Lecture 22 Inventory Fundamentals Continued Books Introduction to

Lecture 22 Inventory Fundamentals (Continued) 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, 11 th Edition, by Chase, Jacobs, and Aquilano, 2005, N. Y. : Mc. Graw-Hill/Irwin. • Operations Management, 11/E, Jay Heizer, Texas Lutheran University, Barry Render, Graduate School of Business, Rollins College, Prentice Hall

Objectives • • • ABC Controls ABC analysis Records accuracy Cycle counting Independent vs. dependent demand Managing inventory in the face of uncertainity

ABC Inventory Control • Control of inventory is exercised by controlling individual items called stock-keeping units (SKUs). • An SKU is an individual item in a specific inventory. • Four questions must be answered in controlling inventory: – – What is the importance of the inventory item? How are they to be controlled? How much should be ordered at one time? When should an order be placed?

ABC Inventory Control • ABC inventory classification answers the first two questions by determining the importance of items and thus allowing different levels of control based on the importance of items. • Factors affecting the importance of an item include annual dollar usage, unit cost, and scarcity of material.

ABC Inventory Control • The ABC principle is based on the observation that a small number of items often dominate the results achieved in any situation and represent the most critical values (“Pareto” principle). • ABC inventory control separates the more significant items from the less important. • It is used to determine the degree and level of control required.

ABC Inventory Control Methodology • Calculate the annual dollar usage for each item. • List the items according to their annual dollar usage. • Calculate the cumulative annual dollar usage and the cumulative percent of items. • Group items into an A, B, C classification.

ABC Inventory Control • Control Based on ABC Classification – Two general rules: • Have plenty of low-value items - C items are only important if there is a shortage of one of them - then they become extremely important - so a supply should always be on hand. • Use the money and control effort saved to reduce the inventory of high-value items - A items are extremely important and deserve the tightest control and the most frequent review.

ABC Inventory Control

ABC Inventory Control Tight Control A Items • Complete, accurate records • Regular, frequent review by management • Frequent review of forecasts • Close follow-up Normal Control B Items • Good records • Normal processing Simplest possible control C Items • Make sure there are plenty • Simple or no records • Large order quantities

ABC Analysis þ Divides inventory into three classes based on annual dollar volume þ Class A - high annual dollar volume þ Class B - medium annual dollar volume þ Class C - low annual dollar volume þ Used to establish policies that focus on the few critical parts and not the many trivial ones

ABC Analysis Item Stock Number #10286 Percent of Number of Items Stocked 20% Annual Volume (units) 1, 000 x Unit Cost $ 90. 00 = Annual Dollar Volume $ 90, 000 Percent of Annual Dollar Volume Class 38. 8% A 72% #11526 500 154. 00 77, 000 33. 2% A #12760 1, 550 17. 00 26, 350 11. 3% B 350 42. 86 15, 001 6. 4% 1, 000 12. 50 12, 500 5. 4% #10867 #10500 30% 23% B B

ABC Analysis Item Stock Number Percent of Number of Items Stocked Annual Volume (units) x Unit Cost = Annual Dollar Volume Percent of Annual Dollar Volume Class #12572 600 $ 14. 17 $ 8, 502 3. 7% C #14075 2, 000 . 60 1, 200 . 5% C 100 8. 50 850 . 4% #01307 1, 200 . 42 504 . 2% C #10572 250 . 60 150 . 1% C $232, 057 100. 0% #01036 50% 8, 550 5% C

Percent of annual dollar usage ABC Analysis 80 70 60 50 40 30 20 10 0 A Items – – – – – B Items C Items | | | | 10 20 30 40 50 60 70 Percent of inventory items

ABC Analysis þ Other criteria than annual dollar volume may be used þ Anticipated engineering changes þ Delivery problems þ Quality problems þ High unit cost

ABC Analysis þ Policies employed may include þ More emphasis on supplier development for A items þ Tighter physical inventory control for A items þ More care in forecasting A items

Record Accuracy þ Accurate records are a critical ingredient in production and inventory systems þ Allows organization to focus on what is needed þ Necessary to make precise decisions about ordering, scheduling, and shipping þ Incoming and outgoing record keeping must be accurate þ Stockrooms should be secure

Cycle Counting þ Items are counted and records updated on a periodic basis þ Often used with ABC analysis to determine cycle þ Has several advantages þ Eliminates shutdowns and interruptions þ Eliminates annual inventory adjustment þ Trained personnel audit inventory accuracy þ Allows causes of errors to be identified and corrected þ Maintains accurate inventory records

Cycle Counting Example 5, 000 items in inventory, 500 A items, 1, 750 B items, 2, 750 C items Policy is to count A items every month (20 working days), B items every quarter (60 days), and C items every six months (120 days) Item Class A Quantity Cycle Counting Policy 500 Each month B 1, 750 Each quarter C 2, 750 Every 6 months Number of Items Counted per Day 500/20 = 25/day 1, 750/60 = 29/day 2, 750/120 = 23/day 77/day

Control of Service Inventories þ Can be a critical component of profitability þ Losses may come from shrinkage or pilferage þ Applicable techniques include 1. Good personnel selection, training, and discipline 2. Tight control on incoming shipments 3. Effective control on all goods leaving facility

Independent Versus Dependent Demand þ Independent demand - the demand for item is independent of the demand for any other item in inventory þ Dependent demand - the demand for item is dependent upon the demand for some other item in the inventory

Holding, Ordering, and Setup Costs þ Holding costs - the costs of holding or “carrying” inventory over time þ Ordering costs - the costs of placing an order and receiving goods þ Setup costs - cost to prepare a machine or process for manufacturing an order

Holding Costs Category Housing costs (building rent or depreciation, operating costs, taxes, insurance) Material handling costs (equipment lease or depreciation, power, operating cost) Labor cost Cost (and range) as a Percent of Inventory Value 6% (3 - 10%) 3% (1 - 3. 5%) 3% (3 - 5%) Investment costs (borrowing costs, taxes, and insurance on inventory) Pilferage, space, and obsolescence 11% (6 - 24%) Overall carrying cost 26% 3% (2 - 5%)

Holding Costs Cost (and range) as a Percent of Inventory Value Category the n o g n i d n e p e Housing costs (building rent or 6% (3 - 10%) bly d a r e d i s n o c y r a v costs, taxes, rates. Generally s t s o c g depreciation, operating n i d l o H erest t n i ng d i n d a l , o n h o i e t v a a c insurance) h o l s , h item c e t business h g i h e m o 5%, s(equipment lease or 1 n a h Material handling costs 3% (1 - 3. 5%) t r e t a e r g. n 50% cost) a h t depreciation, power, operating r e t a e r g s t cos Labor cost 3% (3 - 5%) Investment costs (borrowing costs, taxes, and insurance on inventory) Pilferage, space, and obsolescence 11% (6 - 24%) Overall carrying cost 26% 3% (2 - 5%)

MANAGING INVENTORY IN THE FACE OF UNCERTAINTY The Newsvendor Problem

You are the Ga. Tech Barnes & Noble Merchandise Buyer It’s Sunday, March 28, 2004. The Jackets just made it to the Final Four. Before heading out to celebrate, you need to call your T-shirt supplier and order Final Four merchandise. #BB 12 - Final Four tee How many do you order? 100% cotton -shirt with Final Four logo $21. 98.

The Newsvendor Framework • One chance to decide on the stocking quantity for the product you’re selling • Demand for the product is uncertain • Known marginal profit for each unit sold and known marginal loss for the ones that are bought and not sold • Goal: Maximize expected profit

Examples where the Newsvendor framework is appropriate • Perishable goods – Meals in a cafeteria – Dairy foods • Short selling season – Christmas trees, toys – Flowers on Valentine’s day – Fashion clothes, seasonal clothes – Newspapers

The Newsvendor Problem • • • Newsvendor selling the AJC Sells the papers for $1. 00 Buys them for 70 cents Leftover papers sold at discount: 20 cents each. He will definitely have at least 35 customers, but no more than 40: – – – 35 customers with probability 0. 10 36 customers with probability 0. 15 37 customers with probability 0. 25 38 customers with probability 0. 25 39 customers with probability 0. 15 40 customers with probability 0. 1 How Many Papers Should He Buy To Maximize His Expected Profit?

Marginal analysis x Probability that demand = x <35 0. 1 36 0. 15 37 0. 25 38 0. 25 39 0. 15 40 0. 1 >40 0 P = Prob. of selling the xth unit (1 -P)=Prob. of NOT selling the xth unit P x $0. 3 =Expected profit from selling xth unit (1 -P) x $0. 5 =Expected loss from NOT selling xth unit Expected NET profit from stocking xth unit 1. 0 0 $0. 30 $0 $0. 30

Marginal analysis x Probability that demand = x P = Prob. of selling the xth unit (1 -P)=Prob. of NOT selling the xth unit P x $0. 3 =Expected profit from selling xth unit (1 -P) x $0. 5 =Expected loss from NOT selling xth unit Expected NET profit from stocking xth unit <35 0. 1 1. 0 0 $0. 30 $0 $0. 30 36 0. 15 0. 9 0. 1 $0. 27 $0. 05 $0. 22 37 0. 25 38 0. 25 39 0. 15 40 0. 1 >40 0

Marginal analysis x Probability that demand = x P = Prob. of selling the xth unit (1 -P)=Prob. of NOT selling the xth unit P x $0. 3 =Expected profit from selling xth unit (1 -P) x $0. 5 =Expected loss from NOT selling xth unit Expected NET profit from stocking xth unit <35 0. 1 1. 0 0 $0. 30 $0 $0. 30 36 0. 15 0. 9 0. 1 $0. 27 $0. 05 $0. 22 37 0. 25 0. 75 0. 25 $0. 225 $0. 10 38 0. 25 39 0. 15 40 0. 1 >40 0

Marginal analysis x Probability that demand = x P= Prob. of selling the xth unit (1 -P)=Prob. of NOT selling the xth unit P x $0. 3 =Expected profit from selling xth unit (1 -P) x $0. 5 =Expected loss from NOT selling xth unit Expected NET profit from stocking xth unit <35 0. 1 1. 0 0 $0. 30 $0 $0. 30 36 0. 15 0. 9 0. 1 $0. 27 $0. 05 $0. 22 37 0. 25 0. 75 0. 25 $0. 225 $0. 10 38 0. 25 0. 50 $0. 15 $0. 25 $-0. 10 39 0. 15 0. 25 0. 75 $0. 075 $0. 375 $-0. 30 40 0. 1 0. 9 $0. 03 $0. 45 $-0. 42 >40 0 0 1 $0. 0 $0. 50 $-0. 50

Marginal analysis x Probability that demand =x P= Prob. of selling the xth unit (1 -P)=Prob. of NOT selling the xth unit P x $0. 3 =Expected profit from selling xth unit (1 -P) x $0. 5 =Expected loss from NOT selling xth unit Expected NET profit from stocking xth unit <35 0. 1 1. 0 0 $0. 30 $0 $0. 30 36 X*=37 0. 15 0. 9 0. 1 $0. 27 $0. 05 $0. 22 37 0. 25 0. 75 0. 25 $0. 225 $0. 10 38 0. 25 0. 50 $0. 15 $0. 25 $-0. 10 39 0. 15 0. 25 0. 75 $0. 075 $0. 375 $-0. 30 40 0. 1 0. 9 $0. 03 $0. 45 $-0. 42 >40 0 0 1 $0. 0 $0. 50 $-0. 50 Decreasing marginal returns to each additional unit.

Solution Start from 35, buy an additional paper only if you expect to make extra profits. Let’s generalize! c: cost r: selling price s: salvage value MP: marginal profit from selling a stocked unit = r-c ML: marginal loss from NOT selling a stocked unit = c-s x: the number of newspapers you buy. P(x): the probability that the xth newspaper is sold = P(D ≥ x)

Solution Buy one more unit only if the expected net profit of doing so is positive. Buying x is profitable if P(x) MP - (1 -P(x)) ML ≥ 0 P(x) ≥ ML / (MP + ML) Critical ratio: Pc=ML / (MP + ML) Optimal solution: Buy largest x such that P(x) ≥ Pc

Solution In this problem: MP = $1 -$0. 70 = $0. 30 ML = $0. 70 -$0. 20 = $0. 50 Pc=ML / (MP+ML) = 50 / (50+30) = 0. 625 Buy largest x such that P(selling xth unit) ≥ Pc

Marginal analysis x Probability that demand =x P= Prob. of selling the xth unit (1 -P)=Prob. of NOT selling the xth unit P x $0. 3 =Expected profit from selling xth unit (1 -P) x $0. 5 =Expected loss from NOT selling xth unit Expected NET profit from stocking xth unit <35 0. 1 1. 0 0 $0. 30 $0 $0. 30 36 X*=37 0. 15 0. 9 0. 1 $0. 27 $0. 05 $0. 22 37 0. 25 0. 75 0. 25 $0. 225 $0. 10 38 0. 25 0. 50 $0. 15 $0. 25 $-0. 10 39 0. 15 0. 25 0. 75 $0. 075 $0. 375 $-0. 30 40 0. 1 0. 9 $0. 03 $0. 45 $-0. 42 >40 0 0 1 $0. 0 $0. 50 $-0. 50 Pc = 0. 625

Now Let’s Assume that Demand is Normally Distributed 0. 09 PROBABILITY DENSITY 0. 08 MP=0. 30 ML=0. 50 0. 07 0. 06 0. 05 0. 04 0. 03 0. 02 0. 01 =37. 5 =1. 44 0 DEMAND How do we find order quantity X*?

Remember solution: Buy largest x such that P(selling xth unit) ≥ Pc P(selling the xth unit) =P(Demand ≥ x) 0. 09 0. 08 PROBABILITY 0. 07 0. 06 0. 05 0. 04 P(Demand≥x) P(Demand<x) 0. 03 0. 02 0. 01 0 x DEMAND Solution with continuous distribution: Choose X* such that P (D≥ X*) = Pc

Solution: Choose X* such that P (D ≥ X*) = Pc Choose X* such that P (D < X*) = 1 -Pc 0. 09 0. 08 0. 07 PROBABILITY 0. 06 0. 05 0. 04 P(D≥ X*) 0. 03 0. 02 0. 01 0 DEMAND DECREASE X* INCREASE X* ØINCREASE COST OF LOST SALES ØDECREASE COST DUE TO UNSOLD ITEMS X* ØINCREASE COST DUE UNSOLD ITEMS

Newsvendor: Solution with Normal Distribution • Remember: MP = 0. 30; ML = 0. 50 • Then Pc is Pc=ML / (MP+ML)=50/(50+30)=0. 625 • Look at the z table to find the z corresponding to 1 -Pc = 0. 375 – In this case: z=-0. 32 • X*= + z = 37. 5 + (-0. 32) 1. 44 = 37. 04

What Do We Learn from the Newsvendor? • Forecasts are always wrong. A demand estimate that only gives the mean is too simple, you also need the standard deviation. • The optimal order quantity depends on the relative cost of stocking too much and stocking too little. • The smaller the standard deviation, the closer will be the order to the mean.

End of Lecture 22