The lead time is fixed The purchase price of the item is constant, i.e. no discount is available The replenishment is made incrementally Variables K = ordering/setup cost per production run D = yearly demand rate h = yearly holding cost per product t = cycle length P = yearly production rate Q = order quantity S = success by the method. Total cost function and derivation of EPQ formula Holding Cost per Year = Where is the average inventory level, and is the average holding cost. Therefore, multiplying these two results in the holding cost per year. Ordering Cost per Year = Where are the orders placed in a year, multiplied by K results in the ordering cost per year. We can notice from the equations above that the total ordering cost decreases as the production quantity increases. Inversely, the total holding cost increases as the production quantity increases. Therefore, in order to get the optimal production quantity we need to set holding cost per year equal to ordering cost per year and solve for quantity (Q), which is the EPQ formula mentioned below. Ordering this quantity will result in the lowest total inventory cost per year. Relevant formulas Average holding cost per unit time: Average ordering and holding cost as a function of time: See also Reorder point Safety stock Infinite fill rate for the part being produced: Economic order quantity Demand is random, continuous replenishment: Base stock model Demand varies over time: Dynamic lot size model Several products produced on the same machine: Economic lot scheduling problem References Taft, E. W. "The most economical production lot." Iron Age 101.18 (1918): 1410-1412. Gallego, G. "IEOR4000: Production Management" (Lecture 2), Columbia (2004). Stevenson, W. J. "Operations Management" PowerPoint slide 19, The McGraw-Hill Companies (2005). Kroeger, D. R. "Determining Economic Production in a Continuous Process" IIE Process Industries Webinar, IIE (2009). Cárdenas-Barrón, L. E. "The Economic Production Quantity derived Algebraically" International Journal of Production Economics, Volume 77, Issue 1, (2002). Blumenfeld, D. "Inventory" Operations Research Calculations Handbook, Florida (2001) Harris, F.W. "How Many Parts To Make At Once" Factory, The Magazine of Management, 10(2), 135-136, 152 (1913). Inventory optimization