Business × Computers → Operations workshop
Capacity, queues and accountable decisions
This original workshop connects operations management, arithmetic, software validation and human judgement. All quantities are synthetic. Prerequisites: division, percentages and basic Python execution. Allow approximately 45–75 minutes including experimentation; this is a planning estimate.
Foundation: what capacity means
A queue appears when work arrives before the resources needed to finish it are available. A print shop may accept orders faster than its artwork team can approve files. A customer-support desk may receive requests faster than agents can resolve them. The queue is not merely a computer display: it represents unfinished promises, waiting customers and work that employees must carry forward. Before proposing automation, identify the unit of work. One order, one page and one customer conversation are different units; mixing them makes a capacity estimate meaningless.
Capacity is a rate or a quantity over a stated period. If one person has 480 working minutes and each comparable job needs twelve minutes, their nominal capacity is forty jobs per shift. Two people provide eighty jobs only if the jobs can be shared and neither depends on a separate limiting resource. The computer can calculate that number accurately while the underlying organisational assumption remains wrong. A shared machine, approval bottleneck or unequal skills can prevent the nominal capacities from adding.
Undergraduate: calculate, interpret and test
Let A denote arriving jobs per shift, t the minutes needed for each job, H the usable minutes per employee and n the number of employees. Nominal capacity C = nH/t. The offered load ratio is A/C. In our example A = 100, t = 12 and H = 480. With two employees C = 80 and A/C = 1.25. At least twenty jobs remain unfinished if every stated assumption holds and there is no opening backlog. A ratio greater than one is overload, not proof that employees are performing badly. With three employees capacity is 120 and offered load is approximately 83.33%.
Distinguish this demand-to-capacity ratio from measured utilisation. If demand exceeds capacity, staff cannot physically work at 125% of the stated available time; the excess becomes backlog, delay, lost work or additional resources. The smallest nominal staffing requirement is the ceiling of At/H: ceiling(1200/480) = three. Rounding down would conceal an unfinished workload. Yet rounding up does not guarantee an acceptable waiting time. Even when average demand is below average capacity, bursts of arrivals and variation in job duration can produce queues.
Postgraduate: choose a framework and question its boundaries
Use a five-step capacity review: define the service promise, trace the workflow, estimate demand and effective capacity, compare interventions, and monitor outcomes. Sales defines what was promised; operations identifies feasible throughput; HR evaluates workload and training; finance checks costs; IT makes records and exceptions visible. The departments need a shared definition of arrival, completion and rejection. Otherwise the dashboard rewards one department for accepting work that another cannot finish.
Compare hiring, reducing unnecessary processing, scheduling demand and automating a bounded task. Reducing service time from twelve to nine minutes gives two employees capacity of about 106.67 jobs, leaving very little nominal slack. That might look cheaper than hiring, but a mean duration hides exceptions. An automated classification step may save time on routine requests while sending complex cases to people. Test whether total resolution time improves, whether rework increases and whether customers understand the result. Faster handling of the wrong request is not better service.
Our deterministic model excludes breaks unless already removed from H, absence, training, machine downtime, reopening, multiple stages and random variation. If a stable system averages ten jobs in progress and completes five jobs an hour, Little’s law gives an average time in the system of two hours. This relationship requires consistent boundaries and a stable observation period; it does not mean that every job waits two hours or that our staffing arithmetic predicts a waiting-time distribution.
Research: turn a claim into an investigation
A research question could ask whether a new triage tool reduces end-to-end resolution time without increasing rework or employee strain. Define the intervention, comparison, observation window and unit of analysis before collecting results. An uncontrolled before-and-after comparison is vulnerable to seasonality, changed case mix and staffing changes. Where feasible, compare otherwise similar teams or randomly assign eligible requests while monitoring spillovers. Randomisation is a design choice requiring organisational agreement, not a button that removes all implementation bias.
Measure median and tail resolution times, unfinished work, reopening, service quality and workload alongside the mean. Keep a data dictionary and document excluded cases. A system that drops difficult requests can appear faster without serving customers better. State what evidence would challenge the conclusion. Contribution might come from explaining which request types benefit, how departmental handoffs change, or why adoption fails under specific constraints; simply installing a dashboard is not itself a research contribution.
Runnable lab: predict → run → explain → change
Download queue_capacity.py. Run python3 queue_capacity.py. No external packages or customer data are needed.
- Predict the capacities for two, three and four employees.
- Run the script: capacities should be 80, 120 and 160; unfinished work 20, 0 and 0; minimum nominal staffing three in every row.
- Change arrivals to 140. Three employees now leave twenty jobs unfinished.
- Change available minutes to 420. Three employees have capacity 105, illustrating why usable time matters.
- Try staff = 0 or service time = 0. Explain why rejecting these inputs protects the meaning of the calculation.
- Write a recommendation that includes one intervention, two measurements and one condition that would reverse the choice.
Questions with individual model answers
Why does a 125% load ratio not describe actual utilisation?
It compares offered work with nominal capacity. Available work time remains bounded; excess demand creates unfinished work or requires added capacity. Actual utilisation must be measured from time spent working and cannot be inferred as 125%.
Is three employees a sufficient service guarantee?
No. Three meets average nominal workload in this simplified model. Arrival bursts, duration variation, downtime and workflow dependencies can still create unacceptable delays. A service guarantee needs evidence about variability and the agreed service target.
How should IT and operations share responsibility?
Operations owns the process assumptions and service judgement. IT implements definitions, validation, permissions and traceable records. Both review exceptions and reconcile dashboard totals to source events; management owns the resulting resource decision.
What makes the research claim credible?
A defined outcome and comparison, consistent inclusion rules, attention to case mix and confounding, documented limitations and measures of adverse effects. A falling mean alone is insufficient if hard cases disappear or rework rises.
Nine enquiry prompts and revision
Who decides capacity? Whom does a delayed promise affect? Whose record defines completion? What is the job unit? Where does work wait? When is demand measured? Why does a queue grow? Which intervention fits the constraint? How will the organisation detect harm?
Close the page and reconstruct C = nH/t, the distinction between load and utilisation, and one limitation. Revisit your answer after a day and again after a week; adjust intervals to your recall. For a portfolio, submit predictions, output, two altered scenarios, validation evidence and a short departmental decision memo.