CourseWiki/Materials and Manufacturing Processes/Foundations

Manufacturing Cost and Volume

Estimate unit cost and find where two production methods cost the same.

Count material, processing, quality and overhead costs once

Material, labor, machine time, tooling and scrap all affect the cost of an acceptable part. Setup prepares an operation; cycle time is the time for a repeating operation.

Material: stock purchase, delivery and material lost during production.
Processing: labor, machine time, tools, consumables and energy.
Quality: prevention, inspection, rework, rejects and returns.
Overhead: shared support such as facilities and indirect labor.

Check what a machine rate already includes before adding labor, energy or depreciation. Scrap belongs in the estimate once, even if it appears under both material and quality headings.

Spread fixed cost over the quantity actually needed; Practice

Spread fixed cost over the quantity actually needed

For a simple batch model, C = F + vQ and u = C/Q = F/Q + v. C is total cost, F is fixed batch cost, v is variable cost per part, Q is the number of acceptable parts, and u is average unit cost. Use Q greater than zero.

Fixed cost stays constant within the stated production range; variable cost grows with quantity. Setup and dedicated tooling may be fixed for a batch. Material and processing per part often contribute to v. State the period and cost boundary before classifying a cost.

Illustrative process A costs $120 + $8Q. At 60 parts, total cost is $600 and unit cost is $10.00/part. Producing unwanted parts to spread fixed cost creates inventory; it does not create demand.

Why a shorter cycle does not reduce every cost equally

A 10% reduction in a time-based processing charge reduces that portion by 10%. Material, setup and rent do not automatically fall. Capacity limits, tool replacement, scrap and quantity discounts can change the model outside its assumed range.

Practice unit cost

Set total costs equal to find process break-even; Practice

Set total costs equal to find process break-even

Compare routes that meet the same requirements at the same quantity. From F_A + v_A Q = F_B + v_B Q, obtain Q* = (F_B − F_A)/(v_A − v_B).

Let A cost $120 + $8Q and B cost $720 + $3Q. Then Q* = ($720 − $120)/($8 − $3) = 120 parts. Both cost $1,080 total or $9/part. A costs less below 120; B costs less above 120.

Unit cost curves cross at 120 parts and 9 dollars per part. A costs less below the crossing and B above it.

When there is no positive crossing

Equal variable costs mean the lower fixed cost wins, or both routes tie everywhere if fixed costs also match. A negative crossing lies outside positive production quantities. For a fractional crossing, compare costs at the neighboring whole-part quantities. This is process-cost break-even, not sales-revenue profit break-even.

Practice break-even

Move the volume slider and predict which process wins; Interactive

Move the volume slider and predict which process wins

Start with the original A/B costs and predict the cheaper process at 60 and 240 parts. Then change a setup cost or variable cost and compare at the same demanded quantity. The case selector also includes fractional crossings, parallel lines, an everywhere tie, and a crossing beyond the chart.

Process-cost explorer. Compare C = F + vQ and u = F/Q + v for two routes supplying the same demanded quantity of equivalent acceptable parts in one batch. Use the same included costs and period for each route, count each cost once, and assume the entered rates stay constant. The exercise does not establish equivalent quality, capacity or demand, or recommend a purchase.

Predict, calculate total cost for each route, then divide by the demanded quantity. With A = $120 + $8Q and B = $720 + $3Q:

Original comparison at three demanded quantities
Parts	A total / per part	B total / per part	Lower cost
60	$600 / $10.00	$900 / $15.00	A
120	$1,080 / $9.00	$1,080 / $9.00	Equal
240	$2,040 / $8.50	$1,440 / $6.00	B

Between whole parts: let A = $90 + $6Q and B = $245 + $2Q. Q* = 155/4 = 38.75 parts. At 38 parts A totals $318 and B $321; at 39 parts A totals $324 and B $323. No whole-part quantity ties.

Try the other cases: A = $60 + $4Q and B = $210 + $4Q never cross because their slopes match; A stays $150 lower. If both F and v match, costs tie at every positive quantity. With A = $80 + $2Q and B = $200 + $5Q, A is lower for every positive Q. With A = $100 + $2.50Q and B = $900 + $2Q, the positive crossing is at 1,600 parts, beyond the live graph's 0–300 interval.

The editable explorer accepts fixed cost $0–$100,000, variable cost $0–$1,000/part and whole demand 1–10,000. Dollar entries have at most two decimal places; exact cent totals determine equality. Displayed average unit costs are approximate. A graph ending before a crossing does not prove there is no crossing. Zero on a total-cost graph shows fixed cost; unit cost at zero parts is undefined.

Static comparison: at 60 parts A is $10.00/part and B is $15.00/part; at 240 parts A is $8.50/part and B is $6.00/part. Use Dimensional Analysis to check units and Outsourcing to consider more than cost.

Appears in

DET 130 DET Manufacturing Economics