To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Chapter 12 Inventory Management

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. 2 Inventory Stock of items held to meet future demand Inventory management answers two questions –How much to order –When to order

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. 3 Types of Inventory Raw materials Purchased parts and supplies Labor In-process (partially completed) products Component parts Working capital Tools, machinery, and equipment Finished goods

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. 4 Reasons To Hold Inventory Meet unexpected demand Smooth seasonal or cyclical demand Meet variations in customer demand Take advantage of price discounts Hedge against price increases Quantity discounts

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. 5 Two Forms Of Demand Dependent –items used to produce final products Independent –items demanded by external customers

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. 6 Inventory Costs Carrying 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

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. 7 Inventory Control Systems Fixed-order-quantity system (Continuous) –constant amount ordered when inventory declines to predetermined level Fixed-time-period system (Periodic) –order placed for variable amount after fixed passage of time

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. 8 ABC Classification System Demand volume & value of items vary Classify inventory into 3 categories Class% of Units% of Dollars A B3015 C

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. 9 ABC Classification Example

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. 10 Assumptions Of Basic EOQ Model Demand is known with certainty Demand is relatively constant over time No shortages are allowed Lead time for the receipt of orders is constant The order quantity is received all at once

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. 11 EOQ Model Cost Curves Slope = 0 Total Cost Ordering Cost = C o D/Q Order Quantity, Q Annual cost ($) Minimum total cost Optimal order Q opt Carrying Cost = C c Q/2 Purchase Cost = PD

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. 12 The Inventory Order Cycle Demand rate 0 Time Lead time Lead time Order Placed Order Placed Order Received Order Received Inventory Level Reorder point, R Order qty, Q

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. 13 EOQ Cost Model C O - cost of placing order D - annual demand P – unit priceC C - annual per-unit carrying cost Q - order quantity Annual ordering cost = C O D/QAnnual carrying cost = C C Q/2 Total cost = C O D/Q + C C Q/2+PD

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. 14 EOQ Example C C = $0.75 per yard C O = $150 D = 10,000 yards

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Problem 1 A manufacturer estimate that he will need 18,000 transistors of a particular type over the period of 200 work-day year, or 90 transistors per day, in order to maintain the daily production rate that his output requirements dictate. The cost of holding one unit of transistor for one year is $0.10 and ordering cost is $100 per order. Find the economic order quantity, time between orders, and the minimum inventory cost. 15

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Solution 1 Time between orders = t = 1/m, where m is the number of orders. m = D/Q * = 18000/6000 = 3 Then, t = 200/3 = days Minimum Inventory Cost = TC = 16

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Carrying Cost In many situations, the carrying cost is given as a percentage or fraction of Unit Price C c = f * P 17

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. 18 Quantity Discounts Price per unit decreases as order quantity increases Order SizePrice 0-99$ (d1) (d2)

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. 19 Quantity Discount Model Q opt Carrying cost Ordering cost Inventory cost ($) Q(d 1 ) = 100Q(d 2 ) = 200 TC (d 2 = $6 ) TC (d 1 = $8 ) TC = ($10 ) Purchase cost

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. 20 Quantity Discount Example Order C C = $190 per computer SizePriceC O = $2, $1,400D = ,

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Problem 2 The Smith Company purchases 8000 units of a product each year. The supplier offers the units for sale at $10 per unit for orders up to 500 units and $9 per unit for orders of 500 units or more. What is the economic order quantity if the order cost is $30 per order and the holding cost is 30% per unit cost per year? 21

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Solution 2 The total cost for the single price break quantity of 500 units is as follows: The EOQ for each unit price is as follows: The EOQ with $10 is valid. The EOQ with $9 is invalid since it is not available for quantities less than 500 units. The total cost of the valid EOQ with $10 is as follows: Comparing the total costs of the single price break quantity and the valid EOQ, the minimum cost order quantity is 500 units. 22

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. 23 When to Order Reorder Point -level of inventory at which to place a new order R = dL where d = demand rate per period L = lead time

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. 24 Reorder Point Example Demand = 10,000 yds/year Store open 311 days/year Daily demand = 10,000 / 311 = yds/day Lead time = L = 10 days R = dL = (32.154)(10) = yds

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. 25 Safety Stocks Safety stock –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

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. 26 Reorder Point With A Safety Stock Reorder point, R Q 0 Inventory level LT Time Safety stock

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. 27 Reorder Point With Variable Demand

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. 28 Reorder Point For A Service Level Safety stock R Probability of meeting demand during lead time = service level dL Demand Probability of a stockout

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. 29 Reorder Point For Variable Demand Carpet store wants a reorder point with a 95% service level and a 5% stockout probability

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. 30 Determining Z Value For Service Level Z … Z = Probability of a stockout = 5% Service level = area to left of Z value or 95%