Describe the process first
Every operations analysis starts with a process flow diagram: the steps, the order, where work waits and where it branches. The three measures that describe any process are linked, and you should define them carefully.
| Measure | Definition | Unit |
|---|---|---|
| Throughput (flow rate) | Units completed per unit of time | Orders per day |
| Flow time (cycle time through the system) | Time a unit spends from entry to exit | Days |
| Inventory (work in process) | Units inside the process at a point in time | Orders |
| Capacity | Maximum throughput of a resource | Units per hour |
| Utilization | Throughput divided by capacity | Percent |
Bottlenecks and utilization
The capacity of a process is the capacity of its slowest step, the bottleneck. Improving any other step does not raise output.
Three-step process (hypothetical)
| Step | Capacity (units per hour) | Utilization at demand of 40 per hour |
|---|---|---|
| 1. Cutting | 60 | 40 / 60 = 66.7% |
| 2. Assembly | 45 | 40 / 45 = 88.9% |
| 3. Packing | 50 | 40 / 50 = 80.0% |
Process capacity = 45 units per hour, set by assembly. If demand rose to 55, output would stay at 45 and the unmet 10 per hour would be lost or queued. Adding capacity at cutting would do nothing. Adding 10 units per hour at assembly raises capacity to 50, the new bottleneck becoming packing.
Discuss improving the bottleneck: add equipment or shifts, reduce setup times, remove non-value work, move tasks to other steps, or protect the bottleneck from starvation with a buffer. Remember that an hour lost at the bottleneck is an hour lost for the whole system.
Little's law
Little's law links the three flow measures for any stable process: Inventory = Throughput x Flow time.
Applying Little's law (hypothetical)
A claims office has 120 claims in process and completes 40 per day. Flow time = Inventory / Throughput = 120 / 40 = 3 days.
If the office wants to cut flow time to 2 days at the same throughput, inventory must fall to 40 x 2 = 80 claims. Shorter flow time needs less work in process, which means fewer batches waiting, smaller queues or removing backlog.
The law holds regardless of the arrival pattern, as long as units, time measures and the long-run averages are consistent. Make sure units match: throughput per day goes with flow time in days.
Variability and queues
High utilization looks efficient but produces long waits when demand or processing times vary. For a simple single-server queue with random arrivals and service times (an M/M/1 queue), the average number of units in the system is utilization / (1 - utilization).
| Utilization | Average number in system | Interpretation |
|---|---|---|
| 50% | 0.5 / 0.5 = 1 | Short waits |
| 80% | 0.8 / 0.2 = 4 | Noticeable queue |
| 90% | 0.9 / 0.1 = 9 | Long queue |
| 95% | 0.95 / 0.05 = 19 | Very long queue |
This is why a call center at 95 percent utilization has long waits even though it is nearly fully employed. It is also why Little's law and queueing are often used together: raise utilization and flow time explodes. The cost of waiting must be weighed against the cost of spare capacity. Services with costly waiting, such as emergency care, run at lower utilization.
Ways to reduce variability or its effect include smoothing arrivals with appointments, standardizing work, cross-training staff so capacity moves to where the queue is and using pooled queues instead of separate ones.
Quality measures
Quality assignments usually ask for defect rates and process capability. A common measure is defects per million opportunities (DPMO):
DPMO = defects / (units x opportunities per unit) x 1,000,000
DPMO (hypothetical)
12 defects found in 5,000 units, each with 4 opportunities for a defect. DPMO = 12 / (5,000 x 4) x 1,000,000 = 12 / 20,000 x 1,000,000 = 600 DPMO.
Six Sigma's target is 3.4 defects per million opportunities, which implies a very capable process. Know the DMAIC cycle (define, measure, analyze, improve, control) and the common tools: process maps, Pareto charts to find the vital few causes, fishbone diagrams and control charts to separate normal variation from signals.
| Approach | Focus | Typical tools |
|---|---|---|
| Lean | Eliminate waste and flow time | Value stream maps, 5S, kanban, pull systems |
| Six Sigma | Reduce variation and defects | DMAIC, statistical process control |
| Theory of constraints | Manage the bottleneck | Five focusing steps, buffer management |
Batch size and setup times
Setups consume capacity. When a machine needs time to change over, larger batches spread the setup over more units but lengthen the wait for each unit.
Setup and capacity (hypothetical)
A machine needs a 30-minute setup per batch and takes 2 minutes per unit.
| Batch size | Time per unit including setup | Capacity per hour |
|---|---|---|
| 10 | 2 + 30 / 10 = 5.0 minutes | 60 / 5.0 = 12 units |
| 25 | 2 + 30 / 25 = 3.2 minutes | 60 / 3.2 = 18.75 units |
| 50 | 2 + 30 / 50 = 2.6 minutes | 60 / 2.6 = 23.1 units |
Moving from batches of 10 to 50 nearly doubles capacity. But a batch of 50 takes 50 x 2 = 100 minutes of run time plus setup, so orders wait longer and inventory builds. That is the same trade-off as in inventory: setup cost against holding and flow time. Reducing setup time, the Lean idea behind quick changeover, lets you run small batches without losing capacity.
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Get an instant quoteThe five focusing steps in practice
| Step | Meaning | Example in the three-step process |
|---|---|---|
| 1. Identify the constraint | Find the bottleneck | Assembly at 45 units per hour |
| 2. Exploit it | Get the most from it without new money | No idle time at assembly; staff breaks staggered; no defective parts reach it |
| 3. Subordinate everything else | Align other steps to its pace | Cutting releases work only at the rate assembly can use it, preventing piles of work in process |
| 4. Elevate it | Add capacity if needed | Add a second assembly station: capacity rises toward 50, where packing now limits |
| 5. Repeat | The constraint moves; find the new one | Packing becomes the bottleneck |
Include the cost of elevating: if a second station costs $60,000 and each extra unit an hour contributes $12 over 2,000 hours a year, five extra units an hour add 5 x 12 x 2,000 = $120,000 a year, a payback of six months. That puts a number on step 4.
Structure of a process improvement report
| Section | Contents |
|---|---|
| Problem and scope | What is wrong, which process, and the target |
| Current state | Process map with times, capacities and queues |
| Analysis | Bottleneck, utilization, flow time, causes of variation and defects |
| Options | Changes with costs, benefits and risks |
| Recommendation and plan | Chosen changes, pilot, owners and timeline |
| Measures | Throughput, flow time, quality and cost before and after |
Staffing a service process
Call center (hypothetical)
120 calls arrive per hour and each takes 4 minutes to handle. Workload = 120 x 4 = 480 minutes of work per hour, or 480 / 60 = 8 agents' worth.
| Agents on shift | Utilization (8 / agents) | Typical effect |
|---|---|---|
| 9 | 89 percent | Queues grow quickly when calls bunch up |
| 10 | 80 percent | Workable with some waiting |
| 11 | 73 percent | Better service, higher cost |
The extra agent from 10 to 11 costs about one agent's hourly wage but reduces waiting at peaks. Decide the service target first (for example, 80 percent of calls answered in 20 seconds) and staff to it, using demand by hour, not the daily average.
Value-added versus waiting time
| Step | Work time | Waiting before step |
|---|---|---|
| Receive order | 5 minutes | 60 minutes |
| Credit check | 10 minutes | 240 minutes |
| Pick and pack | 30 minutes | 120 minutes |
| Ship | 15 minutes | 480 minutes |
| Total | 60 minutes | 900 minutes |
Work time is 60 of 960 total minutes, so only 6.25 percent of the elapsed time adds value. Most improvement comes from cutting waits, not from making people work faster.
Writing the analysis
- Draw the process A simple diagram with capacities makes the analysis clear.
- Define each measure and unit Match time units in every calculation.
- Find the constraint Then recommend actions at the constraint, not elsewhere.
- Quantify the improvement Show new capacity, flow time or defect rate.
- Consider trade-offs Cost, service, flexibility and risk.
For linking operations to cost, see our managerial accounting guide. If you want help with an operations assignment, you can order MBA assignment help.