Strategic Cost Management · Simulation

Steps in Simulation Modelling for CMA Final

Updated 11 October 2026 · Fact-checked

Simulation modelling is a structured process of imitating a real system with a model and experimenting on it. The steps are: define the problem, identify variables, build the model, assign probability distributions and random numbers, run the experiment, validate the results, and recommend a decision.

Understand Steps in Simulation Modelling

A simulation imitates the working of a real system on paper or a computer. You use it when the system is too complex, risky or costly to test in real life, or when no neat formula gives the answer. Examples are daily demand with uncertain sales, machine breakdowns, and customer queues.

The method follows a fixed order of stages. First you define the problem and the objective, for example, finding the best stock level to minimise cost. Then you identify the variables: decision variables you control, such as reorder quantity, and uncertain variables you cannot, such as daily demand. You also list the parameters (fixed values like cost per unit) and the measure of performance (profit, cost, waiting time).

Next you build the model: the logical relationship between inputs and the result. You collect past data and turn it into a probability distribution for each uncertain variable. From this you build cumulative probabilities and assign random number ranges. A random number then picks a value of the variable, in proportion to its probability.

Then you run the experiment: draw random numbers, read off values, compute the outcome for each trial, and repeat. More trials give more reliable averages. Finally you validate the model, comparing its output with actual history or checking that its logic is sound. Only then do you analyse results and recommend a decision. Simulation does not give a guaranteed optimum. It shows what is likely under the chosen inputs.

Key rules to remember

Probability from frequency: Probability = Frequency of value ÷ Total frequency; Use it to turn past data into a probability distribution. Probabilities must total 1.
Cumulative probability: Cumulative probability = running total of probabilities; The last cumulative value must equal 1.00 (or 100).
Random number range: Range for a value = (previous cumulative probability, this cumulative probability], on a 00–99 scale for two-digit numbers; Example: probabilities 0.20 and 0.30 give ranges 00–19 and 20–49. Allot ranges exactly as many numbers as the percentage.
Average from simulation: Average = Σ outcomes of all trials ÷ Number of trials; Use it for average demand, cost or profit per period.

How to solve Steps in Simulation Modelling questions

Use this order for any question that asks you to set up or run a simulation, or to describe the process.

1State the problem and the objective in one line, for example, estimate average daily profit.
2List the variables: decision variables, uncertain variables, parameters and the performance measure.
3Convert the given data into probabilities, then cumulative probabilities.
4Assign random number ranges to each value, using two digits (00–99) when probabilities are in whole percentages.
5Take the random numbers given in the question in the order given. Read off the value for each trial.
6Compute the outcome for each trial in a neat table, then total and average it.
7Comment on validity: the number of trials, the data quality and what real results should be compared against.
8Give a clear recommendation or conclusion linked to the objective.

Quickest way: Table-first approach

When to use it: Use it when the question gives random numbers and asks for a simulation run or an average over a few days.

Draw one table: value, probability, cumulative probability, random number range.
Check the last cumulative figure is 1.00 before you move on.
Write each trial row with its random number, value drawn and outcome.
Total the outcome column, divide by trials and underline the answer.
Add one line on validation and limits if the question asks for the steps or evaluation.

Common mistakes in Steps in Simulation Modelling

Listing the steps in the wrong order, such as running trials before assigning random number ranges.
Students memorise the names of steps but not the logic that links them.
Fix: Remember the chain: problem, variables, model, distributions, ranges, run, validate, decide. Each step needs the output of the one before.
Overlapping or gapped random number ranges, for example 0–20 and 20–50.
Students copy cumulative probabilities as range ends without adjusting the start.
Fix: Start each range one above the previous end. With 0.20 and 0.30 use 00–19 and 20–49.
Skipping validation or treating it as optional.
Numerical questions end at the average, so validation feels like theory only.
Fix: Add a line comparing the model with actual history or testing it with known inputs. Mention that results hold only if the data are representative.
Using the random numbers out of sequence.
Students pick numbers that give nicer results or lose their place in the list.
Fix: Use the numbers exactly in the order given, one per variable per trial, and mark each one as used.
Calling the result the optimum or the exact answer.
A numerical answer looks final.
Fix: Say it is an estimate from a limited number of trials. More trials improve reliability but never make it certain.

Worked examples

Example 1

A shop's daily demand is 10 units (probability 0.30), 20 units (0.50) and 30 units (0.20). Assign random number ranges, then find demand for three days using the random numbers 18, 73 and 94.

Show the solution

Probabilities total 0.30 + 0.50 + 0.20 = 1.00, so the data are consistent.
Cumulative probabilities: 0.30, 0.80, 1.00.
Ranges on a 00–99 scale: 10 units = 00–29; 20 units = 30–79; 30 units = 80–99.
Day 1: random number 18 falls in 00–29, so demand = 10 units.
Day 2: 73 falls in 30–79, so demand = 20 units.
Day 3: 94 falls in 80–99, so demand = 30 units.
Average demand = (10 + 20 + 30) ÷ 3 = 20 units.

Answer: Demand is 10, 20 and 30 units on the three days. Average = 20 units per day.

Example 2

A firm sells an item at ₹50 per unit with variable cost ₹30. Daily demand is 100 units (probability 0.40) or 200 units (0.60). Fixed cost is ₹1,000 per day. Using random numbers 25, 60 and 38, simulate daily profit for three days and give the average. Also name the step that checks the model's reliability.

Show the solution

Cumulative probabilities: 0.40 and 1.00.
Ranges: 100 units = 00–39; 200 units = 40–99.
Contribution per unit = ₹50 − ₹30 = ₹20.
Day 1: 25 is in 00–39, demand 100. Profit = 100 × 20 − 1,000 = ₹1,000.
Day 2: 60 is in 40–99, demand 200. Profit = 200 × 20 − 1,000 = ₹3,000.
Day 3: 38 is in 00–39, demand 100. Profit = ₹1,000.
Total profit = 1,000 + 3,000 + 1,000 = ₹5,000.
Average = 5,000 ÷ 3 = ₹1,666.67 per day (approx.).
The reliability check is validation: compare the model's output with actual past profit and run more trials.

Answer: Daily profits are ₹1,000, ₹3,000 and ₹1,000. Average profit is about ₹1,667 per day. The check is validation.

Exam tips

Theory questions on this topic usually ask for the steps, so write them in order with one line of explanation each.
In numerical questions, show the table of probabilities, cumulative probabilities and ranges. Marks are often given for it even if the final figure goes wrong.
Always state the number of random digits you use (two digits for whole-percentage probabilities).
Write a closing line on validation, number of trials and limitations to earn the application mark.
For MCQs, watch the wording: the range for a value includes both end numbers, such as 20–49.

Practice questions from Simulation

Steps in Simulation Modelling: frequently asked questions

What are the main steps in simulation modelling?

Define the problem, identify variables, build the model, assign probability distributions and random numbers, run the simulation, validate the results and implement the decision. Some books group these into fewer steps, but the order stays the same.

Why is validation needed in simulation?

A model can be logically neat and still give results far from reality. Validation checks that the model represents the real system, for example by comparing its output with past actual data. Without it, the decision may rest on a flawed model.

How many trials should a simulation have?

There is no fixed number. More trials give more stable averages. In exam questions you simulate only a few trials because of time, so mention that the result is only an estimate.

How do I assign random number ranges?

Convert data to probabilities, then to cumulative probabilities. Give each value as many two-digit numbers as its percentage, starting from 00 and without gaps or overlaps.