Lecture 31 - Independent Demand and Ordering System (Revision). The contents of this chapter include all of the following: What is inventory, cost of inventory, benefits of inventory, multi period model, optimal quantity to order, safety stock, periodic review system, single period inventory model.
Lecture 31 Independent Demand and Ordering System (Revision) Books • Introduction to Materials Management, Sixth Edition, J. R. Tony Arnold, P.E., CFPIM, CIRM, Fleming College, Emeritus, Stephen N. Chapman, Ph.D., CFPIM, North Carolina State University, Lloyd M. Clive, P.E., CFPIM, Fleming College • Operations Management for Competitive Advantage, 11th Edition, by Chase, Jacobs, and Aquilano, 2005, N.Y.: McGrawHill/Irwin • Operations Management, 11/E, Jay Heizer, Texas Lutheran University, Barry Render, Graduate School of Business, Rollins College, Prentice Hall Objectives • • • • • • • • What is Inventory Cost of Inventory Benefits of Inventory Multi period model Optimal quantity to order Safety stock Periodic review system Single period Inventory model What is inventory? Inventory is the raw materials, component parts, workinprocess, or finished products that are held at a location in the supply chain Why do we care? At the macro level: Inventory is one of the biggest corporate assets ($) Investment in inventory is currently over $1.25 Trillion (U.S. Department of Commerce). This figure accounts for almost 25% of GNP Enormous potential for efficiency increase by controlling inventories Why do we care? At the firm level: – – Sales growth: right inventory at the right place at the right time Cost reduction: less money tied up in inventory, inventory management, obsolescence Higher profit Why do we care? Each of Solectron’s big customers, which include Cisco, Ericsson, and Lucent was expecting explosive growth for wireless phones and networking gear….when the bottom finally fell out, it was too late for Solectron to halt orders from all of its 4,000 suppliers Now, Solectron has $4.7 billion in inventory (BW, March 19, 2001) “When Palm formally reported its quarterly numbers in June, the damage was gruesome Its loss totaled $392 million, a big chunk of which was attributable to writing down excess inventory - piles of unsold devices.” (The Industry Standard, June 16, 2001) “Liz Claiborne said its unexpected earnings decline is the consequence of higher than anticipated excess inventories” (WSJ, August 1993) How do you manage your inventory? How much do you buy? When? • • • • • • Soda Milk Toilet paper Gas Cereal Cash What Do you Consider? • • • • • • Cost of not having it. Cost of going to the grocery or gas station (time, money), cost of drawing money Cost of holding and storing, lost interest Price discounts How much you consume Some safety against uncertainty Costs of Inventory • Physical holding costs: – – • • out of pocket expenses for storing inventory (insurance, security, warehouse rental, cooling) All costs that may be entailed before you sell it (obsolescence, spoilage, rework ) Opportunity cost of inventory: foregone return on the funds invested Operational costs: – – – Delay in detection of quality problems Delay the introduction of new products Increase throughput times Benefits of Inventory • Hedge against uncertain demand • Hedge against uncertain supply • Economize on ordering costs • Smoothing To summarize, we build and keep inventory in order to match supply and demand in the most cost effective way Decide what Service Level you want to provide (Service level = probability of NOT stocking out) Service level Probability of stock-out Safety Stock Safety stock = (safety factor z)(std deviation in LT demand) Service level Probability of stock-out Safety Stock Read z from Normal table for a given service level Caution: Std deviation in LT demand Variance over multiple periods = the sum of the variances of each period (assuming independence) Standard deviation over multiple periods is the square root of the sum of the variances, not the sum of the standard deviations!!! Average Inventory = (Order Qty)/2 + Safety Stock Inventory Level Order Quantity EOQ/2 Safety Stock (SS) Lead Time Place order Receive order Time Average Inventory How to find ROP & Q 2SD H Order quantity Q = EOQ = To find ROP, determine the service level (i.e., the probability of NOT stocking out.) ◆ ◆ Find the safety factor from a ztable or from the graph. Find std deviation in LT demand: square root law std dev in LT demand = ( std dev in daily demand ) days in LT σ LT = σ D LT ◆ Safety stock is given by: SS = (safety factor)(std dev in LT demand) ◆ Reorder point is: ROP = Expected LT demand + SS Average Inventory is: SS + EOQ/2 Example (continued)… Back to the car lot… recall that the lead time is 10 days and the expected yearly demand is 5000. You estimate the standard deviation of daily demand demand to be d = 6. When should you reorder if you want to be 95% sure you don’t run out of cars? Since the expected yearly demand is 5000, the expected demand over the lead time is 5000(10/365) = 137. The zvalue corresponding to a service level of 0.95 is 1.65. So ROP 137 1.65 10(36) 168 Order 548 cars when the inventory level drops to 168 Why Companies Don’t Always Use Optimal Order Quantity It is not unusual for companies to order less or more than the EOQ for several reasons: • They may not have a known uniform demand; • Some suppliers have minimum order quantity that are beyond the demand Justifying Smaller Order Quantities JIT or “Lean Systems” would recommend reducing order quantities to the lowest practical levels • Benefits from reducing Q’s: – – – • • Improved customer responsiveness (inventory = Lead time) Reduced Cycle Inventory Reduced raw materials and purchased components Justifying smaller EOQ’s: Q 2DS H Reduce Q’s by reducing setup time (S). “Setup reduction” is a well documented, structured approach to reducing S Determining Safety Stock and Service Levels • If demand or lead time is uncertain, safety stock can be added to improve ordercycle service levels – – • R = dL +SS Where SS =zσ dL, and Z is the number of standard deviations and σ dL is standard deviation of the demand during lead time Ordercycle service level – The probability that demand during lead time will not exceed onhand inventory – A 95% service level (stockout risk of 5%) has a Z=1.645 Periodic Review Systems • • Orders are placed at specified, fixedtime intervals (e.g. every Friday), for a order size (Q) to bring onhand inventory (OH) up to the target inventory (TI), similar to the minmax system Advantages are: – – • No need for a system to continuously monitor item Items ordered from the same supplier can be reviewed on the same day saving purchase order costs Disadvantages: – – – Replenishment quantities (Q) vary Order quantities may not quality for quantity discounts On the average, inventory levels will be higher than Q systemsmore stockroom space needed Periodic Review Systems: Calculations for TI Targeted Inventory level: TI = d(RP + L) + SS d = average period demand RP = review period (days, wks) L = lead time (days, wks) SS = zσRP+L • Replenishment Quantity (Q)=TIOH • P System: an auto parts store calculated the EOQ for Drive Belts at 236 units and wants to compare the Total Inventory Costs for a Q vs. a P Review System. Annual demand (D) is 2704, avg. weekly demand is 52, weekly σ is 1.77 belts, and lead time is 3 weeks. The annual TC for the Q system is $229; H=$97, S=$10 Q x 52weeks D 236 x52 2704 • Review Period • Target Inventory for 95% Service Level • RP TI d(RP L) SS d(RP L) zσRP TI 52 units 1.645 1.77 5wks L 416 424 belts Average OnHand OHavg= TIdL=424(52belts)(3wks) = 268 belts • Annual Total Cost (P System) 52 268 TCp $10 $0.97 115 130 $245 Annual Cost Difference $245 $229 $16 Single Period Inventory Model The SPI model is designed for products that share the following characteristics: – – – • Sold at their regular price only during a singletime period Demand is highly variable but follows a known probability distribution Salvage value is less than its original cost so money is lost when these products are sold for their salvage value Objective is to balance the gross profit of the sale of a unit with the cost incurred when a unit is sold after its primary selling period SPI Model Example: Tshirts are purchase in multiples of 10 for a charity event for $8 each. When sold during the event the selling price is $20. After the event their salvage value is just $2. From past events the organizers know the probability of selling different quantities of tshirts within a range from 80 to 120 Payoff Table Prob. Of Occurrence.20 25 .30 .15 .10 Customer Demand 80 90 100 110 120 # of Shirts Ordered Profit 80 $960 $960 $960 $960 $960 $960 90 $900 $1080 $1080 $1080 $1080 $1040 Buy 100 $840 $1020 $1200 $1200 $1200 $1083 110 $780 $ 960 $1140 $1320 $1320 $1068 120 $720 $ 900 $1080 $1260 $1440 $1026 Sample calculations: Payoff (Buy 110)= sell 100($20$8) –((110100) x ($8$2))= $1140 Expected Profit (Buy 100)= ($840 X .20)+($1020 x .25)+($1200 x .30) + ($1200 x .15)+($1200 x .10) = $1083 End of Lecture 31 ... “Our? ?inventory? ?consists? ?of? ?up to 35,000 different kinds of? ?building materials, home improvement supplies, and? ?lawn? ?and? ?garden products.” “We currently offer thousands? ?of? ?products in our online store.” “We offer approximately 250,000 more products ... What is? ?Inventory Cost? ?of? ?Inventory Benefits? ?of? ?Inventory Multi period model Optimal quantity to order Safety stock Periodic review system Single period? ?Inventory? ?model What is? ?inventory? Inventory? ?is the raw materials, component ... Stockout Inventory Point Time Lead Time Place order Receive order Unfilled demand If ROP = expected demand, service level is 50%.? ?Inventory? ?left 50%? ?of? ?the time, stock outs 50%? ?of? ?the time Inventory