OP 2202 Introduction to Operations Management Inventory Management

OP 2202: Introduction to Operations Management Inventory Management Anupam Das, Ph. D

OP 2202: Introductions to Operations Management Lesson 14, Page 2 Outline for the Week 14 þ þ þ þ GLOBAL COMPANY PROFILE: AMAZON. COM FUNCTIONS OF INVENTORY þ Types of Inventory INVENTORY MANAGEMENT þ ABC Analysis Record Accuracy þ Cycle Counting þ Control of Service Inventories INVENTORY MODELS þ Independent versus Dependent Demand þ Holding, Ordering, and Setup Costs INVENTORY MODELS FOR INDEPENDENT DEMAND þ Basic Economic Order Quantity (EOQ) Model þ Minimizing Costs þ Reorder Points þ Production Order Quantity Model þ Quantity Discount Models PROBABILISTIC MODELS WITH CONSTANT LEAD TIME FIXED PERIOD (P) SYSTEMS Anupam Das, Ph. D

AMAZON. com OP 2202: Introductions to Operations Management Lesson 14, Page 3 • Jeff Bezos, in 1995, started AMAZON. com as a “virtual” retailer – no inventory, no warehouses, no overhead; just a bunch of computers. • Growth forced AMAZON. com to excel in inventory management! • AMAZON is now a worldwide leader in warehouse management and automation. Anupam Das, Ph. D

OP 2202: Introductions to Operations Management Lesson 14, Page 4 Order Fulfillment at AMAZON 1. You order items; , computer assigns your order to distribution center [closest facility that has the product(s)] 2. Lights indicate products ordered to workers who retrieve product and reset light. 3. Items placed in crate with items from other orders, and crate is placed on conveyor. Bar code on item is scanned 15 times – virtually eliminating error. 4. Crates arrive at central point where items are boxed and labeled with new bar code. 5. Gift wrapping done by hand (30 packages per hour) 6. Box is packed, taped, weighed and labeled before leaving warehouse in a truck. 7. Order appears on your doorstep within a week Anupam Das, Ph. D

OP 2202: Introductions to Operations Management Lesson 14, Page 5 What is Inventory? • Stock of materials • Stored capacity • Examples © 1995 Corel Corp. © 1984 -1994 T/Maker Co. © 1995 Corel Corp. Anupam Das, Ph. D

OP 2202: Introductions to Operations Management Lesson 14, Page 6 The Functions of Inventory • To ”decouple” or separate various parts of the production process • To provide a stock of goods that will provide a “selection” for customers • To take advantage of quantity discounts • To hedge against inflation and upward price changes Anupam Das, Ph. D

OP 2202: Introductions to Operations Management Lesson 14, Page 7 Types of Inventory • • Raw material Work-in-progress Maintenance/repair/operating supply Finished goods Anupam Das, Ph. D

OP 2202: Introductions to Operations Management Lesson 14, Page 8 The Material Flow Cycle Anupam Das, Ph. D

OP 2202: Introductions to Operations Management Lesson 14, Page 9 Disadvantages of Inventory • Higher costs – Item cost (if purchased) – Ordering (or setup) cost • Costs of forms, clerks’ wages etc. – Holding (or carrying) cost • Building lease, insurance, taxes etc. • Difficult to control • Hides production problems Anupam Das, Ph. D

OP 2202: Introductions to Operations Management Lesson 14, Page 10 Inventory Classifications Inventory Proces s stage Number & Value Raw Material WIP Finished Goods A Items B Items C Items © 1984 -1994 T/Maker Co. Deman d Type Other Independen t Dependent Maintenanc e Operating Anupam Das, Ph. D

OP 2202: Introductions to Operations Management Lesson 14, Page 11 The Material Flow Cycle Input Other Wait Time Move Time Queu e Time Setup Time Run Time Output Cycle Time 1 Run time: Job is at machine and being worked on 2 Setup time: Job is at the work station, and the work station is being "setup. " 3 Queue time: Job is where it should be, but is not being processed because other work precedes it. 4 Move time: The time a job spends in transit 5 Wait time: When one process is finished, but the job is waiting to be moved to the next work area. 6 Other: "Just-in-case" inventory. Anupam Das, Ph. D

ABC Analysis OP 2202: Introductions to Operations Management Lesson 14, Page 12 • Divides on-hand inventory into 3 classes – A class, B class, C class • Basis is usually annual $ volume – $ volume = Annual demand x Unit cost • Policies based on ABC analysis – Develop class A suppliers more – Give tighter physical control of A items – Forecast A items more carefully Anupam Das, Ph. D

OP 2202: Introductions to Operations Management Lesson 14, Page 13 Classifying Items as ABC Class A B C % Annual $ Usage 100 80 60 % $ Vol 80 15 5 % Items 15 30 55 A 40 B 20 C 0 0 50 100 % of Inventory Items Anupam Das, Ph. D

Cycle Counting OP 2202: Introductions to Operations Management Lesson 14, Page 14 • Physically counting a sample of total inventory on a regular basis • Used often with ABC classification – A items counted most often (e. g. , daily) Anupam Das, Ph. D

OP 2202: Introductions to Operations Management Lesson 14, Page 15 Advantages of Cycle Counting • Eliminates shutdown and interruption of production necessary for annual physical inventories • Eliminates annual inventory adjustments • Provides trained personnel to audit the accuracy of inventory • Allows the cause of errors to be identified and remedial action to be taken • Maintains accurate inventory records Anupam Das, Ph. D

Techniques for Controlling Service Inventory Include: OP 2202: Introductions to Operations Management Lesson 14, Page 16 • Good personnel selection, training, and discipline • Tight control of incoming shipments • Effective control of all goods leaving the facility Anupam Das, Ph. D

OP 2202: Introductions to Operations Management Lesson 14, Page 17 Independent versus Dependent Demand • Independent demand - demand for item is independent of demand for any other item • Dependent demand - demand for item is dependent upon the demand for some other item Anupam Das, Ph. D

Inventory Costs OP 2202: Introductions to Operations Management Lesson 14, Page 18 • Holding costs - associated with holding or “carrying” inventory over time • Ordering costs - associated with costs of placing order and receiving goods • Setup costs - cost to prepare a machine or process for manufacturing an order Anupam Das, Ph. D

OP 2202: Introductions to Operations Management Lesson 14, Page 19 Holding (Carrying) Costs • • Obsolescence Insurance Extra staffing Interest Pilferage Damage Warehousing Etc. Anupam Das, Ph. D

OP 2202: Introductions to Operations Management Lesson 14, Page 20 Inventory Holding Costs (Approximate Ranges) Category Cost as a % of Inventory Value Housing costs (building rent, depreciation, operating cost, taxes, insurance) Material handling costs (equipment, lease or depreciation, power, operating cost) 6% (3 - 10%) 3% (1 - 3. 5%) Labor cost from extra handling 3% (3 - 5%) Investment costs (borrowing costs, taxes, and insurance on inventory) 11% (6 - 24%) Pilferage, scrap, and obsolescence Overall carrying cost 3% (2 - 5%) 26% Anupam Das, Ph. D

Ordering Costs • • • OP 2202: Introductions to Operations Management Lesson 14, Page 21 Supplies Forms Order processing Clerical support Etc. Anupam Das, Ph. D

Setup Costs • • OP 2202: Introductions to Operations Management Lesson 14, Page 22 Clean-up costs Re-tooling costs Adjustment costs Etc. Anupam Das, Ph. D

OP 2202: Introductions to Operations Management Lesson 14, Page 23 Inventory Models • Fixed order-quantity models – Economic order quantity – Production order quantity – Quantity discount Help answer the inventory planning questions! • Probabilistic models • Fixed order-period models Anupam Das, Ph. D

OP 2202: Introductions to Operations Management Lesson 14, Page 24 EOQ Assumptions • • • Known and constant demand Known and constant lead time Instantaneous receipt of material No quantity discounts Only order (setup) cost and holding cost No stockouts Anupam Das, Ph. D

OP 2202: Introductions to Operations Management Lesson 14, Page 25 Inventory Usage Over Time Inventory Level Order quantity = Q (maximum inventory level) Minimum inventory 0 Usage Rate Average Inventory (Q*/2) Time Anupam Das, Ph. D

OP 2202: Introductions to Operations Management Lesson 14, Page 26 EOQ Model, How Much to Order? Annual Cost ve r u t. C s Minimu m total cost T o C l a ot Hol C g n i e rv u C st o d Order (Setup) Cost Curve Optimal Order Quantity (Q*) Order quantity Anupam Das, Ph. D

OP 2202: Introductions to Operations Management Lesson 14, Page 27 Why Holding Costs Increase • More units must be stored if more are ordered Purchase Order Description Qty. Microwave 1 Order quantity Purchase Order Description Qty. Microwave 1000 Order quantity Anupam Das, Ph. D

OP 2202: Introductions to Operations Management Lesson 14, Page 28 Why Order Costs Decrease Cost is spread over more units Example: You need 1000 microwave ovens 1 Order (Postage $ 0. 33) 1000 Orders (Postage $330) Purchase Order Description Qty. Microwave 1000 Purchase. Order Description Qty. Purchase Description Qty. 1 Microwave Description Qty. Microwave 11 Microwave 1 Order quantity Anupam Das, Ph. D

OP 2202: Introductions to Operations Management Lesson 14, Page 29 Deriving an EOQ 1. Develop an expression for setup or ordering costs 2. Develop an expression for holding cost 3. Set setup cost equal to holding cost 4. Solve the resulting equation for the best order quantity Anupam Das, Ph. D

OP 2202: Introductions to Operations Management Lesson 14, Page 30 EOQ Model, When To Order Inventory Level Average Inventory (Q*/2) Optimal Order Quantity (Q*) Reorder Point (ROP) Lead Time Anupam Das, Ph. D

OP 2202: Introductions to Operations Management Lesson 14, Page 31 EOQ Model Equations 2 ×D ×S H D Expected Number of Orders =N= Q* Optimal Order Quantity = Q* = Working Days. Year Expected Time Between Orders = = T N d= D Working Days. Year ROP = d × L D = Demand per year S = Setup (order) cost per order H = Holding (carrying) cost d = Demand per day L = Lead time in days Anupam Das, Ph. D

OP 2202: Introductions to Operations Management Lesson 14, Page 32 The Reorder Point (ROP) Curve Q* Inventory level (units) Slope = units/day = d ROP (Units) Lead time = L Time (days) Anupam Das, Ph. D

OP 2202: Introductions to Operations Management Lesson 14, Page 33 Production Order Quantity Model • Answers how much to order and when to order • Allows partial receipt of material – Other EOQ assumptions apply • Suited for production environment – Material produced, used immediately – Provides production lot size • Lower holding cost than EOQ model Anupam Das, Ph. D

OP 2202: Introductions to Operations Management Lesson 14, Page 34 EOQ POQ Model, When To Order Inventory Level Maximu m inventor y level Both production and usage take place Usage only takes place Time Anupam Das, Ph. D

OP 2202: Introductions to Operations Management Lesson 14, Page 35 EOQ POQ Model, When To Order Inventory Level Average Inventory Optimal Order Quantity (Q*) Reorder Point (ROP) Lead Time Anupam Das, Ph. D

OP 2202: Introductions to Operations Management Lesson 14, Page 36 Reasons for Variability in Production Most variability is caused by waste or by poor management. Specific causes include: q employees, machines, and suppliers produce units that do not conform to standards, are late or are not the proper quantity q inaccurate engineering drawings or specifications q production personnel try to produce before drawings or specifications are complete q customer demands are unknown Anupam Das, Ph. D

OP 2202: Introductions to Operations Management Lesson 14, Page 37 POQ Model Inventory Levels Inventory Level Production portion of cycle Demand portion of cycle with no supply Supply Begins Supply Ends Time Anupam Das, Ph. D

OP 2202: Introductions to Operations Management Lesson 14, Page 39 POQ Model Equations Optimal Order Quantity = Q* = p Maximum inventory level = Q* Setup Cost Holding Cost = D Q 2*D*S d H* 1 p ( ) 1 - d p * S ( ) = 0. 5 * H * Q 1 - d p D = Demand per year S = Setup cost H = Holding cost d = Demand per day p = Production per day Anupam Das, Ph. D

OP 2202: Introductions to Operations Management Lesson 14, Page 40 Quantity Discount Model • Answers how much to order & when to order • Allows quantity discounts – Reduced price when item is purchased in larger quantities – Other EOQ assumptions apply • Trade-off is between lower price & increased holding cost Anupam Das, Ph. D

OP 2202: Introductions to Operations Management Lesson 14, Page 41 Quantity Discount Schedule Discount Number 1 2 3 Discount Quantity 0 to 999 Discount (%) No discount 1, 000 to 1, 999 4 2, 000 and over 5 Discount Price (P) $5. 00 $4. 80 $4. 75 Anupam Das, Ph. D

OP 2202: Introductions to Operations Management Lesson 14, Page 42 Quantity Discount – How Much to Order Anupam Das, Ph. D

OP 2202: Introductions to Operations Management Lesson 14, Page 43 Probabilistic Models • Answer how much & when to order • Allow demand to vary – Follows normal distribution – Other EOQ assumptions apply • Consider service level & safety stock – Service level = 1 - Probability of stockout – Higher service level means more safety stock • More safety stock means higher ROP Anupam Das, Ph. D

OP 2202: Introductions to Operations Management Lesson 14, Page 44 Probabilistic Models. When to Order? Inventory Level Frequenc y Service Level Optimal Order Quantity P(Stockout) SS X ROP Reorder Point (ROP) Safety Stock (SS) Place order Lead Time Receive order Time Anupam Das, Ph. D

OP 2202: Introductions to Operations Management Lesson 14, Page 45 Fixed Period Model • Answers how much to order • Orders placed at fixed intervals – Inventory brought up to target amount – Amount ordered varies • No continuous inventory count – Possibility of stockout between intervals • Useful when vendors visit routinely – Example: P&G representative calls every 2 weeks Anupam Das, Ph. D

OP 2202: Introductions to Operations Management Lesson 14, Page 46 Inventory Level in a Fixed Period System Various amounts (Qi) are ordered at regular time intervals (p) based on the quantity necessary to bring inventory up to target maximum Q 1 Target maximum Q 4 Q 2 On-Hand Inventory Q 3 p p p Time Anupam Das, Ph. D

OP 2202: Introductions to Operations Management Lesson 14, Page 47 Fixed Period Model. When to Order? Inventory Level Period Target maximum Period Time Anupam Das, Ph. D