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## Economic Order Quantities (EOQs)

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**Economic Order Quantities (EOQs)**• The concept of an economic-order quantity addresses the question of how much to order at one time. • Definition: The Economic order quantity (EOQ) is the optimum ordering quantity for an item of stock that minimizes cost. • To calculate the EOQ a mathematical model of reality must be constructed. • Some assumptions are made to simplify reality . • When an assumption is modified or deleted a new model must be constructed.**Assumptions for EOQ Basic Model**• Demand is uniform i.e. constant and continuous over time. • There is no limit on order size due either to stores capacity or other constraints. • The cost of placing is independent of the size of order and delivery charge is also independent of the size of order. • The cost of holding a unit of stock does The lead time is constant and certain. • All prices are constant and certain. There are no bulk purchase discounts. • Exactly the same quantity is ordered each time that a purchase is made.**Algebraic Formula for EOQby Ford Harris in1913**• The basic EOQ formula is developed from a total cost equation involving procurement cost and inventory carrying cost. It is expressed as ______ • √2ca /h • Q= order quantity in units • A= Annual usage in units • C= Acquisition cost per unit • P= price per unit • H= holding cost per unit • If the holding cost is given as percentage of for example**Example**• A manufacturer has an annual requirement of 6000 units of a component. • Each component costs 2 L.E. • Ordering costs 15L.E.per order • Holding cost of one unit is 5% of its price (cost) • There are no bulk discounts • Calculate the optimum order quantity by examining 10 possibilities from ordering once a year to ten times a year. • Use a graphical method to show your answer. • Calculate the EOQ using the Algebraic Formula**Using the Formula**• EOQ =square root of 2ca/h • square root of 2x15x6000/5%x2=1342**Demand Ordering System**• Demand ordering systems answers the question of when to place a replacement order at one time. • An order may be placed when needed or at a specific time ( e.g.every month) or when stock falls to a predetermined level.**Basic reorder systems**Three basic systems are used to determine when to order • Order point system • periodic review system • material requirements planning. The first two are for independent demand items, the last is for dependent demand items.**Order Point System**• When a quantity of an item onhand falls to a predetermined level, called an order point, an order is placed. The quantity ordered is usually precalculated and based on EOQ concepts. • The item is ordered when the quantity on hand falls to a level equal to the demand during the lead time plus the safety stock.**OP=DDLT=SS**where OP= order point DDLT= demand during the lead time SS= safety stock.**Example**• Demand is 200 units a week, the lead time is three weeks, and safety stock is 300 units. Calculate the order point. • Answer OP= DDLT + SS =200x3=300 =900 units**Determining Safety Stock**• Safety stock increases as the uncertainty increases • Uncertainty is reflected in the deviation of actual demand from the forecast demand • The standard deviation Sigma isused to measure how closely the individual values cluster about the average**How to calculate Standard deviation (Sigma)**• Calculate the deviation for each period by subtracting the actual demand from the forecast demand • Square each deviatiion • Add the squares of the deviations • Divide the value is step3 by the number of periods to determine the average of the squared deviations. • Calculate the square root of the value calculated in step 4. This is the standard deviation.**Example**• Given the data in the following table calculate the standard deviation (sigma) and use the answer to calculate the safety stock for an 84%(1 Sigma) service level. • If a safety stock equal to two standard deviations is carried, calculate the safety stock and the order point if the demand during the lead time is 1000 units.**Answer**• Average of the square deviation =380000/10=38000 • Sigma=square root of 38000=194.9=195 units • Safety stock if service level is 84%= 1Sigma=1x195=195 units • Order point=DDLT+SS • =1000+195=1195 • with this order point and level of safety stock on the average there are no stock outs 84% of the time when a stockout is possible**Safety Stock and Service level**• Safety Stock is a calculated extra amount of stock carried and is generally used to protect against quantity uncertainty during the lead time. • The service level is a statement of the percentage of time there is no stock out when a stock out is possible. • The service level is directly related to the number of standard deviations provided as safety stock called ( safety factor)**Example**• If the standard deviation is 200 units, what safety stock should be carried to provide a service level of 90%? If the expected demand during the lead time is 1500 units, what is the order point**Periodic Review**• Using the periodic review system the quantity on hand of a particular item is determined at specified, fixed-time intervals,and an order is placed • The review period is fixed and the order quantity is allowed to vary. • A maximum level of inventory is set that covers the demand during the review period and the safety stock this is the maximum inventory level. • The quantity ordered will be this Maximum - the quantity on hand • Q= M-q • Q quantity ordered=M maximum inventory level- quantity on hand**Answer**• From the table of of safety factor, the safety factor for a service level of 90% is 1.28. Therefore, Safety stock= sigmax safety factor = 200x 1.28 =256 Order Point = DDLT+SS =1500+256 =1756**Advantagesof the periodic review system**• More convenient to review inventories on a definite schedule • A large number of items can be ordered from the same supplier thus reducing transport costs and ordering cost