page_title: Economic production quantity
section_title: Total cost function and derivation of EPQ formula
hierarchical_section_title: Economic production quantity / Overview / Total cost function and derivation of EPQ formula
caption_attribution_description: English: Economic Production Quantity graph
context_page_description: The economic production quantity model determines the quantity a company or retailer should order to minimize the total inventory costs by balancing the inventory holding cost and average fixed ordering cost. The EPQ model was developed by E.W. Taft in 1918.
  This method is an extension of the economic order quantity model. The difference between these two methods is that the EPQ model assumes the company will produce its own quantity or the parts are going to be shipped to the company while they are being produced, therefore the orders are available or received in an incremental manner while the products are being produced. While the EOQ model assumes the order quantity arrives complete and immediately after ordering, meaning that the parts are produced by another company and are ready to be shipped when the order is placed.
  In some literature, "economic manufacturing quantity" model is used for "economic production quantity" model. Similar to the EOQ model, EPQ is a single product lot scheduling method. A multiproduct extension to these models is called product cycling problem.
context_section_description: 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.
caption: This figure graphs the holding cost and ordering cost per year equations. The third line is the addition of these two equations, which generates the total inventory cost per year. This graph should give a better understanding of the derivation of the optimal ordering quantity equation, i.e., the EPQ equation
exif: {}