Managing Business Process Flows: Ch 7 Supply Chain Management Managing the Supply Chain Economies of Scale (Chapter 6) Managing Flow Variability:

Managing Business Process Flows: Ch 7

Supply Chain Management Managing the Supply Chain Economies of Scale (Chapter 6) Managing Flow Variability: Safety Inventory (Chapter 7)

– Characteristics of Forecasts– Continuous Review System (Reorder Point Policy)– Inventory Pooling– Accurate Response (Newsvendor model)– Postponement / Delayed Differentiation

1Copyright © 2013 Pearson Education Inc. publishing as Prentice Hall

Demand-Supply Mismatch

Apples’s iPhone broke sales record when it sold 1.7 million units on release day. Yet people were lining up to buy the gadget a week later. It is estimated that Apple could have sold upto 2-2.5 million if could produce more units.

• Financial Times, January 2011 During 2007, Ninentdo’s game system Wii was hard to get due to supply shortages.

Analysts estimate that the company was leaving close to $1.3 billion on the table in unmet demand.

• techspot.com, December 17, 2007 Mumbai’s real estate is said to be hot property. However, in the last quarter, sales

have dipped so low that builders are getting worried ... At the current pace of consumption, it will take two years and four months to exhaust this stock. This is alarming because, a healthy market is supposed to have only an eight month inventory pile-up.

• MumbaiMirror.com, February 8, 2011


Demand-Supply Mismatch

An inventory write-off widened fourth quarter losses at Bluefly, despite a substantial increase in revenues at the online fashion retailer. Fourth quarter revenues were up 10% to US$29.7m, but the inventory write-off knocked back gross profit by 7%, while the company's net loss for the quarter widened to $5.6m from $3.5m last year.

• Just-Style.com, March 27, 2008

In a December report released by the Canadian Pharmacists Association, nearly 90 per cent of pharmacists across the country said shortages have greatly increased in the past year. Antibiotics, anti-nausea and heart drugs are among the top medications that pharmacists say are in shortest supply... people who can’t get access to their primary drug of choice, may be forced to go without or take alternatives, which could lead to serious side effects ... left unabated, the situation could cause someone with depression to commit suicide or lead other patients to experience serious health problems because they couldn’t get the drugs they needed.

• The Globe and Mail, January 31, 2011


http://www.just-style.com/companies/bluefly_id106

Is it all in the forecast?


Demand uncertainty and forecasting

Year Demand Forecast Error 1986 270 1987 309 1988 274 1989 268 1990 268 1991 316


Demand uncertainty and forecasting

Forecasts depend on– historical data– “market intelligence”

Forecasts are usually (always?) wrong.

A good forecast has at least 2 numbers (includes a measure of forecast error, e.g., standard deviation).

Aggregate forecasts tend to be more accurate.

The longer the forecast horizon, the less accurate the forecast.


Palü Gear:Service levels & inventory management

In reality, a Palü Gear store’s demand fluctuates from week to week. In fact, weekly demand at each store had a standard deviation of about 30 jackets assume roughly normally distributed. Recall that average weekly demand was about 59 jackets; the order lead time is two weeks; fixed order costs are $2,200/order and it costs $50 to hold one jacket in inventory during one year.

Questions: 1. If the retailer uses the ordering policy discussed before, what will the

probability of running out of stock in a given cycle be?

2. The Palü retailer would like the stock-out probability to be smaller. How can she accomplish this?

3. Specifically, how does it get the service level up to 95%?


Example: say we increase ROP to 140 (and keep order size at Q = 520)

1. On average, what is the stock level when the replenishment arrives?

2. On average, what is the inventory profile?

3. What is the probability that we run out of stock?

4. How do we get that stock-out probability down to 5%?

0

100

200

300

400

500


Safety Stocks & Service Levels: The relationship

Raise ROP until we reach appropriate SL

To do numbers, we need: Mean and stdev of demand during lead time Use Excel such that CSL = normsdist(z) or z = normsinv(CSL)

mean ROP

F(z)

demand during supply lead time

Stock-out probability

Cycle Service Level (CSL)

Is = z

0 z


Applications: – Demand over the leadtime L has standard deviation = RL – Pooled demand over N regions or products has standard deviation = RN

R R R…

Sum of N independent random variables, each with identical standard deviation Rhas

standard deviation =

Safety stock: How find of lead time demand?A Fundamental Statistics Result: The Portfolio Effect


Palü Gear: Determining the required Safety Stock for 95% service

DATA:

R = 59 jackets/ week R = 30 jackets/ week

H = $50 / jacket, year

S = $ 2,200 / order L = 2 weeks

QUESTION: What should safety stock be to insure a desired cycle service level of 95%?

ANSWER:

1. Required # of standard deviations z* for SL of 95% = 1.65

2. Determine lead time demand = RL = 30 2 = 42

3. Answer: Safety stock Is = z* lead time demand = 1.65 42 = 70


Comprehensive Financial Evaluation:Inventory Costs of Palü Gear

1. Cycle Stock (Economies of Scale)

1.1 Optimal order quantity = 520

1.2 # of orders/year = 5.9

1.3 Annual ordering cost per store = $13,009

1.4 Annual cycle stock holding cost. = $13,009

2. Safety Stock (Uncertainty hedge)

2.1 Safety stock per store = 70

2.2 Annual safety stock holding cost = $3,500.

3. Total Costs for 5 stores = 5 (13,009 + 13,009 + 3,500)

= 5 x $29,500 = $147.5K.


Learning Objectives safety stocks

Safety stock is a hedge against uncertainty

Which factors drive safety stock ? – level of service z

Impact of increased service level on required safety stock– demand variability or forecast error R,– delivery lead time L for the same level of service,– delivery lead time variability for the same level of service.

Applications:– How measure safety stock in practice?– What is the value of a better information system?

LzI Rs *


The standard normal distribution F(z)

z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.090.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.53590.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.57530.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.61410.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.65170.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.68790.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.72240.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.75490.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.78520.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.81330.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.83891.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.86211.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.88301.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.90151.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.91771.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.93191.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.94411.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.95451.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.96331.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.97061.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.97672.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.98172.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.98572.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.98902.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.99162.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.99362.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.99522.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.99642.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.99742.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.99812.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.99863.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.99903.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.99933.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.99953.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997

F(z)

z0

• Transform X = N() to z = N(0,1)

z = (X - ) / .

F(z) = Prob( N(0,1) < z)

• Transform back, knowing z*:

X* = + z*.


Improving Supply Chain Performance:1. The Effect of Pooling/Centralization

System A (Decentralized) System B (Centralized)

Which of the two systems provides a higher level of service for a given levelof safety stock?


Palü Gear’s Internet restructuring:Centralized inventory management

Weekly demand per store = 59 jackets/ week with standard deviation = 30 / week

Holding cost: H = $ 50 / jacket, yearFixed order cost: S = $ 2,200 / orderSupply lead time: L = 2 weeksDesired cycle service level F(z*) = 95%.

Palü Gear now is considering restructuring to an Internet store.

Avg. lead-time demand =

Stdev. lead-time demand =

Thus, safety stock =


Palü Gear’s Internet restructuring: comprehensive financial inventory evaluation

1. Cycle Stock (Economies of Scale)1.1 Optimal order quantity = x 520 = 11631.2 # of orders/year = 5 x 5.9 = 13

1.3 Annual ordering cost of e-store = $29,0891.4 Annual cycle stock holding cost= $29,089

2. Safety Stock (Uncertainty hedge)2.1 Safety stock for e-store = 156

2.2 Annual safety stock holding cost = $7,800.

3. Total Costs for consolidated e-store = 29,089 + 29,089 + 7,800

= $65,980 = 147.5/ 5


Concept of Centralization

Physical Centralization Information Centralization Specialization Commonality Postponement


Learning Objectives:Centralization/pooling

Centralization reduces safety stocks (pooling) and cycle stocks (economies of scale) Can offer better service for the same inventory investment or same service with

smaller inventory investment.

Different methods to achieve pooling efficiencies:– Physical centralization,Information centralization, Specialization,

Commonality, Postponement/late customization. Cost savings are proportional to square root of # of locations pooled.


Periodic Review Policy


Review inventory periodically– Why?

Place orders to bring inventory position up to a target level, called Order Upto Level (OUL).

Contrast with Continuous Review Policy, where– Review inventory continuously– Order fixed quantity (Q) whenever inventory position drops to a certain level

(ROP)

Periodic Review Policy Structure


Periodic Review Policy: Safety Inventory (zero leadtime)

6 111

Order Qty. = 130

Order Upto Level = 200 (say)

Inv. On hand = 70

Review Period T= 5 (say)Lead time L = 0 (say)

205 unitsRecd.

Review Period T=5 Review Period T=5

Review Inv.;Place Order

Order Qty = 150 units

Inv. On Hand = 50

8

Q: What is my exposure toStock-out?


Periodic Review Policy: safety inventory (positive leadtime)

6 111

Order Qty. = 205

Order Upto Level = 305

Inv. On hand = 100

Review Period T= 5 (say)Lead time L = 2 (say)

3

205 unitsRecd.

Lead Time L=2

Review Period T=5

Review Inv;Place Order


OrderRecd.

Lead Time L=2

Review Period T=5


OrderRecd.

Order Qty = 185 units

Inv. On Hand = 120

8

Q: What is my exposure toStock-out?


Periodic Review Policy

Safety stock is now a function of the review period (Tr) and replenishment leadtime (L)

Demand during review period plus lead time– Mean

– SD:

Then, safety stock =

OUL =

RLTD r RT L

( )rT L R

RLTDz

( )rR T L SS


Palü Gear: Determining the required Safety Stock for 95% service under continuous review policy

DATA:

D = 59 jackets/ week D = 30 jackets/ week

Q = 4x59 = 236 (4 weeks) L = 2 weeks

QUESTION: What should safety stock and ROP be to insure a desired cycle service level of 95% under continuous review with Q = 4x59 = 236

ANSWER:

1. Required # of standard deviations z* for SL of 95% = normsinv(.95) = 1.65

2. Determine L = DL = 30 = 42

3. Answer: Safety stock Is = z* L = 1.65 42 = 70

4. Reorder Point ROP = D[L] + Is = 59x2 + 70 = 188

5. Average cycle time = Q/D = 4 weeks


Palü Gear: Determining the required Safety Stock for 95% service under periodic review policy

DATA:

D = 59 jackets/ week D = 30 jackets/ week

T = 4 weeks L = 2 weeks

QUESTION: What should safety stock and order-up-to level be to insure a desired cycle service level of 95%? What is corresponding cycle stock?

ANSWER:

1. Required # of standard deviations z* for SL of 95% = normsinv(.95) = 1.65

2. Determine L+T = DL+T) = 30 6 = 73.5

3. Answer: Safety stock Is = z* L+T = 1.65 73.5 = 121

4. Order-up-to Level OUL = D[L+T] + Is = 59x6 + 121 = 476

5. Average order Q = DT = 59x4 = 236 Ic = Q/2 = 118

Notice the significant increase in safety stock due to periodicreview; increase from 70 to 121 units


Key learning

Periodic review increases inventory Key lever: try and decrease the review period length


Optimal Service Level:The newsvendor problem


Palü Gear’s is planning to offer a special line of winter jackets, especially designed as gifts for the Christmas season. Each Christmas-jacket costs the company $250 and sells for $450. Any stock left over after Christmas would be disposed of at a deep discount of $195. Marketing had forecasted a demand of 2000 Christmas-jackets with a forecast error (standard deviation) of 500

How many jackets should Palü Gear’s order?

Optimal Service Level and Accurate Response to Demand Uncertainty when you can order only once: Palü Gear

0.5%0.9%

2.2%

4.5%

7.8%

11.6%

14.6%

15.9%

14.6%

11.6%

7.8%

4.5%

2.2%

0.9%0.5%

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200 3400

Demand forecast for Christmas jackets


What would you do if there was no demand uncertainty?That is, you know that D = 2000 for sure


What happens if I order one more unit (on top of Q = 2000)?

Sell the extra unit withprobability …

= …..

Do not sell the extra unit with probability …

= …..

Expected profit from additional unit E() = So? ... Order more?

Towards the newsvendor model Suppose you placed an order of 2000 units but you are not sure if you should order more.


0 CapacityLevel

Demand

Demand matchesSupply

ShortageSurplus

Accurate Response to Risk: balancing surplus and shortage risks


• In general: raise service level (i.e., order an additional unit) if and only if

E() = (1-SL)MB – SLMC > 0 Sell Do not sell

Thus, optimal service level SL* (= Newsvendor formula)

• Example: use formula for Palu-Gear Christmas order

1. SL* = 2. So how much should Palu order then?

How does this compare to forecasted demand of 2000?

The Value-maximizing Service Level The newsvendor formula

Demand Prob. Cum. Prob.800 1% 1%

1,000 1% 2%1,200 3% 5%1,400 6% 12%1,600 10% 21%1,800 13% 34%2,000 16% 50%2,200 16% 66%2,400 13% 79%2,600 10% 88%2,800 6% 95%3,000 3% 98%3,200 1% 99%

21

1

pp

cp

MCMB

MB


Accurate response

Marginal benefit of stocking an additional unit = MB (e.g., retail price - purchase price)

Marginal cost of stocking an additional unit = MC (e.g., purchase price - salvage price)

Given an order quantity Q, increase it by one unit if and only if the expected benefit of being able to sell it exceeds the expected cost of having that unit left over.

At optimal Q,

Prob(Demand )MB

QMB MC


Learning Objectives

Service level is an economic tradeoff between cost of under and over stocking

Good model for Accurate Response for “fashion” goods


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recording, or otherwise, without the prior written permission of the publisher. Printed in the United States of America.

Copyright © 2013 Pearson Education Inc. publishing as Prentice Hall

Documents

Managing Business Process Flows: Ch 7 Supply Chain Management Managing the Supply Chain Economies of Scale (Chapter 6) Managing Flow Variability: