Chapter 12. Inventory Management. Operations Management - 5 th th Edition. Roberta Russell & Bernard W. Taylor, III.

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1 Chapter 1 Inventory Management Operations Management - 5 th th Edition Roberta Russell & Bernard W. Taylor, III Copyright 006 John Wiley & Sons, Inc. Beni Asllani University of Tennessee at Chattanooga Lecture Outline Elements of Inventory Management Inventory Control Systems Economic Order uantity Models uantity Discounts Reorder Point Order uantity for a Periodic Inventory System Copyright 006 John Wiley & Sons, Inc. 1-1

2 What Is Inventory? Stock of items kept to meet future demand Purpose of inventory management how many units to order when to order Copyright 006 John Wiley & Sons, Inc. 1-3 Types of Inventory Raw materials Purchased parts and supplies Work-in-process (partially completed) products (WIP) Items being transported Tools and equipment Copyright 006 John Wiley & Sons, Inc. 1-4

3 Inventory and Supply Chain Management Bullwhip effect demand information is distorted as it moves away from the end-use customer higher safety stock inventories to are stored to compensate Seasonal or cyclical demand Inventory provides independence from vendors Take advantage of price discounts Inventory provides independence between stages and avoids work stop-pages pages Copyright 006 John Wiley & Sons, Inc. 1-5 Two Forms of Demand Dependent Demand for items used to produce final products Tires stored at a Goodyear plant are an example of a dependent demand item Independent Demand for items used by external customers Cars, appliances, computers, and houses are examples of independent demand inventory Copyright 006 John Wiley & Sons, Inc

4 Inventory and uality Management Customers usually perceive quality service as availability of goods they want when they want them Inventory must be sufficient to provide high-quality customer service in TM Copyright 006 John Wiley & Sons, Inc. 1-7 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 Copyright 006 John Wiley & Sons, Inc

5 Inventory Control Systems Continuous system (fixed- order-quantity) constant amount ordered when inventory declines to predetermined level Periodic system (fixed-time time- period) order placed for variable amount after fixed passage of time Copyright 006 John Wiley & Sons, Inc. 1-9 ABC Classification Class A 5 15 % of units % of value Class B 30 % of units 15 % of value Class C % of units 5 10 % of value Copyright 006 John Wiley & Sons, Inc

6 ABC Classification: Example PART UNIT COST ANNUAL USAGE 1 $ Copyright 006 John Wiley & Sons, Inc ABC Classification: Example (cont.) TOTAL % OF TOTAL % OF TOTAL PART VALUE PART UNIT VALUECOST UANTITY ANNUAL % CUMMULATIVE USAGE 9 $30, $ , A 14, , , B , , % OF TOTAL % OF TOTAL 58.0 CLASS ITEMS VALUE UANTITY 5 3, ,400 A 9, 8, C ,700 B 1, 4, $85,400 C 6, 5, 10, Example 10.1 Copyright 006 John Wiley & Sons, Inc

7 Economic Order uantity (EO) Models EO optimal order quantity that will minimize total inventory costs Basic EO model Production quantity model Copyright 006 John Wiley & Sons, Inc Assumptions of Basic EO Model Demand is known with certainty and is constant over time No shortages are allowed Lead time for the receipt of orders is constant Order quantity is received all at once Copyright 006 John Wiley & Sons, Inc

8 Inventory Order Cycle Order quantity, Inventory Level Demand rate Reorder point, R 0 Lead time Order Order placed receipt Lead time Order Order placed receipt Time Copyright 006 John Wiley & Sons, Inc EO Cost Model C o - cost of placing order C c - annual per-unit carrying cost D - annual demand - order quantity Annual ordering cost = Annual carrying cost = C o D Total cost = + C o D C c C c Copyright 006 John Wiley & Sons, Inc

9 EO Cost Model Deriving opt C o D TC = + TC C o D = + C 0 D 0 = + opt = C o D C c C c C c C c Proving equality of costs at optimal point C o D = opt = C c = C o D C c C o D C c Copyright 006 John Wiley & Sons, Inc EO Cost Model (cont.) Annual cost ($) Minimum total cost Slope = 0 Total Cost Carrying Cost = C c Ordering Cost = C o D Optimal order opt Order uantity, Copyright 006 John Wiley & Sons, Inc

10 EO Example C c = $0.75 per yard C o = $150 D = 10,000 yards opt = C o D C c C o D TC min = + C c opt = (150)(10,000) (0.75) (150)(10,000) min = +,000 TC min (0.75)(,000) opt =,000 yards Orders per year = D/ opt = 10,000/,000 = 5 orders/year TC min = $750 + $750 = $1,500 Order cycle time = 311 days/(d/ opt = 311/5 = 6. store days opt ) Copyright 006 John Wiley & Sons, Inc Production uantity Model An inventory system in which an order is received gradually, as inventory is simultaneously being depleted AKA non-instantaneous receipt model assumption that is received all at once is relaxed p - daily rate at which an order is received over time, a.k.a. production rate d - daily rate at which inventory is demanded Copyright 006 John Wiley & Sons, Inc

11 Inventory level Production uantity Model (cont.) (1-d/p) Maximum inventory level (1-d/p d/p) Average inventory level 0 Order receipt period Begin order receipt End order receipt Time Copyright 006 John Wiley & Sons, Inc Production uantity Model (cont.) p = production rate d = demand rate Maximum inventory level = - p = 1 - Average inventory level = 1 - C o D C c TC = d p d d p d p opt = C c C o D 1 - d p Copyright 006 John Wiley & Sons, Inc. 1-11

12 Production uantity Model: Example C c = $0.75 per yard C o = $150 D = 10,000 yards d = 10,000/311 = 3. yards per day p = 150 yards per day C o D (150)(10,000) opt = = =,56.8 yards C c 1 - d p 150 opt C o D C c d TC = p = $1,39,56.8 Production run = = = days per order p 150 Copyright 006 John Wiley & Sons, Inc Production uantity Model: Example (cont.) D 10,000 Number of production runs = = = 4.43 runs/year,56.8 d Maximum inventory level = 1 - =, p = 1,77 yards Copyright 006 John Wiley & Sons, Inc

13 uantity Discounts Price per unit decreases as order quantity increases where C o D C c TC = + + PD P = per unit price of the item D = annual demand Copyright 006 John Wiley & Sons, Inc uantity Discount Model (cont.) ORDER SIZE PRICE 0-99 $ (d 1 ) (d ) TC = ($10 ) TC (d 1 = $8 ) TC (d = $6 ) Inventory cost ($) Carrying cost Ordering cost (d 1 ) = 100 (d ) = 00 opt Copyright 006 John Wiley & Sons, Inc

14 uantity Discount: Example UANTITY PRICE 1-49 $1, , C o = $,500 C c = $190 per computer D = 00 C opt = o D (500)(00) = = 7.5 PCs 190 opt For = 7.5 C c C o D C c opt TC = + + PD = $33,784 opt For = 90 C o D C c TC = + + PD = $194,105 Copyright 006 John Wiley & Sons, Inc Reorder Point Level of inventory at which a new order is placed where R = dl d = demand rate per period L = lead time Copyright 006 John Wiley & Sons, Inc

15 Reorder Point: Example Demand = 10,000 yards/year Store open 311 days/year Daily demand = 10,000 / 311 = yards/day Lead time = L = 10 days R = dl = (3.154)(10) = yards Copyright 006 John Wiley & Sons, Inc 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 Copyright 006 John Wiley & Sons, Inc

16 Variable Demand with a Reorder Point Inventory level Reorder point, R 0 LT Time LT Copyright 006 John Wiley & Sons, Inc Reorder Point with a Safety Stock Inventory level Reorder point, R 0 LT Safety Stock Time LT Copyright 006 John Wiley & Sons, Inc

17 Reorder Point With Variable Demand R = dl + zσ d L where d = average daily demand L = lead time σ d = the standard deviation of daily demand z = number of standard deviations corresponding to the service level probability zσ d L = safety stock Copyright 006 John Wiley & Sons, Inc Reorder Point for a Service Level Probability of meeting demand during lead time = service level Probability of a stockout Safety stock zσ d L dl Demand R Copyright 006 John Wiley & Sons, Inc

18 Reorder Point for Variable Demand The carpet store wants a reorder point with a 95% service level and a 5% stockout probability d = 30 yards per day L = 10 days σ d = 5 yards per day For a 95% service level, z = 1.65 R = dl + z σ d L = 30(10) + (1.65)(5)( 10) = 36.1 yards Safety stock = z σ d L = (1.65)(5)( 10) = 6.1 yards Copyright 006 John Wiley & Sons, Inc Order uantity for a Periodic Inventory System where zσ d = d(t b + L) ) + zσ d t b + L - I d = average demand rate t b = the fixed time between orders L = lead time = standard deviation of demand σ d t b + L = safety stock I = inventory level Copyright 006 John Wiley & Sons, Inc

19 Fixed-Period Model with Variable Demand d = 6 bottles per day σ d = 1. bottles t b = 60 days L = 5 days I = 8 bottles z = 1.65 (for a 95% service level) = d(t b + L) ) + zσ d t b + L - I = (6)(60 + 5) + (1.65)(1.) = bottles Copyright 006 John Wiley & Sons, Inc Copyright 006 John Wiley & Sons, Inc. All rights reserved. Reproduction or translation of this work beyond b that permitted in section 117 of the 1976 United States Copyright Act without express permission of the copyright owner is unlawful. Request for further information should be addressed to the Permission Department, John Wiley & Sons, Inc. The purchaser may make back-up copies for his/her own use only and not for distribution or resale. The Publisher assumes no responsibility sibility for errors, omissions, or damages caused by the use of these programs s or from the use of the information herein. Copyright 006 John Wiley & Sons, Inc