Economic Order Quantities (EOQs) The concept of an economic-order quantity addresses the question of how much to order at one time. 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. 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. To calculate the EOQ a mathematical model of reality must be constructed. Some assumptions are made to simplify reality. Some assumptions are made to simplify reality. When an assumption is modified or deleted a new model must be constructed. 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. 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. 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 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. 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. 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. Exactly the same quantity is ordered each time that a purchase is made.

Algebraic Formula for EOQ by 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 The basic EOQ formula is developed from a total cost equation involving procurement cost and inventory carrying cost. It is expressed as ______ ______ √ 2ca /h √ 2ca /h Q= order quantity in units Q= order quantity in units A= Annual usage in units A= Annual usage in units C= Acquisition cost per unit C= Acquisition cost per unit P= price per unit P= price per unit H= holding cost per unit H= holding cost per unit If the holding cost is given as percentage of for example If the holding cost is given as percentage of for example

Example A manufacturer has an annual requirement of 6000 units of a component. A manufacturer has an annual requirement of 6000 units of a component. Each component costs 2 L.E. Each component costs 2 L.E. Ordering costs 15L.E.per order Ordering costs 15L.E.per order Holding cost of one unit is 5% of its price (cost) Holding cost of one unit is 5% of its price (cost) There are no bulk discounts There are no bulk discounts Calculate the optimum order quantity by examining 10 possibilities from ordering once a year to ten times a year. 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. Use a graphical method to show your answer. Calculate the EOQ using the Algebraic Formula Calculate the EOQ using the Algebraic Formula

Using the Formula EOQ =square root of 2ca/h EOQ =square root of 2ca/h square root of 2x15x6000/5%x2=1342 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. 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. 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 Order point system periodic review system periodic review system material requirements planning. 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. 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. 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. Demand is 200 units a week, the lead time is three weeks, and safety stock is 300 units. Calculate the order point. Answer Answer OP= DDLT + SS =200x3+300 =200x3+300 =900 units =900 units

Determining Safety Stock Safety stock increases as the uncertainty increases Safety stock increases as the uncertainty increases Uncertainty is reflected in the deviation of actual demand from the forecast demand Uncertainty is reflected in the deviation of actual demand from the forecast demand The standard deviation Sigma is used to measure how closely the individual values cluster about the average The standard deviation Sigma is used 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 Calculate the deviation for each period by subtracting the actual demand from the forecast demand Square each deviatiion Square each deviatiion Add the squares of the deviations Add the squares of the deviations Divide the value is step3 by the number of periods to determine the average of the squared 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. 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. 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. 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 Average of the square deviation =380000/10=38000 Sigma=square root of 38000=194.9=195 units Sigma=square root of 38000=194.9=195 units Safety stock if service level is 84%= 1Sigma=1x195=195 units Safety stock if service level is 84%= 1Sigma=1x195=195 units Order point=DDLT+SS Order point=DDLT+SS = =1195 = =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 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. 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 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) The service level is directly related to the number of standard deviations provided as safety stock called ( safety factor)

Table of 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 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

Answer From the table of of safety factor, the safety factor for a service level of 90% is Therefore, From the table of of safety factor, the safety factor for a service level of 90% is Therefore, Safety stock= sigma x safety factor = 200x 1.28 = 200x 1.28 =256 =256 Order Point = DDLT+SS = = =1756 =1756

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 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. 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. 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 The quantity ordered will be this Maximum - the quantity on hand Q= M-q Q= M-q Q quantity ordered=M maximum inventory level- quantity on hand Q quantity ordered=M maximum inventory level- quantity on hand

Order Quantity for a Periodic Inventory System Example Q = d(t b + L) + z  d t b + L - I where d= average demand rate t b = the fixed time between orders L= lead time  d = standard deviation of demand z  d t b + L= safety stock z  d t b + L= safety stock I= inventory level

Periodic Review System

Advantages of the periodic review system More convenient to review inventories on a definite schedule 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 A large number of items can be ordered from the same supplier thus reducing transport costs and ordering cost