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Stock or Capacity: Tuning the Production Process
for Optimum Performance
Ralph Seeley
PA Consulting Group
Alan Tullo
British Steel, General Steels, Teesside Works
Reduced stock and greater flexibility in responding to customer
demand are now recognised to be highly desirable, and not necessarily
incompatible, objectives. General Steels initiated a project to
explore the extent to which they could operate in such a 'demand
pull' mode.
A steelworks is a particularly exacting environment for 'demand
pull', because the resources being 'pulled' become inherently
less responsive as the blast furnace - the primary iron-making
resource - is approached. Resource inter-dependence resulting
from reliance on a common primary plant adds further complexity.
In attempting to resolve these issues the authors were forced
to examine some of the fundamental means of meeting variable demand
from resources of strictly limited capacity and flexibility.
INTRODUCTION
Much has been written about the virtue of reducing stock levels.
For most companies it is undoubtedly a worthy objective. The ideal
level of stock is not usually zero however. Generally a point
will eventually be reached below which further stock reductions
either endanger customer service or require a facilitating investment
whose cost exceeds the available saving. Find this 'ideal stock
level' and you can set priorities and targets for inventory reduction
projects more objectively.
Stock represents one way of matching resources of inherently
limited flexibility with uncertain and irregular demand from impatient
customers. The usual alternative is to invest in plant so as to
increase its ability to cope with demand peaks. Since either route
implies a commitment of capital to under-employed assets, the
'best' choice is the one which satisfies customers' service requirements
at minimum cost - whether that means stock, extra or more flexible
capacity or a judicious mixture of both.
Finding the combination of stock buffer size and capacity margin
which meet a target customer service level at the lowest possible
cost is a task for which we know no solution combining rigour
and practicality. In writing this paper we hope to raise the awareness
of the problem, to solicit other experiences and approaches, and
by describing how we tackled a particular problem, perhaps advance
the subject a little.
APPLICATION
The ideas that are discussed in this paper arose from a project
that the authors undertook for General Steels, Teesside during
an eight month period terminating in April 1991. Where company
confidentiality permits, we have used the results and insights
gained during that project to illustrate this paper.
The objective of the project was to explore the extent to which
steel production could be organised on a 'demand pull' basis,
whereby customer requirements were much more immediately matched
by production, rather than via pools of intermediate stocks. Because
it represented the greatest challenge, it was decided to focus
attention on the primary steel-making process.
Primary steel-making is a difficult process to convert to a demand
pull mode of operation, since it is only one process step downstream
from the blast furnace. The blast furnace is an almost perfect
example of 'material push' because its thermo-chemical process
is intrinsically continuous.
Each process step from the final finishing mills back to the
blast furnace (potentially) contributes towards the reconciliation
of customer's highly varied requirements and the plant's inherently
limited capabilities - between the 'demand pull' of the customer
and 'material push' of the blast furnace. By concentrating on
primary steel making we were investigating the process at which
most of the reconciliation occurs and at which, therefore, decisions
are made which influence stock levels throughout the company.
OBJECTIVE
The project was required to answer two specific questions:
- Could primary steel making be made more responsive to demand?
Could a 'demand pull' regime be instituted, and if so, to what
extent?
- Would it be cost effective to make particular (quite specific)
investments to improve plant flexibility?
APPROACH
We adopted a 'two-pronged' approach.
- we built a simulation model. By varying the lead time margin
we adjusted the planning flexibility available to the plant
scheduler.
- we sought to develop a theoretical model in parallel with
the empirical one. If we could use the results from the simulation
to validate and calibrate the theoretical model then we might
be able to suggest improvements rather than simply estimate
the cost and benefit of externally-generated proposals.
Simulation Model
An outline of the structure of the model we built is shown below:
The simulation was used to investigate the consequences of reducing
the plant scheduler's normal flexibility in deciding an order's
make date. This flexibility can result in raised stock levels.
Faced with a 'lumpy' demand pattern, schedulers use the flexibility
to make some orders early in order to achieve a smooth production
pattern. The model alters the scheduler's flexibility by adjusting
the length of the time window within which the manufacture of
an order must be initiated.
Using historically recorded demand for primary steel products,
a rolling forward order book was simulated. A margin of flexibility
was added to each product's normal production lead time to determine
the manufacturing window - the 'make window' - for each order.
This 'make window' or 'lead time margin' provides what we subsequently
refer to as the 'planning flexibility'.
Scheduling primary steel manufacture is an extremely complex
problem for which manual methods have so far proved best. In the
interests of realism the scheduling of the simulated order book
was also done manually.
Each simulated day the model determines which orders have just
become 'visible' - i.e. simulated time has reached the start of
their make window. As much as possible of the outstanding order
book is then satisfied from existing stock. The remaining unplanned
orders are presented to the planner for scheduling.
The above process is repeated day-by-day until the end of the
simulated period is reached. The model then analyses the final
schedule and produces statistics on plant throughput, stock levels,
customer service achievements and operating costs.
The simulation model yielded unambiguous answers:
- The proposed plant enhancement investment was demonstrably
cost-effective. (The decision to make this investment has now
been made and the equipment is due to come on-stream during
1992)
In reaching the first conclusion, the simulation model provided
two points on a curve of capacity versus planning flexibility.
Although these two points were in-line with what might be have
been expected from theoretical considerations, they were insufficient
to validate or calibrate the theoretical model.
Outline Theoretical Model
In the event, although we made some progress, we did not obtain
sufficient data from the simulation runs to validate our theoretical
work. Nevertheless we have outlined the progress we did make because
we consider that the approach looks fruitful and because it offers
the prospect of answering difficult questions with much less effort.
In addition any progress towards balancing the flexibility of
the constituent processes of an integrated plant (as discussed
in 'Flexibility Balancing' towards the end of this paper) is likely
to require a reasonably concise sub-model for each process.
Basic considerations
Unless they are lucky most plant or factory managers face demand
something like this:
In terms of its statistical properties, this profile is similar
to the weekly demand on Teesside for raw steel. The average demand
represented by this sequence is indicated by the lower line.
The plant's capacity is indicated by the upper line. Over a long
enough period, it must be greater than average demand, otherwise
overdue orders would increase without limit - a condition which
few customers tolerate even if the organisation itself would.
However it is achieved, we start by assuming that long term capacity
exceeds long term demand by some margin. We are interested in
learning how that capacity margin and the variability of demand
to which the plant is subject, combine to influence stock levels.
The obvious way of matching variable demand to fixed capacity
is represented by 'peak-lopping'.
When demand exceeds capacity the excess is held (overdue) until
a lull occurs. In effect the peaks are 'swept' into the troughs.
The greater the margin between capacity and average demand, the
smaller the peaks will be compared to the troughs, and the shorter
the average distance travelled by a peak before it falls into
a trough. Viewed this way, each day travelled is a negative contribution
to service level.
For such a simple case, it should be possible to establish an
approximate theoretical relationship between service level, capacity
excess and demand variability. Indeed, if orders are processed
in the order in which they are received this can be considered
to be a queuing situation for which the objective is as short
a waiting period as possible. In fact this very simplistic model
predicts very short waiting periods - an average of ~1 day for
the data illustrated above.
Few organisations would contemplate a system for which some delay
is almost inevitable, and the obvious means of avoiding doing
so is to launch a job into the production schedule earlier than
its work content would suggest. Thus, if an average queuing time
of 1 day was expected, it might be prudent to be prepared to start
jobs up to 3 days early. Some jobs would still be overdue because
they had arrived as part of a peak, but their proportion would
be small, and it could be made still smaller by extending the
3 days to (say) 6 days.
If jobs which incur an average delay of 1 day are started 6 days
early, then finished product stock equivalent to ~5 days demand
will be generated.
Average stock levels can therefore be made a function of:
- demand
- demand variability
- capacity
- required service level
If the demand characteristics are considered given, and customer
service level is a matter of company policy, then this argument
yields stock as a function of capacity. Associate appropriate
financing costs to both capacity and stock and, for this highly
simplistic example, stock can be traded-off against capacity.
Product Mix Variability
The previous example is simplistic in a number of ways. The most
serious simplification, certainly from General Steel's stand-point,
is that demand has been considered to vary only in terms of quantity,
whereas in fact it varies considerably in product mix. It is this
latter variability that is the root of most production control
problems.
Rather than modify the definition of demand variability we have
chosen to generalise the concept of 'capacity'.
Generalised Capacity
Capacity is an elusive measure for a complex plant. Many factors
must be defined before the term has much meaning. Obvious examples
include the speed of working, the number of shifts, the possibility
of overtime, whether maintenance or breakdowns should be included..
. When all that is done the answer will still be highly dependent
on the number and severity of the product changeovers required
by the mix of products demanded. (It must also be a function of
the extent to which real schedules are sub-optimum, but since
that deficiency can be expected to be reasonably consistent we
shall ignore it.)
If the product mix is defined to be typical of, or identical
to, that experienced during a particular historic period, then
potential throughput may be considered a function of the average
planning flexibility - the lead time margin or 'make window' that
we have already defined. In the interests of brevity we use the
term 'Generalised Capacity' to mean the maximum possible throughput
as a function of the planning flexibility.
The basic shape of the Generalised Capacity curve must be similar
to those illustrated to this:
The origin represents the capacity available when there is no
scope to re-sequence jobs in order to minimise the impact of product
changeovers. We call this the unscheduled capacity. As the flexibility
to juggle jobs is increased, so is the available capacity. The
gain is high at first but becomes progressively less as the changeover
rate - and hence the scope to make further savings - is reduced.
The shape of the curve is a function of the average product mix
and the flexibility of the plant to respond to that mix. If the
three curves represented different plants response to the same
product demand mix, then the upper one would represent the plant
most suitable for a 'demand pull' or JIT mode of operation since
it represents the plant for which the impact of reducing lead
time margin is least.
In terms of the queuing analogy, capacity has become a function
of queue length, and the queue discipline is no longer FIFO but
prioritised so as to provide the maximum capacity gain. This complicates
matters significantly, but it is still possible to employ queuing
theory to obtain first order estimates of the probability that
the queue represents the production of any specified period. In
this way average queue lengths and expected stock levels can be
estimated.
To use this theoretical relationship in practice it is first
necessary to estimate the form of the generalised capacity curve.
The curve must then be expressed mathematically before it is possible
to apply the appropriate formulae. Lacking sufficient data to
parameterise this curve fully, we were only able to estimate stock
levels for plausible realisations of it. Limited as such an exercise
was, the extent of the dependency of stock levels on the form
of this curve was gratifyingly high - the greater the resemblance
to the lower of three generalised capacity curves above, the higher
stock levels have to be kept to provide a desired capacity. Trying
to run too close to the asymptotic maximum proves particularly
unwise.
This concept of generalised capacity offers the prospect of qualifying
the natural desire to run plant at the highest possible throughput,
and it also suggests ways in which our original objective of finding
the best way to meet customer requirements at minimum overall
cost might be achieved.
General Steel's own circumstances are such that increased flexibility
or greater 'flatness' for the generalised capacity curve is a
more obvious objective than raising the height of the curve as
a whole - there is, after all, no possible requirement to process
more steel than the blast furnace can produce.
Flexibility Balancing
Recognising that one process among several might carry the brunt
of matching demand to capacity within an integrated plant leads
to the conclusion that improving the flexibility of other processes
may be futile if it exacerbates the task required of the limiting
process. And if improving the flexibility of a particular non-limiting
processes is pointless, then (theoretically) a slightly less flexible
plant might have been a better solution in the first instance.
Apply this idea, in concert, to all non-limiting processes and
it is possible to conceive of an integrated plant for which flexibility
is balanced between constituent processes.
Fascinating as these latter ideas are, the authors did not have
the time to pursue them, nor, since the investments have already
been made, would it have made much sense to do so. In different
circumstances, they may be relevant or they may have been applied
and we invite comment or references.
CONCLUSION
In the interests of readability, we have skipped much detail
and we have explored few of the complexities which can arise in
practice. If, for example, obtaining the required throughput means
extending the lead time margin to the point at which customer
demand must (to some extent) be predicted, then stock levels must
be further enlarged to include an element of safety stock.
Cursory as this paper has inevitably been, we hope it serves
to trigger interest and debate about a subject which is not only
fascinating, but also of relevance to almost all manufacturing
concerns. Although we have not derived formal mathematical expressions
we have shown service level, stock, demand and capacity margin
to be related. Variability has been introduced - directly for
quantity, and indirectly (via the concept of Generalised Capacity)
for the mix of product demand.
In fact underlying the whole discussion is the recognition that
most production control problems stem from the variability and
unpredictability of demand. Although the explicit recognition
of uncertainty introduces a measure of complexity - particularly
in the theoretical domain - it does represent reality. It is the
authors' belief that much of what is now attributed to 'Sod's
Law' is caused by using deterministic models to represent realities
which invariably include a healthy measure of randomness.
ACKNOWLEDGEMENTS
The authors would like to thank:
British Steel, General Steels Teesside Works for permission to
publish this paper.
Messrs John McEwan and Roger Miles and the other members of the
Countdown team with whom the authors worked during the course
of undertaking their project.
Mr Matthew Robinson and Miss Coral Wigg for programming the simulation
model
Mr Mike Coleman of General Steels for his patience and diligence
in not only scheduling the simulated order book, but for providing
much valuable advice about the constraints faced by the production
planning team.
REFERENCES
Queuing theory:
Donald Gross and Carl M Harris; 'Fundamentals of Queuing Theory';
1985; John Wiley & Sons Inc.
BIOGRAPHIES
Ralph Seeley BSc FSS MILDM
Ralph Seeley is a principal consultant in the Logistics Practice
of PA Consulting Group where he specialises in the use of analytic
tools and computer modelling to assess and to effect business
improvements. Ralph worked in the oil, defence computer and engineering
industries before joining PA eight years ago.
Alan Tullo BSc PhD AFIMA
Dr Alan Tullo is the manager of General Steel's Teesside Works
OR Department. The OR Department has developed and implemented
planning and scheduling systems, expert systems, stock control
algorithms and plant operation computer simulations. Alan was
a mathematics lecturer before joining General Steels.
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To improve the responsiveness
of primary steelmaking significantly by reducing planning
flexibility would incur greater expense in terms of increased
operating costs, reduced customer service and reduced capacity
than it would provide benefit in the form of a reduction
in stock. A halving of the planning flexibility resulted
in overall stock levels down by about one third. However,
the value of this reduction was more than offset by reduced
customer service, increased operating costs (up by around
7%) and reduced throughput (down by between 0.5% and 1.0%).
