Total cost curve
Setup cost falls as lot size grows; holding cost rises. EPQ sits at the minimum of the combined curve.
Total cost
Setup cost
Holding cost
EPQ (optimum)
What is Economic Production Quantity?
Economic Production Quantity (EPQ) is the production lot size that minimizes the total of setup cost and inventory holding cost when you manufacture an item yourself. It is the production-side counterpart of the Economic Order Quantity (EOQ).
The key difference: EOQ assumes a full order arrives instantly in one delivery, so peak inventory equals the whole order. EPQ assumes you build units gradually at a finite production rate while you are also consuming them — so inventory builds up slowly and peaks below the full lot. That lowers average holding cost and pushes the optimal lot size higher than EOQ.
The EPQ formula
EPQ = √( (2 × D × S) / ( H × (1 − d/p) ) )
D = annual demand (units/year) · S = setup cost per run ($) · H = holding cost per unit per year ($)
d = daily demand rate · p = daily production rate · requires p > d
The term (1 − d/p) is what separates EPQ from EOQ. As your production rate p gets very large relative to demand d, this term approaches 1 and EPQ collapses back to EOQ — because instant production is the same as instant delivery.
Why it matters on the shop floor
Using EOQ when you actually produce in-house systematically under-sizes your runs. You end up changing over more often than necessary, burning setup time and capacity. EPQ also tells you the run time per batch and the cycle length between runs — the numbers you need to schedule production, not just size it.
Frequently asked questions
What is the Economic Production Quantity (EPQ)?
EPQ is the optimal production lot size that minimizes combined setup and holding cost when a company produces inventory in-house at a finite rate, rather than receiving a full order at once.
How is EPQ different from EOQ?
EOQ assumes inventory arrives instantly in one delivery, so peak inventory equals the whole order. EPQ assumes you produce units gradually while also consuming them, so peak inventory stays below the full lot. This makes EPQ larger than EOQ and lowers average holding cost.
What is the EPQ formula?
EPQ = √((2 × D × S) / (H × (1 − d/p))), where D is annual demand, S is setup cost per run, H is annual holding cost per unit, d is the daily demand rate, and p is the daily production rate. The model requires p > d.
When should I use EPQ instead of EOQ?
Use EPQ when you manufacture the item yourself and production happens over time at a finite rate. Use EOQ when you purchase the item and receive the full order in a single delivery.