EOQ Inventory Management

Why Do We Want Inventory Improve customer service Reduce certain costs such as ordering costs Stock out costs acquisition costs start-up quality costs Contribute to the efficient and effective operation of the production system

Why We Do Not Want Inventory Certain costs increase such as carrying costs cost of customer responsiveness cost of coordinating production cost of diluted return on investment reduced-capacity costs large-lot quality cost cost of production problems

Inventory Stock of items held to meet future demand Inventory management answers two questions How much to order When to order

Inventory EOQ Models Basic EOQ EOQ for Production Lots EOQ with Quantity Discounts

Inventory Costs Carrying Cost Ordering Cost Shortage Cost Cost of holding an item in inventory Ordering Cost Cost of replenishing inventory Shortage Cost Temporary or permanent loss of sales when demand cannot be met

2DCo Ch Basic EOQ Model Q* = Co - cost of placing order Ch - annual per-unit holding/carrying cost D - annual demand EOQ or Q*– economic order quantity Q* = 2DCo Ch

EOQ Costs Annual carrying cost = (Q/2)Ch Annual ordering cost = (D/Q)Co Total cost (TC) = (Q/2)Ch + (D/Q)Co

EOQ Cost Model 2DCo Ch Q* = Annual cost ($) Total Cost Carrying Cost = Minimum total cost Ordering Cost = CoD Q Optimal order Q* Order Quantity, Q

EOQ: Economic Order Quantity EOQ balances the cost of placing an order against the cost of storing product in inventory The cost of storing a product in inventory can include warehouse costs, shipping costs, and cost of capital tied up in inventory Notice that nowhere did the cost of the merchandise being sold enter into the equations EOQ is vitally important in any retail business and most businesses where stocked items are managed

Safety Stocks Safety stock Stockout Service level buffer added to on hand inventory during lead time Stockout an inventory shortage Service level probability that the inventory available during lead time will meet demand

Basis for setting the Reorder Point During the lead time, customers continue to draw down the inventory It is during this period that the inventory is vulnerable to stockout (run out of inventory) Customer service level is the probability that a stockout will not occur during the lead time

Basis for setting the Reorder Point Thus, the order point is set based on the demand during lead time (DDLT) and the desired customer service level Reorder point (ROP) = Expected demand during lead time (EDDLT) + Safety stock (SS) The amount of safety stock needed is based on the degree of uncertainty in the DDLT and the customer service level desired

Ideal Inventory Order Cycle Demand rate Time Lead time Order placed Order receipt Inventory Level Reorder point, R Order quantity, Q

Variable Demand with a Reorder Point point, R Q LT Time Inventory level stockout

Reorder Point with a Safety Stock point, R Q LT Time Inventory level Safety Stock

Calculating ROP Reorder Point (ROP) = d x L - d = daily demand - L = lead time for delivery after an order With Safety Stock (SS) we get the following: ROP = d x L + SS

ROP Using Service Level The customer service level is converted into a Z value using the normal distribution table The safety stock is computed by multiplying the Z value by the std dev of DDLT. The order point is set using ROP = EDDLT + SS, or by substitution ROP = d x L + Z ( std dev D) D = demand during lead time

Using Discounts in EOQ Under this condition, material cost becomes an incremental cost and must be considered in the determination of the EOQ The total cost (TC) = material cost + ordering cost + carrying cost TC = DC + (D/Q) Co + (Q/2)Ch D = annual demand in units C = cost per unit

EOQ for production: EPQ D = annual demand in units Qp = quantity produced in one batch Cs = setup cost per setup Ch = cost of holding or carrying p = daily production rate d = daily demand rate Qp = 2DCs Ch(1-d/p)