13-1 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Inventory Management Chapter 13 Inventory Management

13-2 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Inventory Management Inventory Inventory--a stock or store of goods

13-3 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Inventory Management Types of Inventories Raw materials & purchased parts Partially completed goods called work in progress Finished-goods inventories –(manufacturing firms) or merchandise (retail stores)

13-4 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Inventory Management Types of Inventories (Cont’d) Replacement parts, tools, & supplies Goods-in-transit to warehouses or customers (aka “pipeline” inventory)

13-5 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Inventory Management Functions of Inventory To permit operations To meet anticipated demand To smooth production requirements To decouple components of the production-distribution To protect against stock-outs To take advantage of order cycles To hedge against price increases or take advantage of quantity discounts

13-6 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Inventory Management Poor inventory management can result in either overstocking or understocking Effective inventory management: –A system to keep track of inventory –A reliable forecast of demand –Knowledge of lead times –Reasonable estimates of Holding costs Ordering costs Shortage costs –A classification system Inventory Management

13-7 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Inventory Management Inventory Counting Systems Periodic System Physical count of items made at periodic intervals Perpetual Inventory System System that keeps track of removals from inventory continuously, thus monitoring current levels of each item

13-8 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Inventory Management Lead time: time interval between ordering and receiving the order Holding (carrying) costs: cost to carry an item in inventory for a length of time, usually a year Ordering costs: costs of ordering and receiving inventory Shortage costs: costs when demand exceeds supply Key Inventory Terms

13-9 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Inventory Management ABC Classification System Classifying inventory according to some measure of importance and allocating control efforts accordingly. A A - very important B B - mod. important C C - least important Figure 13-1 Annual $ volume of items A B C High Low Few Many Number of Items

13-10 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Inventory Management Economic order quantity model Economic production model Quantity discount model Economic Order Quantity Models

13-11 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Inventory Management Only one product is involved Annual demand requirements known Demand is even throughout the year Lead time does not vary Each order is received in a single delivery There are no quantity discounts Assumptions of EOQ Model

13-12 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Inventory Management EOQ Total Cost of Inventory Annual carrying cost Annual ordering cost Total cost =+ Q 2 H D Q S TC = + Where:Q=Order quantity H=Holding cost per unit per year D=Demand in units per year S=Ordering costs per order

13-13 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Inventory Management Cost Minimization Goal Order Quantity (Q) The Total-Cost Curve is U-Shaped Ordering Costs QOQO Annual Cost ( optimal order quantity) Figure 13-4

13-14 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Inventory Management Deriving the EOQ Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q.

13-15 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Inventory Management Minimum Total Cost The total cost curve reaches its minimum where the carrying and ordering costs are equal.

13-16 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Inventory Management When to Reorder with EOQ Ordering Reorder Point - When the quantity on hand of an item drops to this amount, the item is reordered Safety Stock - Stock that is held in excess of expected demand due to variable demand rate and/or lead time. Service Level - Probability that demand will not exceed supply during lead time.

13-17 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Inventory Management Safety Stock LT Time Expected demand during lead time Maximum probable demand during lead time ROP Quantity Safety stock Figure 13-12

13-18 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Inventory Management Production done in batches or lots Capacity to produce a part exceeds the part’s usage or demand rate Assumptions of EPQ are similar to EOQ except orders are received incrementally during production Economic Production Quantity

13-19 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Inventory Management Only one item is involved Annual demand is known Usage rate is constant Usage occurs continually Production rate is constant Lead time does not vary No quantity discounts Economic Production Quantity Assumptions

13-20 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Inventory Management EPQ Total Cost of Inventory Carrying cost Setup cost Total cost =+ I max 2 H D Q S TC = + Where:I max =Maximum inventory Q=Run quantity H=Holding cost per unit per year D=Demand in units per year S=Setup costs per run

13-21 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Inventory Management Deriving the EPQ Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q. Where:p=production rate u=usage rate

13-22 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Inventory Management EPQ Equations Cycle time--time between the beginning of runs Run time--the length of the production run Maximum & average inventory

13-23 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Inventory Management Orders are placed at fixed time intervals Order quantity for next interval? Suppliers might encourage fixed intervals May require only periodic checks of inventory levels Fixed-Order-Interval Model

13-24 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Inventory Management Tight control of type A items Items from same supplier may yield savings in: –Ordering –Packing –Shipping costs May be practical when inventories cannot be closely monitored Fixed-Interval Benefits

13-25 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Inventory Management Requires a larger safety stock Increases carrying cost Costs of periodic reviews Fixed-Interval Disadvantages

13-26 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Inventory Management Too much inventory –Tends to hide problems –Easier to live with problems than to eliminate them –Costly to maintain Wise strategy –Reduce lot sizes –Reduce safety stock Operations Strategy