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RSM270 · Operations Management · Fall 2026

Week 2: Process Analysis

This week, you will separate capacity from demand in a one-teller bank, find the constraint in a six-step sandwich line, and test how proposed changes affect capacity and flow time.

Several employees coordinating orders at the service window of a commercial kitchen
A process is a team of connected activities; improving one station may simply move the constraint. Photo: Adhitya Sibikumar / Unsplash.

Capacity can be higher than demand

One bank teller takes 15 minutes per customer. One customer arrives every 30 minutes. Use one hour as the common time unit.

Capacity
60 minutes/hour ÷ activity time (minutes/customer)
Long-run throughput
smaller of input rate and capacity
Utilization
throughput ÷ capacity
Calculate the operating rates

Use 60 minutes/hour to convert each time into a rate. Enter only the number in each field; the required unit is shown beside it.

customers/hour
customers/hour
%

The teller has spare capacity

  1. Arrivals2 customers/hour
  2. Teller capacity4 customers/hour50% utilized
  3. Served2 customers/hour
What this figure shows: arrivals limit long-run throughput to 2 customers/hour even though the teller can serve 4 customers/hour. Capacity is a ceiling, not a promise that 4 customers/hour will arrive.
Show the calculations
Capacity
60 minutes/hour ÷ 15 minutes/customer = 4 customers/hour
Input rate
60 minutes/hour ÷ 30 minutes/customer = 2 customers/hour
Throughput
min(2 customers/hour, 4 customers/hour) = 2 customers/hour
Utilization
2 customers/hour ÷ 4 customers/hour = 50%

These are long-run rates. Work already waiting in a buffer can make short-run output differ while that inventory builds or drains.

Find the constraint in a sandwich line

Follow one order containing one hot breakfast sandwich, from taking the order to delivery. Cooked patties are assumed available; the customer queue is outside this boundary. Assume unlimited demand and activity times that do not vary.

  1. CashierTake order8 seconds/order
  2. Worker 1 + toasterToast buns10 seconds/order
  3. Worker 2Add dressing8 seconds/order
  4. Worker 3Add patties6 seconds/order
  5. Worker 4Wrap/package2 seconds/order
  6. Worker 5Deliver2 seconds/order
What this figure shows: one order passes through all six activities. Add their times to find no-wait flow time; compare their capacities to find the process constraint. If the question is total customer time, also include the queue and any meat-cooking delay.
No-wait flow time
sum of one order's task times
Stage capacity
3,600 seconds/hour ÷ seconds/order
Process capacity
lowest stage capacity
Calculate the baseline

Use the process map and relationships above. Choose one value for each measure.

The toaster sets the pace

  1. Take order8 seconds/order450 orders/hour80% utilized
  2. Toast buns10 seconds/order360 orders/hour100% utilized · bottleneck
  3. Add dressing8 seconds/order450 orders/hour80% utilized
  4. Add patties6 seconds/order600 orders/hour60% utilized
  5. Wrap/package2 seconds/order1,800 orders/hour20% utilized
  6. Deliver2 seconds/order1,800 orders/hour20% utilized
What this figure shows: at the modeled 360 orders/hour throughput, the toaster is 100% utilized and has the lowest capacity, so it limits the line.
One order's no-wait path
36 seconds
Process capacity
360 orders/hour
Time between completions
10 seconds

Why 36 seconds and 10 seconds can both be right

What this figure shows: each order spends 36 seconds in the six tasks, but staggered work lets completed orders leave every 10 seconds.
Show the baseline calculations
No-wait flow time
8 seconds/order + 10 seconds/order + 8 seconds/order + 6 seconds/order + 2 seconds/order + 2 seconds/order = 36 seconds/order
Resource capacities
Take order: 3,600 seconds/hour ÷ 8 seconds/order = 450 orders/hour; toast buns: 3,600 seconds/hour ÷ 10 seconds/order = 360 orders/hour; add dressing: 3,600 seconds/hour ÷ 8 seconds/order = 450 orders/hour; add patties: 3,600 seconds/hour ÷ 6 seconds/order = 600 orders/hour; wrap/package: 3,600 seconds/hour ÷ 2 seconds/order = 1,800 orders/hour; deliver: 3,600 seconds/hour ÷ 2 seconds/order = 1,800 orders/hour.
Process capacity
min(450 orders/hour, 360 orders/hour, 450 orders/hour, 600 orders/hour, 1,800 orders/hour, 1,800 orders/hour) = 360 orders/hour
Cycle time
3,600 seconds/hour ÷ 360 orders/hour = 10 seconds/order

Common trap: process capacity is not 3,600 seconds/hour ÷ 36 seconds/order. That reciprocal works for a single-stage, single-server/resource process; here, the bottleneck rate governs the multistage process.

Test process changes

Select each proposed change and compare its capacity, no-wait flow time, cycle time, and bottleneck with the baseline. Open the calculations to see why the result changes—or does not.

Baseline

ChangeNo change to the six-stage line
ConstraintToast buns · 360 orders/hour
ResultProcess capacity remains 360 orders/hour
Process capacity
360 orders/hour
No-wait flow time
36 seconds
Cycle time
10 seconds
Bottleneck(s)
Toast buns
What this figure shows: with unlimited demand, the 360 orders/hour toaster capacity limits both process capacity and throughput.
Show calculations for the baseline
Stage capacities
450 orders/hour, 360 orders/hour, 450 orders/hour, 600 orders/hour, 1,800 orders/hour, and 1,800 orders/hour
Process capacity
min(450 orders/hour, 360 orders/hour, 450 orders/hour, 600 orders/hour, 1,800 orders/hour, 1,800 orders/hour) = 360 orders/hour
Flow and cycle time
8 seconds/order + 10 seconds/order + 8 seconds/order + 6 seconds/order + 2 seconds/order + 2 seconds/order = 36 seconds/order; 3,600 seconds/hour ÷ 360 orders/hour = 10 seconds/order

Add a cashier

ChangeOrdering capacity: 450 orders/hour → 900 orders/hour
ConstraintToast buns · 360 orders/hour
ResultThe added cashier does not change process capacity
Process capacity
360 orders/hour
No-wait flow time
36 seconds
Cycle time
10 seconds
Bottleneck(s)
Toast buns
What this figure shows: the second cashier raises ordering capacity to 900 orders/hour, but the toaster still limits the process to 360 orders/hour. If work is split evenly, each cashier is 40% utilized.
Show calculations for the added cashier
Ordering capacity
One cashier: 3,600 seconds/hour ÷ 8 seconds/order = 450 orders/hour. Two cashiers: 2 cashiers × 450 orders/hour/cashier = 900 orders/hour.
Process capacity
min(900 orders/hour, 360 orders/hour, 450 orders/hour, 600 orders/hour, 1,800 orders/hour, 1,800 orders/hour) = 360 orders/hour
Flow, cycle, and cashier use
Flow = 36 seconds; cycle = 3,600 seconds/hour ÷ 360 orders/hour = 10 seconds/order; each cashier receives 360 orders/hour ÷ 2 cashiers = 180 orders/hour/cashier, and 180 orders/hour/cashier ÷ 450 orders/hour/cashier = 40% utilized

Add a toaster

ChangeToasting capacity: 360 orders/hour → 720 orders/hour
ConstraintTaking orders and adding dressing · 450 orders/hour
ResultProcess capacity rises to 450 orders/hour
Process capacity
450 orders/hour
No-wait flow time
36 seconds
Cycle time
8 seconds
Bottleneck(s)
Take order and add dressing — tie at 450 orders/hour
What this figure shows: adding a toaster raises process capacity to 450 orders/hour, where taking orders and adding dressing become co-bottlenecks. Aggregate toasting-stage utilization is 450 orders/hour ÷ 720 orders/hour = 62.5%. This assumes Worker 1 can operate both toasters without slowing the activity.
Show calculations for the added toaster
Toasting capacity
One toaster: 3,600 seconds/hour ÷ 10 seconds/order = 360 orders/hour. Two toasters: 2 toasters × 360 orders/hour/toaster = 720 orders/hour.
Process capacity
min(450 orders/hour, 720 orders/hour, 450 orders/hour, 600 orders/hour, 1,800 orders/hour, 1,800 orders/hour) = 450 orders/hour
Flow, cycle, and toaster use
Flow = 36 seconds; cycle = 3,600 seconds/hour ÷ 450 orders/hour = 8 seconds/order; aggregate toaster utilization = 450 orders/hour ÷ 720 orders/hour = 62.5%

Shorten the non-bottleneck tasks

ChangeFive non-bottleneck tasks are shorter; toasting remains 10 seconds/order
ConstraintToast buns · 360 orders/hour
ResultNo-wait flow time falls; capacity does not change
Process capacity
360 orders/hour
No-wait flow time
26 seconds
Cycle time
10 seconds
Bottleneck(s)
Toast buns
What this figure shows: shortening the non-bottleneck tasks reduces no-wait flow time to 26 seconds, but the unchanged 10 seconds/order toasting stage keeps process capacity at 360 orders/hour.
Show calculations for the shorter tasks
New task times
Take order: 4 seconds/order; toast buns: 10 seconds/order; add dressing: 6 seconds/order; add patties: 4 seconds/order; wrap/package: 1 second/order; deliver: 1 second/order
New stage capacities
900 orders/hour, 360 orders/hour, 600 orders/hour, 900 orders/hour, 3,600 orders/hour, and 3,600 orders/hour
Process capacity
min(900 orders/hour, 360 orders/hour, 600 orders/hour, 900 orders/hour, 3,600 orders/hour, 3,600 orders/hour) = 360 orders/hour
Flow and cycle time
4 seconds/order + 10 seconds/order + 6 seconds/order + 4 seconds/order + 1 second/order + 1 second/order = 26 seconds/order; 3,600 seconds/hour ÷ 360 orders/hour = 10 seconds/order

Model boundary and assumptions

One sandwich per order; order-to-delivery scope; cooked patties available; unlimited demand; stated activity times do not vary; no failures, setups, or rework. The added-toaster case also assumes Worker 1 can operate two toasters simultaneously without slowing the activity.

Same toasting capacity, different time per sandwich

Two parallel toasters 2 toasters × 360 orders/hour/toaster = 720 orders/hour One sandwich still toasts for 10 seconds.
One faster toaster 1 toaster × 720 orders/hour/toaster = 720 orders/hour One sandwich toasts for 5 seconds.
What this figure shows: both designs provide 720 orders/hour of toasting capacity, but one sandwich spends 10 seconds in a parallel 10-second toaster and 5 seconds in the faster toaster. Equal capacity does not mean equal activity time.

Make the recommendation

Actual demand, cost, quality, and operating reliability are examples of evidence—not values supplied by this model.