How this calculation works
Within each price tier, minimize the convex ordering-plus-holding cost at feasible integers around its EOQ, clipped to that tier’s bounds. Compare complete annual costs including purchase price across tiers.
Annual total = demand × tier price + demand/order quantity × order cost + order quantity/2 × annual holding per unitA worked example
For annual demand 1,000, order cost 50 and 20% annual holding, quantity 500 qualifies for the 8.5 all-units price. Purchase 8,500 plus ordering 100 plus holding 425 gives 9,025 per year, lower than the feasible EOQ in the 9-per-unit tier.
Good to know
Deterministic all-units EOQ, not incremental price breaks. Whole order quantities but long-run fractional annual order count. No safety stock, expiry, capacity, shortages or lead-time risk.
Reference: MIT OpenCourseWare: logistics and inventory course materials (opens in a new tab) ↗
All-units and incremental discounts differ
An all-units tier applies its price to every purchased unit once the order qualifies. An incremental contract charges different portions at different prices and needs another model.
Annual purchase cost must remain in the comparison because it changes with the qualifying unit price even when annual demand is constant.
Keep the EOQ candidate inside its price tier
A continuous EOQ can fall below a tier’s minimum or above its maximum. The page clips it to the feasible range and evaluates neighboring whole quantities.
For the convex per-tier cost, those feasible integer neighbors locate the minimum under the stated model. The global comparison then selects the cheapest candidate across all tiers.
Average inventory and annual orders are long-run quantities
The model uses average cycle stock Q/2 and demand/Q orders per year. A fractional annual order count is a long-run rate, not a literal instruction to place part of an order.
An actual calendar purchasing plan can have ending stock, minimum packs and financing constraints. Those are not inferred from this steady-demand scenario.
Use the result with the next measurement
The multi product break even calculator concerns the sales contribution mix. Replenishment quantities and inventory holding costs answer a separate operating decision from sales break-even.
Deterministic all-units EOQ, not incremental price breaks. Whole order quantities but long-run fractional annual order count. No safety stock, expiry, capacity, shortages or lead-time risk.
A few questions, answered
Does the price apply to all ordered units?
Yes, this is an all-units discount model.
Are annual orders forced to an integer?
No, demand/Q is a long-run replenishment rate.
Are infeasible EOQs used?
No, candidates stay inside each tier’s bounds.