Service bottleneck calculation: test a staffing change

Which decision does a service bottleneck calculation support?

A service bottleneck calculation helps decide where an additional independent worker could change the output of a serial process. This exercise produces two different deliverables: a theoretical operating-rate ceiling and a count of completions during a shift that starts empty. You will also compare a useful staffing change with an off-bottleneck change that does not raise the modelled output.

Think of a fictional fulfilment service that receives a job, prepares it and checks it before release. Every job follows that sequence once. All jobs are identical and sufficient input work is available from time zero. The example is an authored teaching model, not a measured business operation, an Anar client story or evidence that hiring someone will produce a promised return.

The fixed-component kit calculation asks how many sets existing parts can support. This exercise instead considers time, simultaneous work at separate stages, an initially empty pipeline and a bottleneck that moves after a staffing change. Merely finding the smallest ratio is not the final deliverable; trace the changed schedule and explain the difference between rate and completed work.

Write the staffing and service-time contract first

Use a net shift of 420 minutes after excluded breaks. Receiving requires six minutes per job, preparation ten and final checking four. Initially each stage has one dedicated worker. Each worker can serve only one job at a time, without interruption, and cannot help another stage. Travel, rework, setup, machine downtime and variations in job type are excluded from the teaching model.

An additional worker must be able to perform the entire stage independently on another job. Two people sharing a single constrained workstation do not automatically double stage capacity. The model assumes sufficient independent space and equipment, unlimited intermediate waiting space and a rule that a free worker starts the next available job immediately. Record these assumptions before using a parallel-worker multiplier.

Keep the unit of work identical across rows. Counting customer orders at receiving and individual items at preparation would make the ratios incomparable unless an explicit conversion is supplied. Likewise, use one common net-time basis. A stage with a different availability calendar needs its own scheduling treatment rather than an unexplained mix of paid hours, available minutes and measured handling time.

Calculate the operating ceiling, not a shift promise

The stage-rate calculation is net minutes multiplied by independent parallel workers, divided by minutes per job. It gives 420/6=70, 420/10=42 and 420/4=105 jobs per shift-equivalent. The smallest capacity is preparation at 42. In this deterministic serial model it sets the long-run operating ceiling when enough work is available and all stated resource assumptions hold.

Now start the actual teaching schedule with every stage empty. The first job finishes receiving at minute six, preparation at minute sixteen and checking at minute twenty. Subsequent final completions occur every ten minutes in the baseline. Count the sequence 20, 30, 40 and onward, including the completion exactly at minute 420. There are 41 completed jobs, not 42.

The formula for this particular baseline sequence is one plus floor((420−20)/10), where floor means round downward. Do not generalize that expression to arbitrary staffing patterns without checking the schedule. Jobs still waiting or in service at the cutoff are not finished output. The distinction between a shift-equivalent rate and finite-horizon completions is essential whenever a pipeline starts empty.

Move the constraint with a controlled staffing change

Add a second independent preparation worker while retaining one receiver and one checker. Stage capacities become 70, 84 and 105 per shift-equivalent. Receiving is now the limiting stage. Preparation capacity doubled, but overall theoretical capacity increased from 42 to 70 rather than doubling. Label both the old and new constraints so the calculation does not become a misleading percentage headline.

The first completion is still at minute twenty. Receiving releases a job every six minutes. Two preparation workers alternate jobs, each completing ten minutes of work before its next turn arrives. Checking takes four minutes and can keep up with the six-minute arrival spacing. Final completions occur at 20, 26, 32 and onward through minute 416, giving 67 finished jobs.

For a contrasting scenario, return to the baseline and add a second checker instead. Capacities become 70, 42 and 210. Preparation still limits the process and the empty-start schedule still completes 41 jobs. This does not prove another checker has no value for quality, breaks or resilience. It shows only that this specific deterministic throughput calculation does not justify the change on output grounds alone.

Separate handling time, output spacing and elapsed time

The preparation service time remains ten minutes after adding a worker. Two workers each handle a separate job; the model does not assume two people complete one preparation in five minutes. The interval between consecutive final completions changes from ten minutes to six in the useful scenario. Neither interval is the total elapsed time a particular job spends travelling through the process.

Takt time describes the output interval required by customer demand. No demand input has been supplied here, so a takt calculation would be invented. A job’s elapsed lead time may include waiting between stages, which is explicitly distinct from its handling time. In the baseline, the preparation queue grows because receiving feeds work faster than preparation can serve it.

Use separate labels in a review: stage service minutes, spacing between final completions and end-to-end elapsed minutes. The first job’s twenty-minute path does not mean every later job also spends twenty minutes in the system. If a promise to a customer depends on waiting time, the staffing-rate table alone is insufficient. Inspect arrival patterns, queue size and due dates separately.

Build a reviewable card and stop on invalid inputs

Open Notepad from Windows Start, create a blank document and copy the card below. Record 420 net minutes, 6/10/4 service times and 1/1/1 dedicated workers. Use Calculator from Start for arithmetic. For a fifteen-minute planning target, trace the first three jobs rather than copy hundreds of events. At each stage choose the earliest-free worker, start at the later of the preceding-stage finish and that worker’s availability, then add service time. Baseline stage intervals are J1: 0–6/6–16/16–20, J2: 6–12/16–26/26–30, J3: 12–18/26–36/36–40. For this model only, 20+10(k−1) yields 41 completions through 420. Two preparation workers give 20+6(k−1), with job 67 finishing at 416. Do not generalize these sequences without checking the resource schedule.

Common net shift minutes: [...]
Stage order, service time, independent workers: [...]
Assumptions and unresolved resources: [...]
Stage rates and limiting stage: [...]
First completion and inclusive cutoff: [...]
Empty-start completed jobs: [...]
Changed staffing, new ceiling and constraint: [...]
Excluded queues, variability and shared resources: [...]

Zero, negative or unknown service time stops this simple calculation. A mandatory stage with zero workers cannot process the flow. Worker counts must be nonnegative whole numbers, and a zero count is handled as a stopped process rather than a division trick. Unknown availability remains unresolved. Shared staff, overlapping calendars and mixed job types need a different explicit schedule; do not hide them in a convenient average.

Executed event arithmetic supports the fictional counts here, not a test of your application or a measured operational improvement. Review an equipment cost comparison before spending. Keep purchase quantities, supplier costs and a cash forecast as separate decisions. Save this card with its assumptions and one proposed observation to collect next. Record baseline 42/41, added preparation 70/67 and added checking 42/41 as separate rate/count pairs. Choose File → Save As, select Documents and save flow-card-V1.txt; use another name if it exists rather than overwrite it. Close Notepad and reopen that file from Documents in File Explorer. Find 6/10/4, the empty start, inclusive 420 cutoff, first completion 20 and job 67 at 416. Keep unobserved operational evidence fictional; do not label readback completed until you perform it.