Print quantity tolerance planner

Purpose and output set

This calculator is a print quantity tolerance planner. You enter a quantity and two contractual percentage allowances, then read three results: the minimum whole-unit delivery, the maximum whole-unit delivery, and a conservative order estimate for the entered minimum need. The outputs are arithmetic consequences of the entered assumptions. They do not establish a Teal allowance, an accepted shortfall, a payment obligation, or a guaranteed minimum. Use the results to compare scenarios and prepare written terms, not to replace them.

Inputs and what each number represents

Quantity is entered as a unit count. Maximum overrun (%) is the upper allowance above the ordered quantity. Maximum underrun (%) is the lower allowance below the ordered quantity. Enter percentages as percent values, so 10 means 10 percent, not 0.10. The underrun input cannot reach 100 percent, which keeps the retained fraction above zero. The overrun input can be zero, and the underrun input can be zero. The same Quantity field serves two roles: for the two delivery bounds it is the planned order quantity; for the order-to-cover result it is the minimum need you must receive. If your planned order and protected need differ, run the calculator twice with the appropriate Quantity value.

How the delivery bounds are calculated and rounded

The minimum whole-unit delivery is the ceiling of the ordered quantity multiplied by one minus the underrun percentage divided by 100. The maximum whole-unit delivery is the floor of the ordered quantity multiplied by one plus the overrun percentage divided by 100. Ceiling and floor are used because delivered units are whole. The lower bound rounds upward so the displayed minimum does not fall below the percentage floor. The upper bound rounds downward so the displayed maximum does not exceed the percentage ceiling. If the product is already a whole number, rounding leaves it unchanged.

Interpreting the order-to-cover result

The order-to-cover row estimates an order whose retained quantity reaches the minimum need before delivery rounding. It divides that need by the retained fraction and rounds up. The minimum delivery row rounds up separately, so a smaller order can sometimes meet the same whole-unit bound. Overrun does not affect this result because the question is about protecting a floor, not capping a surplus. A larger underrun allowance can raise the order-to-cover figure when it crosses a rounding boundary, because a smaller fraction of the order is assumed to arrive. A zero underrun makes the order-to-cover result equal the entered need.

Worked example with two quantities

At Quantity 1,000 with 10 percent overrun and 10 percent underrun, the minimum whole-unit delivery is 900, the maximum is 1,100, and the order to cover a minimum need of 1,000 is 1,112. At Quantity 10,000 with the same allowances, the results are 9,000, 11,000, and 11,112. The second case scales the first case by ten before rounding. The order-to-cover figure is larger than the need because the underrun allowance reduces the retained fraction. In both cases the overrun allowance affects only the maximum delivery, while the underrun allowance affects the minimum delivery and the order-to-cover estimate.

Why changing an input changes the outputs

Increasing Quantity raises all three outputs in proportion before rounding, so small quantity changes can move a bound by one unit when a fractional result crosses an integer. Increasing the overrun percentage can raise only the maximum whole-unit delivery. Increasing the underrun percentage can lower the minimum whole-unit delivery and raise the order estimate. Any row can remain unchanged until its rounding boundary is crossed. Setting overrun to zero makes the maximum delivery equal the ordered quantity. Setting underrun to zero makes the minimum delivery equal the ordered quantity and makes order-to-cover equal the minimum need. These directions follow from the formulas and the whole-unit rounding, not from a separate policy rule.

Edge cases and contractual limits

A high underrun allowance makes the order-to-cover result grow quickly because the retained fraction becomes small. That is a mathematical property of the model, not a recommendation to order that amount. Fractional percentage inputs can produce fractional products; the ceiling and floor steps decide the displayed whole-unit bounds. If both allowances are zero, all three outputs equal the entered Quantity. The allowances are contract assumptions entered by you, not a Teal policy. Payment, accepted shortfalls, and guaranteed minimums need written agreement. The calculator does not determine legal status, safety, certification, or whether a delivered quantity will be accepted.

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