BUSINFO 705 Chap.5 Comparing Policies with Simulation Evidence
Comparing Policies with Simulation Evidence
This chapter compares operating policies under identical uncertain scenarios. Each trial sends the same demand draw through both policy formulas and records a difference in a fixed direction. The mean paired difference, its confidence interval, the win frequency and downside measures provide complementary evidence.
Inventory examples show why sales, leftovers and shortages need piecewise formulas and why a recommendation should include a sensitivity trigger. The paired design is checked by reconciling the difference mean with the two policy means and tracing adverse rows through the operating logic. Statistical advantage is kept separate from implementation certainty.
What this chapter covers
- 01
Piecewise inventory profit logic
- 02
Common random numbers
- 03
Paired policy differences
- 04
Confidence intervals around mean gain
- 05
Win frequency and downside risk
- 06
Sensitivity and implementation triggers
Worked example · free
Interpret a paired policy interval
- 1Define positive differences as favouring Policy B.
- 2Calculate the margin 1.96(91.84)=$180.01.
- 1The confidence interval is approximately [$620,$980].
- 2Because the interval is above zero, it supports a positive mean gain for B under the model, but not a gain in every trial.
Key terms
- Common random numbers
- Using the same uncertain draw for every policy inside a paired simulation trial.
- Paired difference
- One policy output minus another under the same simulated scenario.
- Win frequency
- The proportion of paired trials in which the selected policy produces the better output.
- Shortage cost
- The penalty assigned to demand that cannot be met under an inventory policy.
- Holding cost
- The cost assigned to inventory left unsold after demand is realised.
- Review trigger
- A specified operating change that prompts the model and recommendation to be updated.
Comparing Policies with Simulation Evidence FAQ
Why should policies share the same demand draw?
A shared scenario keeps the uncertain environment constant while the policy changes. This isolates the policy effect and reduces noise in the paired difference. Separate random draws mix the decision effect with two different operating conditions.
What does an interval above zero establish?
When the difference is defined as Policy B minus Policy A, a confidence interval for the mean entirely above zero supports a positive average advantage for B under the simulation model. It does not mean B wins every simulated scenario.
Which sensitivity test matters most?
Vary the assumptions that create the policy trade-off, such as demand variability, holding cost and shortage penalty. Find the first plausible value that reverses the preferred policy, then use that value as a decision boundary or review trigger.
Why report a win frequency beside the mean difference?
The mean describes the average size and direction of the paired advantage, while win frequency shows how often one policy performs better. A policy can win only slightly more often yet have a large average gain if a few favourable scenarios produce unusually large differences.
How can I audit a piecewise inventory payoff?
Recalculate cases with demand below, equal to and above the order quantity. Sales cannot exceed demand or available stock, and leftovers and shortages cannot both be positive in the simple one-period model. Trace at least one adverse simulated row through every revenue and cost component.
Assessment move
Write the piecewise profit relationship and test three deterministic cases before simulating: demand below order quantity, equal to it and above it. Put one demand draw in each trial row and feed it through both policy formulas. Label the difference as B minus A or A minus B before copying formulas. Recalculate several rows by hand and verify the signs.
Summarise the mean difference, confidence interval, win frequency and lower-tail risk, then explain why each measure answers a distinct question. Finish by changing holding cost, shortage penalty and demand variability until the ranking reverses, and state that boundary in the recommendation. Reconcile the average of the paired-difference column with the difference between the two policy averages.
Count positive rows independently to verify win frequency, then inspect one large gain and one large loss through every component of profit. Confirm that sales never exceed demand or stock and that leftovers and shortages cannot both be positive in the same simple period. Write the subtraction direction in the column title, chart caption and recommendation.
Reverse it once as a diagnostic and confirm that every sign and verbal preference changes consistently. Examine whether a large mean gain is supported broadly or driven by rare extreme differences. State whether the confidence interval concerns the average advantage or individual outcomes.
Close with an implementation condition and a measurable review trigger so a positive simulation result is not mistaken for a guarantee in every operating period.
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