Bottleneck capacity

In the single-product example, 480 staffed minutes minus 30 for breaks, 20 for maintenance, 30 for setup and 40 for expected downtime leaves 360 minutes at each operation. Machining, washing and testing take 4, 3 and 5 min/start, giving capacities of 90, 120 and 72 starts per shift. Testing limits this serial route to 72 good units under the no-loss, independent-operator and sufficient-transfer assumptions. Check workload by product mix when several routes share resources.

ETH Zürich distinguishes a capacity bottleneck from constraints such as material supply or managerial restrictions. Paul Schönsleben, ETH Zürich, section 5.1.5b.

Compare required and available hours for the stated mix and period. A slow stage can have spare capacity at current demand.

Establish a consistent time basis

Cycle time is measured time to produce a part or complete a process. Lean Enterprise Institute distinguishes machine cycle, operator cycle and effective machine cycle; its effective-cycle definition includes loading/unloading and changeover time allocated across pieces between changeovers. Production lead time includes the full passage through the process, rather than just time under the tool. Lean Enterprise Institute, cycle time.

Takt time is available production time divided by customer demand. It describes the required production pace, not the demonstrated capability of a machine. Use the same period, unit and definition of available time when comparing takt with a process cycle. A demand change alters takt even when machine performance remains unchanged. Lean Enterprise Institute, takt time.

For a transparent load calculation, use:

required resource minutes = Σ(quantity processed × resource minutes per unit) + scheduled setup minutes + separately modelled rework minutes.

Then compare that load with available resource minutes. Define whether quantities represent starts, completed pieces or accepted good output. For a multi-cavity tool, furnace batch or simultaneous test fixture, convert the operation’s actual batch capacity into the chosen unit rather than treating every piece as an independent machine cycle.

Choose one place to account for each loss. For example, subtract planned setups from available time or include them in required load. Do not do both. Likewise, a measured effective rate that already incorporates downtime should not receive the same downtime deduction again. Keep a short reconciliation from the staffed calendar to the time actually available for the work.

Original example: one product across three operations

All following numbers are invented planning assumptions. Consider one shift and a product passing through machining, washing and testing. There is sufficient input material and transfer capacity; each operation has a separate operator. The example ignores ramp-up and transfer delays and describes a steady repeating flow, not a promise that an empty line finishes this quantity within its first shift.

The assumed processing times are 4 minutes per start at machining, 3 at washing and 5 at testing. Their time-based capacities are therefore 90, 120 and 72 starts per shift, respectively. With no scrap or rework, testing limits this simplified serial route to 72 units per shift. The sum of processing times, 12 minutes, is the work content per unit; dividing 360 by 12 would incorrectly treat the three separately staffed resources as one serially occupied resource.

At demand of 80 units, required testing load is 80 × 5 = 400 minutes, exceeding its 360-minute availability by 40 minutes. Its load/available-time ratio is 111.1%. That is an overload calculation, not a physically achievable utilization. The example’s available-time-per-demand ratio is 360 / 80 = 4.5 minutes per unit; the five-minute test cycle cannot sustain that pace under these assumptions.

If only 95% of test starts become accepted units, with no rework and all upstream supply adequate, expected accepted output is 72 × 0.95 = 68.4 units per shift. The fractional result is a long-run expectation, not a count of a particular shift’s shippable pieces. Alternatively, a plan seeking 80 expected good units would require 80 / 0.95 × 5 = 421.05 test minutes. Do not reduce available time by 5% as well: that would count this same yield loss twice.

Improving washing from three to two minutes raises its calculated capacity from 120 to 180 starts, while testing still permits only 72. Improving testing to four minutes raises its capacity to 90 and brings machining into contention. Recalculate the whole route after an improvement; the former bottleneck need not remain the limiting resource.

Product mix changes the result

A pieces-per-hour figure is meaningful only for its associated work content. For shared resources, retain product-specific times and setup requirements. The following independent example assumes 360 bottleneck minutes after all setups and losses, no other binding constraints, no minimum-order obligations and divisible planning quantities:

Although A has the greater margin per unit, B contributes more per scarce minute. Producing 50 B uses 150 minutes and contributes $900. The remaining 210 minutes produce 35 A and contribute $1,050: 360 minutes and $1,950 total contribution. Filling A first uses 240 minutes; the remaining 120 minutes allow 40 B. That alternative contributes $1,200 + $720 = $1,920, $30 less.

OpenStax explains ranking products by contribution margin per constrained resource, using relevant revenue and variable costs. That rule needs qualifications: demand limits, customer commitments and other constraints can prevent a simple ranking from being the feasible or preferred plan. Contribution margin is not net profit; additional fixed or incremental capacity costs still require evaluation. With several simultaneously binding resources or sequence-dependent setups, construct a feasible schedule or optimization model rather than assuming one ratio solves the allocation. OpenStax, Principles of Accounting, Volume 2, section 10.6.

Diagnose and improve system output

Use observed queues, downtime, starvation, blocking and actual completions to test the calculated constraint. A queue alone does not establish a permanent capacity deficit: releases, batching and temporary interruptions can also create it. Investigate whether the proposed bottleneck lacks work or cannot discharge completed work before purchasing additional equipment.

The theory-of-constraints sequence is to identify the constraint, exploit its existing capacity, subordinate other activity to it, elevate its capacity, and repeat the analysis. ETH’s treatment also explains why releasing work early at non-bottlenecks can accumulate inventory without adding capacity. ETH Zürich, section 5.1.5b.

ASCM’s manufacturing white paper emphasizes identifying demand and the bottleneck, avoiding unnecessary upstream inventory, reducing setup losses and addressing variability from downtime, quality and staffing. It also discusses buffers; this is not a prescription for zero protective inventory or 100% loading everywhere. ASCM, manufacturing research white paper.

For a planning handoff, retain the period, resource calendar, product quantities, routing times, setup sequence, loss assumptions and resulting overload. After a change, compare accepted output and delivery performance with the prediction. A higher local machine count or utilization is not sufficient evidence of increased customer-serving capacity.

Source versions and limits

OpenStax identifies the textbook publication date as February 14, 2019. The LEI lexicon pages and ETH teaching page are cited as live guidance without assigning them an unverified publication date. The ASCM PDF’s primary indexed text was retrievable for this review, but direct PDF access returned HTTP 403; no printed issue date is asserted here. These sources explain planning concepts, not company-specific capacity policies or guaranteed production rates.