Does fitting more cartons on a sheet always reduce the total cost?

One plan fits eight carton blanks on a sheet; another fits ten. Should the ten-up plan be cheaper?

More blanks per sheet can reduce paper use when sheet size, price, production constraints and other costs are genuinely equal. Whether the complete order costs less also depends on what that saving requires.

A carton production plan includes printing equipment, die-cutting and finishing. Esko’s Phoenix description, for example, considers equipment, material and processing costs rather than geometry alone.^[1]

This guide uses a defined teaching example. All quantities, yields and fees are assumptions, not a market quotation, a factory measurement or a demonstrated production layout.

Define what “yield” measures

Blanks per sheet, or the up count, is the number of unfolded carton blanks placed on one sheet. It is not the footprint of assembled boxes.

Area utilisation needs a stated numerator and denominator. Purchased-sheet area and usable area after margins are different denominators. Net blank area and bounding-rectangle area are different numerators.

Planned input sheets also account for setup waste and rejects during production. Dividing the required quantity by the up count is incomplete.

Before comparing two claims of “80% utilisation”, confirm that their measurement bases match.

A geometric fit must also respect production constraints, including the blank shape, bleed and orientation. Tilia Phoenix’s product documentation explicitly links grain direction to permitted rotations. Do not assume arbitrary rotation is possible just to gain two more blanks.^[2]

The example: less paper, but CNY 300 more in total

Assume an order for 9,600 acceptable cartons, with identical finished-product requirements in both plans.

Both use purchased sheets measuring 1,000 × 700 mm, with an area of 0.70 m². Each net blank is assumed to occupy 0.056 m². Plan A is eight-up; plan B is ten-up. The example assumes acceptable margins, grain direction and processing, but has no actual dieline and therefore provides no geometric feasibility validation.

Using net blank area divided by purchased-sheet area, theoretical utilisation is 64% for A and 80% for B. This is not the material yield of the full order after waste.

Scroll horizontally to see the full table.

The example deliberately assigns B a larger one-off cost, such as a new die while A reuses some existing resources. This does not mean higher up counts always need greater fixed investment. It tests whether the order’s savings recover the added investment.

Avoid double counting: the 100 setup sheets are separate from the 96% production pass rate. Sheet processing applies to all input sheets. The per-carton fee does not duplicate either item.

Planned input sheets are calculated as:

Setup sheets + round up [acceptable quantity ÷ (blanks per sheet × production pass rate)].

Plan A requires 100 + 9,600 ÷ (8 × 96%) = 1,350 sheets. Plan B requires 100 + 9,600 ÷ (10 × 96%) = 1,100 sheets. These are plans based on an assumed yield, not guaranteed output.

Scroll horizontally to see the full table.

B saves 250 sheets, CNY 500 in paper and CNY 100 in sheet processing. Its one-off cost is CNY 900 higher, leaving the modelled total CNY 300 higher.

The model contains only the listed costs. It excludes transport, taxes, sales margin and other unlisted items, and is not a customer sales quotation.

A larger order can change the result

Under exactly the same assumptions, both plans cost CNY 8,940 at 14,400 acceptable cartons.

Before sheet-rounding effects, B saves CNY 0.0625 in paper and sheet processing per acceptable carton. Recovering its extra CNY 900 therefore requires:

900 ÷ 0.0625 = 14,400 cartons.

This is specific to this teaching model. It is not a general economic order quantity or a minimum order quantity. Rounding input sheets causes steps near the equality point; actual waste, price tiers and process changes require recalculation.

For repeat orders, check whether tooling can be reused and how its cost is allocated. Do not apply the first-order result automatically to every repeat.

If B has no additional one-off investment and the other assumptions remain unchanged, it would cost CNY 600 less at 9,600 cartons. What determines the result is the complete set of conditions.

Request a complete comparison, not just a layout picture

A buyer need not build an optimisation algorithm. Ask for both plans on a consistent basis: dieline revision, sheet size and grade, grain direction, up count, setup and running-waste assumptions, new plates or dies, sheet-based, item-based and one-off fees, and anything awaiting a sample or trial.

If a plan changes the board, equipment or processing route, ask the factory to explain each cost change and confirm the finished product still meets the brief. Do not attribute every saving to layout efficiency.

An unexplained claim that “utilisation improved by 20%” is insufficient without its calculation basis, constraints and cost scope.

A useful comparison traces its inputs, identifies constraints, makes paper use reproducible, and distinguishes geometric feasibility, production cost and a customer quotation.

First establish that the layout fits. Then establish that it can be produced. Finally compare the full cost of the order, including investment required to achieve the saving.

All fees, yields, sheet and blank areas, up counts and their combinations here are independent teaching assumptions. They are not vendor prices or test results from the cited software. The arithmetic has been checked; actual geometry, factory capability, waste and quotation conditions require order-specific validation.

Carton production-plan comparison checklist
Packaging Supply
https://globewhim.com/guides/carton-imposition-yield-total-cost/

[ ] Acceptable quantity to deliver:

[ ] Dieline ID / revision and approval status:

[ ] Sheet dimensions / grade / grain direction:

[ ] Blanks per sheet and verified layout constraints:

[ ] Area-utilisation numerator and denominator:

[ ] Setup waste / production pass rate / estimation basis:

[ ] Paper and processing fees per input sheet:

[ ] Plates / dies / other one-off charges and reuse:

[ ] Other fees per acceptable carton; check overlap:

[ ] Excluded transport / taxes / margin / other fees:

[ ] Sample or production-trial checks still required:

Mark unresolved items as “to confirm”. This checklist supports a supplier discussion and does not establish supply, engineering approval or a quotation.