Business Simulation

Goal

The technique serves a decision whose calculation inputs are not known: an investment, a price, a product launch, an acquisition. A business case is usually built as follows. For each uncertain quantity, take the most likely value, multiply everything together, obtain an amount. That amount has two defects. It says nothing about how far off it can be, and it matches no particularly likely outcome, because the product of the modal values is not the mode of the product. David B. Hertz set out this argument in the Harvard Business Review in 1964: deciding calls for the range of possible outcomes together with their likelihood. His article brought into corporate decision-making the random-sampling method Metropolis and Ulam had published fifteen years earlier, the Monte Carlo method.

The deliverable is twofold. The distribution of the outcome is read in percentiles and as the probability of crossing a threshold that matters. The ranking of the inputs by their contribution to the spread says which of the unknowns weighs on the answer. The second is often the more useful: it turns "we do not know" into a short list of things to go and measure before deciding.

Usage

When to use it

• No historical data: a product that has never been sold, a market with no precedent; a range elicited from experts stands in for the missing series.
• Intangible quantities at the heart of the calculation: brand value, reputational effect, public acceptance are easier to bracket than to measure.
• A "what happens if" question: a price rise, a change in regulation, the loss of the largest customer.
• A real experiment that is impossible or irreversible: a merger, a market-wide price change, a divestment.
• A decision committing an amount out of all proportion to the cost of the model: a few days of analysis against several million.

When not to use it

• Queues and capacity are in play: a resource-constrained process calls for process simulation.
• Two or three discrete outcomes of known probability: a decision tree gives the same answer in an hour.

Description

The boundary with process simulation

Two techniques in the toolbox carry the word simulation and answer different questions. Process simulation starts from a process that has been mapped and measures its behaviour; business simulation starts from a formula, most often with no process to model at all.

In everyday usage the words "business simulation" and "business game" also name the management game used in training, where teams run a fictional company over several trading periods. The technique described here serves a real decision and returns a number meant for a steering committee.

The three families

The IIBA guide files three families under one name, told apart by the nature of the question and therefore by the way the model is built.

The first two families share one set of tools: a formula, ranges, draws. The third models stocks, flows and feedback loops whose behaviour depends on time, the discipline of system dynamics founded by Jay Forrester in 1961.

Describing an input with a distribution

A distribution describes an uncertain quantity by the values it can take and the likelihood of each. Three shapes cover most of what a business case needs, plus one special case. The triangular distribution is defined by three numbers: the minimum, the most likely value and the maximum. It is the natural shape for a range elicited from an expert. The uniform distribution asks only for two bounds and says that inside them nothing is known. The normal distribution suits a measured quantity whose mean and standard deviation are known. A binary event, a permit refused for instance, is modelled by a variable that takes the value zero or one with its probability.

Eliciting those three numbers is the work of the technique. Ask for the extremes first, then for the most likely value: the reverse order anchors the expert on their central estimate and they tighten the bounds around it, the anchoring effect Tversky and Kahneman described in 1974. The minimum and the maximum are posed as scenarios to be told: what would have to happen for the unit cost to reach CHF 52? A bound nobody can attach a story to is an invented bound; where nobody will sign alone, the Delphi method brings a group to convergence. Each distribution finally receives a written provenance: measured, fitted to a historical series, elicited from a named person or assumed. A study where every provenance says "assumed" produces a distribution of fictions.

Dependencies between variables

Drawing each variable independently is the default setting of every tool. It is also the assumption most often false. If the raw-material price and the volume sold both depend on the business cycle, drawing them separately produces impossible combinations: a record volume with materials at their cheapest. The output distribution comes out too wide or too narrow depending on the direction of the relationship, and the P90 becomes a target the business will never hit. Three answers exist, in order of cost. Set a correlation between the two variables where the tool allows it. Replace both with a single common factor drawn once, from which both follow. Or declare independence as an assumption somebody owns, written into the report.

Running the study

Write down the question and the unit of the answer before any model. "Is the price rise a good idea?" is not an executable question. "What annual contribution margin should we expect from a price raised by 10% and with what probability does it do worse than the current price?" is.

Write the calculation model, the relationship that leads from the inputs to the result. The IIBA guide points out that this model comes from domain knowledge, from business rules and from watching how the people who take the decision go about it. No dataset is its starting point. Write the business constraints into it at this stage: a production capacity, a regulatory ceiling, a headcount. A model that ignores them produces a tail of the distribution the company could not deliver.

Sort the variables between those that carry the uncertainty and those that are known: a quantity fixed by contract stays a number. The count of random variables decides how readable the study is. Three or four can be explained to a committee; fifteen cannot.

Run the draws. A few thousand are enough to stabilise the usual percentiles. Fix the generator's seed so that the study can be replayed identically.

Rank the inputs by their contribution to the spread of the result. Most tools render it as a tornado chart, where the contribution reads as the share of the result's variance an input explains. This step meets sensitivity analysis and produces the actionable part of the work: narrowing the range of the dominant variable tightens the distribution, whereas measuring the others changes nothing.

Reading the output

A percentile is the value below which a given proportion of the draws falls: 90% of the draws exceed the P10, half exceed the P50. The triplet P10, P50, P90 is the standard reading of a simulation result. Beside it, a threshold probability answers the question the committee puts: what chance does this project have of returning less than what we already do or of clearing the acceptance threshold of the business case. It is also the form in which a net present value becomes something a committee can debate: not CHF 2.4 million, but a 73% chance of being positive.

The IIBA guide notes one last use of the model: handed to stakeholders as self-service, it lets them change an input and watch the output move. A committee that moves the adoption-rate slider itself retains more of the sensitivity of the case than it would from a chart somebody else drew.

The traps

The point estimate taken for a result

This is the trap Hertz wrote against. The check costs one line: work out where the point estimate lands in the distribution obtained, then say it.

The range out of nowhere

Three numbers invented in a meeting to unblock the building of the model are indistinguishable from three numbers elicited from the head of production: same decimals, same apparent authority. The provenance column exists for that.

The result nobody can explain

The IIBA guide states it in so many words among the limitations of the technique: the output of a simulation is hard to explain, because of the number of variables in play.

The number of draws mistaken for precision

Going from ten thousand to a million draws tightens the sampling noise of the reading, never the error of the model nor that of the ranges. A distribution obtained from a million draws on assumed inputs is still a distribution of assumptions, with three more decimals.

The model that outlives its question

The workbook is reused the following year for a neighbouring decision, without anyone reopening the ranges or the dependency assumptions. The domain of validity is written into the file: the question it answers, the date of the data, the business constraints hard-coded in it.

AI considerations

The first useful job is drafting the ranges. A language model asked for the plausible bracket of a material cost or a regulatory lead time, with the public sources it can cite, replaces the blank page with a proposal to be argued out with the person who knows the variable. The proposal stays marked "assumed" in the provenance column until somebody takes it on as their own.

The second is writing the sampling code, a few lines that put the technique within reach of an analyst who does not program. The third is fitting a distribution to a historical series where the series exists, mechanical work where attention gives out. The fourth is drafting the summary from the percentiles obtained, where the numbers are supplied and nothing is invented.

Two limits hold. A language model asked "what happens if we raise prices by 10%" makes up a plausible number: it has drawn no sample and there is no distribution behind that number. The technique exists to produce what that answer does not contain. And the provenance of the ranges is a property of the organisation: next year's material cost is negotiated at a supplier, the capacity of the workshop is measured in the workshop. The IIBA guide adds a reservation: other modelling approaches are judged more effective, reinforcement learning for instance, and neural networks are gaining accuracy on the outcomes simulation is used to predict.

Examples

An SME in French-speaking Switzerland making components is considering raising its price from CHF 87 to CHF 96 a unit. Last year it sold 24'000 units at a variable cost of CHF 44, a contribution margin of CHF 1'032'000. Two quantities are unknown for the year ahead, the price being the object of the decision.

The point estimate announced +11% and the median result gives +6%: the gap comes from the asymmetry of the two ranges, two thirds of it from the unit cost. In both ranges the upper bound lies far from the mode while the lower bound lies close to it. The committee receives two numbers the classical calculation could not produce, a one-in-five chance of doing worse than today and a named culprit for close to two thirds of the uncertainty.

Visualisations

One thing alone calls for a drawing: the path from the input ranges to the output distribution. The input is already a curve and the output is another one; that change of shape is what rows in a table cannot show. The register of inputs and the table of percentiles are written in columns, each with its provenance or its interpretation alongside.

A study received is audited with three questions. Where does each range come from and who signed it? Does the report give percentiles and a threshold probability rather than a single number? Where does the point estimate fall in the distribution the study itself produced? A case that answers none of the three has given its uncertainty a shape without having measured it.

Cost

Tooling

The spreadsheet is the usual home of the technique. Its native functions are enough to draw a uniform or a normal distribution and to build a triangular one. The limit arrives with correlations and with reading the contributions, which are awkward to rig up there. Simulation add-ins for spreadsheets (@RISK and ModelRisk from Lumivero, Crystal Ball from Oracle) add the catalogue of distributions, the correlation matrices, the tornado chart and the percentile report, without leaving the workbook that management accounting already knows how to read.

Python and R take over as soon as the study has to be replayed, versioned or built into a pipeline. Some fifteen lines with NumPy cover the common case and the code file is itself the documentation of the model. For the third family, system dynamics tools (Vensim, Stella, Powersim, Insight Maker) natively carry the stocks, the flows and the feedback loops a spreadsheet cannot express.

In project management, quantitative risk tools (Primavera Risk Analysis, Safran Risk, Acumen Risk) hook the sampling onto a schedule or a budget and return a distribution of finish dates or of cost at completion. That variant is the form in which PMI treats the technique, under quantitative risk analysis, downstream of the risk register covered by risk analysis and management.

Sources

• IIBA, Guide to Business Data Analytics, §3.1 Business Simulation: the definition, the four situations that call for the technique, the three families, the variables and their distribution, the self-service model, the strengths and the limitations.
• David B. Hertz, Risk Analysis in Capital Investment, Harvard Business Review, vol. 42, January-February 1964, pp. 95-106, reprinted September-October 1979: the founding article, the critique of the point estimate and the reading of the result as a distribution.
• Nicholas Metropolis and Stanislaw Ulam, The Monte Carlo Method, Journal of the American Statistical Association, vol. 44, no. 247, 1949, pp. 335-341: the mathematical origin of the sampling method and the name that stuck to it.
• Amos Tversky and Daniel Kahneman, Judgment under Uncertainty: Heuristics and Biases, Science, vol. 185, no. 4157, 1974, pp. 1124-1131: anchoring and adjustment, the bias that governs the order of the questions put to an expert.
• PMI, The Standard for Risk Management in Portfolios, Programs, and Projects, 2019: PMI's normative framework, including the quantitative risk analysis in which the sampling applies to cost and schedule.
• Jay W. Forrester, Industrial Dynamics, MIT Press, 1961: the founding work of system dynamics, the discipline behind dynamic simulation.
• System Dynamics Society, Origin of System Dynamics: the genesis of the discipline and its reach.