For example,
element is
formulation of
depending upon
present in the data,
certain structures may or may not be present in the model. We reiterate that
the model
(PAM) discussed
in the previous section
_____1_____lIillllli_l____I__
PAMS O.R. PAPER, draft l(rwb), 21 January 1987
was merely
the point
of departure
page 19
for our implementation work,
and the creation of a generator for a family of models.
The MIP models generated thus
have tended
to be
quite large.
far
the PAMS
the
Eastern Region
As many as 1000 slates for each
of three plants were generated by
included in
for
models.
the Site
Optimization Map and
Moreover, the models incorporate
upward of 1000 customers demands over a typical
monthly planning
horizon.
Automatic
procedures
implemented,
but
have
resulting models
columns.
above,
not
have a
Using the
the
customer
yet
aggregation
been
extensively
The
few thousand rows and as many as 10,000
simplifications and
models
used.
were
are
usually
first approximation, within a few
approximations outlined
optimized, at least to a close
CPU
minutes
on
an
IBM 3083
computer.
We believe
that the
lead to shifts
patterns.
in
the
PAMS in the Eastern Region has
prevailing
However,
applications, it
use of
as
is
is difficult
production
often
the
and distribution
case
to substantiate
in
real-world
this belief with
experimental results, for the simple and obvious reason that PAMS
is
not
run
in
fluctuate from
an
experimental
context.
Customer
demands
month to month, and there is no "control" process
to show what would have been done in the absence of a model.
A "base
case" was
run early in the project, in which PAMS
was used to second guess a
The
model
solutions
with a decrease in
recent month's
showed
allocation decisions.
an increase in distribution costs,
production costs
that more
than compensates
PAMS O.R. PAPER, draft l(rwb), 21 January 1987
for this
increase.
Overall, the estimate is that PAMS produces
monthly production/distribution
lower in
page 20
strategies
that
are
1%
to 2%
total cost than solutions that would have been obtained
without it.
VII.
CONCLUSIONS AND FUTURE RESEARCH
PAMS has proven itself to be a useful and important planning
tool at Linde.
Its success demonstrates once again that computer
technology has at last reached a level of
development permitting
mathematical programming models to be implemented and effectively
applied to business
project
skills
was
and
programming,
also
planning
due
to
a
experience
in
chemical
and
computer
Finally, the support of
radically new
problems.
success
of this
felicitous blending of scientific
engineering,
systems
Linde's top
approach to
The
design
mathematical
and
programming.
management in
supporting a
planning was crucial to the project's
success.
PAMS is currently being
national regions.
In this
Optimization
is
Map
several production
extended
for
use
in
other Linde
regard, experimentation with the Site
required
for
plants that
Two of the authors (Hansen and
those
sites
consisting of
can be linked in different ways.
Bonaquist (1986))
have developed
an MIP model for calculating slates for these more complex sites.
A related area of future
Optimization
Map
more
experimentation
directly
directed decomposition methods
to
(see
the
is
to
link
the Site
PAMS models via price
Shapiro
(1979)).
-1--1-- ------
·_
The idea
_·_ _I_ __II__ I_
^ L-i
II1
PAMS O.R. PAPER, draft l(rwb), 21 January 1987
would be
page 21
to occasionally use shadow prices from the mathematical
programming model to price
out slates
produced by
the SOM, and
select new slates for the PAMS model.
Once models for all Linde's regions have been developed, the
intention is to construct
strategic
planning
addressed by such
a
longer
purposes.
a
model
range,
The
national
types
include
of
contract
model for
problems
to be
negotiations with
customers and electric utilities, long term plant shut-downs, and
economic evaluations of new markets.
Moving in the
scope,
a
new
other
project
direction
is
with
underway
to
respect
to
time and
convert the production
planning sub-model in PAMS to a production scheduling model.
reader may
have noted
that the
combination of slates,
but
model (PAM)
makes
no
sequence in which they should be used.
selects an optimal
attempt
to
schedule the
In the short-term when we
consider distinct production periods with varying
plant, and
The
demands on the
recognize that inventory storage for gas is extremely
limited, the
slates can
sequencing
be viewed
of
slates
as fine
becomes
important.
These
tuned adjustments of the tactical
planning slates selected by PAMS.
Finally, generalizations of the
should be
applicable to
models
developed
other process manufacturing industries.
The underlying principle in performing modeling
area
is
to
better
for PAMS
understand
optimization models, which provide
how
to
imbed
research in this
process control
an instantaneous prescription
for the plant, in one or more mathematical programming models for
PAMS O.R. PAPER, draft l(rwb), 21 January 1987
page 22
production planning and scheduling. We believe the models in PAMS
are an important step in this research direction.
VIII. REFERENCES
P. S. Bender, R. W.
"Improving
Brown,
Purchasing
M.
H.
Isaac,
Productivity
at
and
IBM
J.
with
F. Shapiro,
a
Normative
Decision Support System," Interfaces, 15, May-June, 1985, pp 106115.
P.
S.
Bender,
W.
D.
Northup
and
Modeling for Resource Management,"
March-April 1981,
J.
Harvard
F. Shapiro, "Practical
Business Review, 59,
pp 163-173.
Bonaquist and Hansen (1986) SOM in preparation
R. W.
Brown, W.
D. Northup
and Optimization System for
Computer
Assisted
Decision
and J. F. Shapiro "LOGS: A Modeling
Business
Making,
Planning,"
pp
227-241 in
edited by G. Mitra, North-
H9lland, 1986.
D. L.
Martin and
Adaptive Randomly
J. L.
Gaddy, "Progress
Directed Search,"
Optimization with the
AIChE Symposium Series, 78,
1982, pp 79-107.
J.
F.
Shapiro,
Mathematical
Programming:
Structures
and
Algorithms, John Wiley and Sons, 1979.
B. Wang
and R. Luus, "Reliability of Optimization Procedures for
Obtaining Global Optimum," AIChE Journal, 24, 1978, pp 619-626.