Compute the Economic Production Quantity for gradual (build-while-you-use) replenishment, or switch to the quantity-discount EOQ mode to find the lowest-total-cost order size across price breaks. Everything recomputes live in your browser.
The Economic Production Quantity (EPQ), also called the Production Order Quantity or POQ model, extends the classic EOQ to the realistic case where inventory is replenished gradually — you produce units while you are simultaneously consuming them — rather than receiving a whole order at once. This calculator computes the optimal run size, the maximum and average inventory, the number of runs, the cycle and production times, and the total annual cost. A second mode solves the EOQ-with-quantity-discounts problem across multiple price breaks. Everything runs live in your browser.
In EOQ, an entire order arrives instantly, so inventory jumps to Q and is drawn down to zero. In EPQ, production happens at rate p (units/day) while demand draws stock down at rate d (units/day), so inventory builds at the net rate (p − d) during the production phase and then depletes at rate d once production stops. The optimal run size is EPQ = √(2DS / (H·(1 − d/p))). The term (1 − d/p) is the key difference from EOQ: because you never hold the full batch at once, the effective holding cost is lower and the optimal run is larger than the equivalent EOQ. The model requires p > d — otherwise production can never keep up with demand.
The peak inventory is never the full run size. It is Imax = EPQ·(1 − d/p), reached at the moment production stops; average inventory is half of that. The number of production runs per year is D/EPQ, and the cycle length (run-to-run time) is EPQ/d. The production phase within each cycle lasts EPQ/p days, after which the line switches to another product or idles while the built-up stock is consumed. The total annual cost balances setup cost (D/EPQ)·S against holding cost (Imax/2)·H, and at the EPQ these two are equal — the same elegant balance that defines the EOQ.
When suppliers offer lower unit prices for larger orders, the basic EOQ is no longer enough because the purchase cost (D × price) now depends on order size. The standard procedure: for each price level, compute the EOQ using that level’s holding cost; if the EOQ is feasible for that price tier, use it; if it falls below the tier’s minimum quantity, raise the order to the break point (the smallest quantity that earns the price). Then compute the total annual cost — purchase + ordering + holding — for each candidate and choose the smallest. A bigger order sometimes wins because the per-unit savings outweigh the extra holding cost; sometimes it does not, which is exactly what the comparison reveals.
There are two conventions for the holding cost in quantity-discount EOQ. If holding cost is a fixed dollar amount per unit per year, it is the same at every price level. If holding cost is expressed as a percentage of the unit price (common, since carrying cost is largely the cost of capital tied up in inventory), then a lower price means a lower holding cost at that tier, which slightly enlarges the EOQ. This calculator supports both: choose a fixed dollar H, or a percentage that is applied to each tier’s discounted price. Always confirm which convention your textbook or company policy uses, because it changes the EOQ at each level.
EOQ assumes the whole order arrives at once, so inventory peaks at the full order size Q. EPQ assumes you produce gradually while also consuming, so inventory peaks at only Q·(1 − d/p) and average holding is lower. As a result the EPQ formula includes the factor (1 − d/p), and the optimal run size is larger than the comparable EOQ.
Because if p ≤ d, you consume units at least as fast as you make them, so inventory can never accumulate and the model breaks down — there is no build-up phase. EPQ requires p > d so that during production the net rate (p − d) is positive and stock grows. This calculator returns an error when p ≤ d.
It is Imax = EPQ·(1 − d/p), reached at the instant production stops. It is always less than the run size because demand is drawing down stock the entire time you are producing. Average inventory, used for the holding-cost calculation, is half of Imax.
They add a purchase-cost term that depends on order size, so you can no longer minimize ordering and holding cost alone. You compute the EOQ at each price level, bump it up to the break quantity if needed, then compare total cost (purchase + ordering + holding) and pick the lowest. The best order is often at a price break rather than at a raw EOQ.
Either is valid, but they give different answers. A fixed dollar H is the same across all tiers. A percentage-of-price H is lower at discounted tiers, which marginally increases the EOQ there. Use whichever convention matches your cost accounting; carrying cost driven mainly by cost of capital is usually modeled as a percentage of unit value.