Put capacity where the demand arrives
Do equal staffing budgets produce equal service?
Entering midway? Revisit When faster work creates a bigger pile for the preceding worked example, or start here and use the explanation below.
Start with a concrete question
Original synthetic scenario. Six service periods have demand [3,3,12,12,6,3]. Three staffing schedules use equal total staff-periods but distribute them differently.
Try the initial inputs, then write a prediction before changing one setting. All calculations run locally on your CPU.
What do you expect?
Will an early-heavy schedule serve as many people as one concentrated near the demand peak?
Change one thing. Inspect what happens.
- Compare all schedules at the same multiplier and productivity.
- Inspect waiting by period as well as total served.
- Reduce staffing and identify where shortages first appear.
- Recommend a schedule using a stated service objective; acknowledge staffing feasibility and unmodeled arrival uncertainty.
Your settingsMechanism
Calculation belowEvidence
Compare outcomes
Compare the current results
Every bar starts at zero and uses the same numeric scale in this chart. The upper bound automatically adjusts to the largest current value (at least 1), so compare the numbers when changing inputs. Units and quantities come from each label; different kinds of quantity are not interchangeable. Displayed values are rounded to at most six significant digits.Follow the calculation
- Period 1: workers 3, capacity 9; waiting 0 + arrivals 3 − served 3 = 0; unused capacity 6.
- Period 2: workers 3, capacity 9; waiting 0 + arrivals 3 − served 3 = 0; unused capacity 6.
- Period 3: workers 3, capacity 9; waiting 0 + arrivals 12 − served 9 = 3; unused capacity 0.
- Period 4: workers 3, capacity 9; waiting 3 + arrivals 12 − served 9 = 6; unused capacity 0.
- Period 5: workers 3, capacity 9; waiting 6 + arrivals 6 − served 9 = 3; unused capacity 0.
- Period 6: workers 3, capacity 9; waiting 3 + arrivals 3 − served 6 = 0; unused capacity 3.
The schedules use equal staff-period budgets but place capacity differently. Compare both total service and when waiting occurs before choosing.
Captures keep your inputs, prediction and observation. Results are recalculated from those inputs. Resetting inputs keeps your captures and challenge history.
Explain the mechanism
What the experiment explains
Original synthetic scenario. Six service periods have demand [3,3,12,12,6,3]. Three staffing schedules use equal total staff-periods but distribute them differently.
Capacity is time-specific: unused service places cannot be stored for later. Equal staff-periods guarantee equal nominal capacity, not equal realized service.
At multiplier three, each schedule uses 18 staff-periods. Even staffing gives nine places each period. The two peak periods then create queues of three and six before later capacity clears them.
A peak-focused schedule may create early waiting while reducing later backlog. No single summary captures every user experience; inspect the full trajectory and choose an objective.
Read the relationship
Capacity = workers × productivity. Served = min(previous queue + arrivals, capacity). Next queue = previous queue + arrivals − served.
Inspect the evidence
The numerical trace is recalculated from your current settings. Compare a controlled pair of trials before changing several inputs together. Inspect intermediate quantities as well as final metrics; state which assumptions make the comparison meaningful.
Boundaries of the model
- Fixed period demand, identical service times, no abandonment or staff break constraints.
- Staff-periods are a workload budget, not a labor-law-compliant shift plan.
Return to the systems thinking and operations course and project to connect this mechanism to the broader investigation.
Try a fresh case
A service begins with 4 people waiting. Eight arrive, two staff can each serve 3 in the period. How many remain waiting?
This is a public practice check. Retries support learning; matching a number does not certify independent proficiency.
Take the investigation further
Choose any extension. These are project prompts for you to carry out; they are not automatically assessed.
School investigation
Use tokens to compare equal staffing totals placed at different times.
College investigation
Optimize staffing under a peak-queue constraint and compare against an independent enumeration.
Workplace investigation
Prepare a staffing proposal including demand evidence, breaks, staff skills and a waiting-time target.
Keep the evidence, choose your next step
Completion records your own decision that you have worked through this investigation. Practice checks and independent project evidence are separate.