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Economic Production Quantity (EPQ)
Optimal production lot size when replenishment is finite (production rate P exceeds demand D).
Inputs
CSV: parameter,value — demandRate, setupCost, holdingCost, productionRate. After Solve, also Export results CSV.
EPQ vs EOQ
EOQ assumes instantaneous replenishment. EPQ (production order quantity) assumes finite production rate P > demand D, so inventory builds gradually during a production run.
Formulas
EPQ = √( 2DS/H × P/(P−D) )
Iₘₐₓ = Q (1 − D/P)
Setup cost/year = (D/Q)×S; holding ≈ (Iₘₐₓ/2)×H.
When to use
In-house manufacturing, batch production, or any setting where stock arrives over a run rather than in one delivery.
D=12,000, S=100, H=2, P=36,000. Compare with EOQ — EPQ is larger because inventory builds gradually.
Frequently Asked Questions
You cannot keep up with demand; EPQ is undefined. Increase capacity or reduce demand.