---------- The "Simple" Version ----------
Many years ago, while starting up a new business, I participated in a
"Small Business Startup" class. A part of that class
called for business plan generation, which, of course, called for
cash flow estimates based on product and resource costs, and sales
forecasts. It's common to use a process-driven* spreadsheet to
do this type of work, but the spreadsheet environment quickly became
complicated and slow. Without an (e.g. VBA) add-on,
spreadsheets don't handle event lists and waiting lines well;
spreadsheets don't have convenient facilities to implement while and
for loops; spreadsheet conditional computations are difficult to
implement; balking, reneging and jockeying are difficult to
model.
Since the output data must be stored in the spreadsheet, usually in a
column, the length of the output series is limited by the maximum
column length. It happened that I'd been working on a generic
discrete event simulation package for several years
(Smalltalk-based), and this offered a meaningful opportunity to get
deeper into the simulation world (see
Simple Simulator
Application in
Application
Development). The figure above right shows some of the output
from that early model. Years later, the model graduated to the
one at left -- built with a commercially available simulation
package (Simul8).
Questions that this model can answer include: "What markup must
I use to sustain my current production environment (i.e.
current labor, plant and supply resource costs, and current
production volume)?"; " Given my current markup and
resource costs, can I sustain the production level I need to meet
expected orders?"; " Given the current production level and
resource availability, am I going to overwork my labor
resources?". Some of the output from this model is shown
at right for multiple one year simulation replications. Supply,
labor and plant resource utilizations show a convergence to
respective long-term expected values. "Jobs waiting for a
resource" and the "number of completed jobs" do not
converge to an expected value for the timeframe and markup value
selected (a markup value of 3) -- indicating there is an availability
issue with one or more of the resources.
There are several interesting aspects of this model. First, the
model shown here isn't strictly discrete event, but a combination of
discrete event and continuous. It happens that there can be
model solution speed and accuracy problems with discrete event
simulations when they try to model continuous or quasi-continuous
behavior. In the cash flow part of this model, for instance, if
cash is represented by discrete money packets that move from point to
point (e.g. from gross to net revenue) in, say, packets of $1000,
then the division of cash into non-$1000 packets for paying labor
resources (for example) disrupts the flow of the model and is
simulation time consuming.
If the packets are smaller, say $10 or even $1, then the solution
time rises exponentially. How does discrete packet size effect
solution speed and accuracy? Do continuous and discrete
solutions converge to the same value and give the same confidence
intervals? The figure to the right shows convergence to a labor
utilization value (~0.75±0.05) for several solution types and
five replications at each type. The abscissa shows that I tried
three discrete event $ packet sizes as well as a combined discrete
event / continuous solution. As you can see, the combined
discrete event / continuous (Flow) model arrives at the
"same" labor utilization and confidence interval as does
the $10 packet discrete event model -- at 1/500th of the solution
time/cost! It should be noted in this figure that the $1000
packet size confidence interval does not include the discrete event /
continuous (Flow) mean value nor does the Flow CI contain the DE mean
value, though the confidence intervals do overlap. What does
this mean? Statistically this means that the two models are
probably solving different problems -- i.e., based on the relative
mean value convergence shown from $1000 packets to $100 packets to
$10 packets, the $1000 packet size model results probably aren't
accurate. For a 99% confidence interval, these models can be
shown to be the "same" (the mean values are covered by the
opposing CIs).
---------- Advanced Versions ----------
This paragraph touches on two updated versions of the
simple cash flow model.
The
first version is described in a downloadable, but rather long,
Microsoft Word presentation of a Microsoft Power Point slide show
(26MB). That document contains a general, high level
description of how I attacked the modeling, and more detailed
descriptions of the model's input/output, verification and
validation. The second model version, described in the
remainder of this paragraph, added several new reporting
features. One of the new abilities for both versions was to
compare constrained and unconstrained business resource models.
An
unconstrained business resource model is one in which the
resources (Labor, Product Supplies and Plant in this case) are free
to seek their optimal levels, given an expected costs of sales and
business income allocation. A
constrained business
resource model is one in which resource floors and/or ceilings are
established (for instance, the number of laborers might be
restricted); the constrained analytical model is then allowed to seek
it's own optimal cash flow level, if possible. In the figure at
right (from the second updated model version), I've described a
possible small business environment with manufacturing, sales,
shipping and cash allocation information. Labor, Product
Supplies and Plant unit availabilities are not constrained.
(Resource "units" are meaningful collections of information
used to capture the essence of each resource and it's cost(s), kind
of a resource building block annotated with costs. A
"Labor Unit" is, in this model, one person that can work at
either a manufacturing, sales or shipping station -- along with
related salary and overhead costs [totaling $2,926/month/unit
here].
A "Product Supply Unit" encapsulates all non-reusable
components necessary to construct one product -- along with primary
and related secondary costs [totaling $10/product here]. A
"Plant Unit" encompasses product manufacturing, sales and
shipping space and any associated space maintenance cost -- such as
cleaning, heating and lighting [totaling $1100/month/unit
here].) Four random input replications generated the output
data and graphs shown in the figure at left, where it's estimated
that an average of 1.92, 1.93 and 2.02 Supply, Labor and Plant
resource units, respectively, will allow the business to function for
one year without running out of cash. (For purposes of this
discussion, we've assumed an ideal business environment where, for
example, there are no process breakdowns and all products are sold
relatively soon after they're manufactured). Average resource
unit utilizations are estimated at 35%, 55% and 54% respectively,
indicating that a significant number of Product Supplies are idle,
that Labor might be slightly under used and that a more efficient use
of Plant space could be looked into.
(At this point in the design/analysis process, the analyst will want
to re-verify and re-validate the model -- including touching base
with domain experts to validate, for example, typical resource
utilizations.) This model is estimating that 640 products can
be shipped in one year (the simulation runs for 1.25 years, including
the three month warm-up), at an average sales price of $246 (~$163
coming from manufacturing costs, $73 from sales costs and $10 from
shipping costs). Constraining the maximum number of available
Labor, Product Supply and Plant resource units to 1 each results in
the data shown at right, where the number of shipped products has
reduced to 624 (down 2.5%), the expected product sales price has not
changed significantly ($241, down 2%), the Product Supplies
utilization has increased to 62%, and the Plant utilization has
increased to to 99%. The Labor resource utilization is also
forecast to be 99%, an unreasonable number for Labor. (In this
model, one Labor unit is automatically associated with one Plant unit
of environment unless explicitly constrained otherwise.)
It should also be noted that the production and sales queues appear
to be somewhat unstable, steadily increasing through time.
Increasing the Labor limit to 2 units and keeping Product
Supplies and Plant limited to 1 unit reduces the Labor utilization to
a more reasonable 57%, while keeping the estimated number of shipped
products about the same (618, see left, now constrained by available
plant units) -- of course, the feasibility of moving two Labor units
into the same Plant space would need to be investigated. The
estimated average sales price remains about the same ($245) and the
production and sales queues now appear to be more-or-less under
control. The confidence intervals for this last run are
comparable to those of the original run, indicating that we're
comparing apples to apples. As an aside, increasing/decreasing
allowable Plant units is equivalent, in the
Real World,
to increasing/decreasing the business floor space (or perhaps moving
to a new, more/less expensive location or finding a less/more
efficient manufacturing process or ...). An increase/decrease
in the maximum number of Product Supply units could reflect a Real
World increase/decrease in customer demand.
----- Minimum Cost, Maximum Profit and Minimum Sales Price -----
For a given business environment (as defined in the
yellow/beige area, for example, in the above "
Advanced
Business Simulation Model" figure or in the figures that
follow), the processes of
minimizing cost and
maximizing
profit are carried out by reducing specific cost-of-sales
factors.
The above cash flow model has focused on
minimizing sales
price by first allowing supply, labor and plant resource
utilizations to self-adjust (to a level dictated by the other
business environment parameters) at the expense of cost-of-sales and
profit -- and then by enforcing maximum resource availability
restrictions that force-adjust resource utilizations to reasonable
values. This shifts the focus from an atomistic one (concerned
with manipulating those many individual business components) to a
holistic one (concerned with manipulating the business as a
whole). This isn't to say that minimizing cost and maximizing
profit by addressing specific cost-of-sales factors isn't important,
I'm just pointing out that perhaps thinking about a minimum sales
price might give additionally valuable information about the
business.
As such, this simulation comes closer to approximating a minimum cost
environment than a maximum profit one. Directly manipulating
the above cash flow model to satisfy a minimum cost objective
function (e.g. minimizing
CostOfSales =
GrossRevenue - NetProfit - Allowances - Taxes - Operations by
varying the "decision variables" Markup, Available
Supplies, Available Labor and Available Plant) gives rise to the
results pictured in the figure at right. Directly manipulating
the cash flow model to satisfy a maximum profit objective function
(e.g. maximizing
Profit = GrossRevenue -
CostOfSales - Allowances - Taxes - Operations by varying the same
decision variables) gives rise to the results pictured in the figure
at left where the product markup has been allowed to approach
5. The similarity between the results of these two models is
that both converged to single Supply, Labor and Plant unit
availabilities. The major differences between these two results
and the results reported in the figure "
2nd
Constrained Simulation Model Output
", above, are that the constrained model settled on using two
labor resources, the average constrained sales price is slightly
lower than that from the minimum cost model and the profit in the
minimum cost model is roughly twice that from the constrained
model. The forecasted number of products delivered is the same,
for all practical purposes, in the constrained model as in the two
optimized models (~1% difference). The overriding major
difference between these models is in resource utilization -- the 97%
labor utilization predicted in the optimized models (for one labor
resource) is clearly unrealistic.
Supply Chain Management
Finally, the above single-business model became a key part of the
chain of entities involved in manufacturing, distributing,
wholesaling, retailing and consuming products. This type of
distribution chain simulation has generally become known as the
"Beer Game" or the "Beer Distribution Game"
simulation, named after an MIT supply chain management game developed
in the early 1960's (
Wikipedia
reference). An initial version of my distribution network is
pictured at right, where only minor modifications to the
single-business model were necessary to incorporate order timing,
volume feedback and income from downstream entities. Each
business cloud (block) at right encapsulates the business structure
presented in previous paragraphs. The figure shows three types
of blocks: (1) Producer, where production is driven by order requests
and constrained by resource availability, and resources are mostly
manufacturing-related, (2) Distributor/Wholesaler/Retailer, where
sales are order driven and resource constrained, and resources are
mostly sales-related, and (3) Customer, where consumption is need
driven and cost constrained. Individual Producer and
Distributor/Wholesale/Retailer blocks (businesses) converged, or
didn't converge, to stable individual business environments depending
not only on internal "controllable" parameters but also on
uncontrollable parameters coming from outside interests. Then,
the network as-a-whole converged, or didn't converge, to a stable
distribution network.
The Bottom Line
The bottom line here is that verified and validated
simulations can provide business owners with a valuable "what
if" tool for reasonably drawing a line between cause and
effect. But, as I point out in the Microsoft Word
document referenced above, "The simulation must accurately
carry out the intent of the model...", "Rigorous model
verification and analysis validation leads to believable process
understandings.", and "Ultimately, verified and validated
simulations provide only estimates of RWS [Real World Systems]
performance.".
* Process-driven: models the logical sequence
of events for each customer, using one row of the spreadsheet for
each customer. Activity-driven: models the activities
that occur during fixed intervals of time, using one row of the
spreadsheet for each time interval. Event-driven:
models the changes in the system at the moment of each stochastic
event, using one row of the spreadsheet for each event.
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