s. chopra/operations/supply chain mgt1 operations management: supply chain management module u...

S. Chopra/Operations/Supply Chain Mgt 1

Operations Management:

Supply Chain Management Module Managing the Supply Chain

» Key to matching demand with supply

» Cost and Benefits of inventory

Economies of Scale» Factors affecting optimal batch size: EOQ

» Levers for improvement

Safety Stock» Factors affecting level of safety stock: ROP

» Levers for reducing safety stock

Improving Performance» Centralization & Pooling efficiencies

» Postponement

» Accurate Response


Corporate Finance

Inventories represent about 34% of current assets for a typical US company; 90% of working capital.

For each dollar of GNP in the trade and manufacturing sector, about 40% worth of inventory was held.

Average logistics cost = 21c/sales dollar = 10.5% of GDP

Cisco SolectronCurrent Assets 7/30/95 8/25/95Cash & Equivalents 204,846 21% 89,959 12%Short-term Investments 234,681 58,643 AR 384,242 254,898 Inventories 71,160 7% 298,809 41%Deferred income taxes 75,297other 25,743 24,049 Total current assets 995,969 100% 726,358 100%

Investments 576,958PPE 136,653 203,609 other 47747 10,888 Total assets 1,757,327 940,855


The Supply Chain

The Procurementor supply system

The OperatingSystem The Distribution System

Raw Materialsupply points

Movement/Transport

Raw MaterialStorage Movement/

TransportMovement/Transport

STORAGE

STORAGE

STORAGE

PLANT 1

PLANT 2

PLANT 3

WAREHOUSE

WAREHOUSE

WAREHOUSE

Movement/Transport

MARKETS

Manufacturing

Finished GoodsStorage

A

B

C


Key Financial Indicators of Supply Chain Performance

Return on Assets Net Present Value … …

These are LAGGING indicators. What must the supply chain do to achieve this?


Costs of not Matching Supply and Demand

Cost of overstocking – liquidation, obsolescence, holding

Cost of under-stocking – lost sales and resulting lost margin


Accurately Matching Demand with Supply is the Key Challenge: Inventories

... by 1990 Wal-Mart was already winning an important technological war that other discounters did not seem to know was on. “Wal-Mart has the most advanced inventory technology in the business and they have invested billions in it”. (NYT, Nov. 95).

WSJ, Aug. 93: Dell Computer stock plunges. The company was sharply off in forecast of demand resulting in inventory writedowns.

BW 1997:


A Key to Matching Supply and Demand

When would you rather place your bet?

A B C D

A: A month before start of DerbyB: The Monday before start of DerbyC: The morning of start of DerbyD: The winner is an inch from the finish line


Where is the Flow Time?

Buffer Operation

Waiting Processing


Why do Buffers Build?Why hold Inventory?

Economies of scale– Fixed costs associated with batches

– Quantity discounts

– Trade Promotions

Uncertainty– Information Uncertainty

– Supply/demand uncertainty

Seasonal Variability Strategic

– Prices, availability

Cycle/Batch stock

Safety stock

Seasonal stock

Strategic stock


Palü Gear: Retail Inventory Management & Economies of Scale

Annual jacket revenues at a Palü Gear retail store are roughly $1M. Palü jackets sell at an average retail price of $325, which represents a mark-up of 30% above what Palü Gear paid its manufacturer. Being a profit center, each store made its own inventory decisions and was supplied directly from the manufacturer by truck. A shipment up to a full truck load, which was over 3000 jackets, was charged a flat fee of $2,200. Stores typically ordered 1500 jackets at a time, twice a year. (Palü’s cost of capital is approximately 20%.)

What order size would you recommend for a Palü store in current supply network?

retailermanufacturer


Economies of Scale: Inventory Build-Up Diagram

R: Annual demand rate,

Q: Number of jackets per replenishment order

Number of orders per year = R/Q.

Average number of jackets in inventory = Q/2 .

Q

Time t

Inventory Profile:# of jackets in inventory over time.

R = Demand rate

Inventory


Costs Associated with Batches

Order costs (S)– Changeover of

production line

– Transportation

– Receiving

Holding costs (H = rC)– Physical holding cost

– Cost of capital

– Cost of obsolescence


Palü Gear: evaluation of current policy of ordering Q = 1500 units each time1. What is average inventory I?

I = Q/2 = Annual cost to hold one unit H = Annual cost to hold I = Holding cost × Inventory

2. How often do we order? Annual throughput R = # of orders per year = Throughput / Batch size Annual order cost = Order cost × # of orders

3. What is total cost? TC = Annual holding cost + Annual order cost =

4. What happens if order size changes?


Find most economical order quantity: Spreadsheet for a Palü Gear retailer

Number of units Number ofper order/batch Batches per Annual Annual Annual

Q Year: R/Q Setup Cost Holding Cost Total Cost50 62 135,385$ 1,250$ 136,635$ 100 31 67,692$ 2,500$ 70,192$ 150 21 45,128$ 3,750$ 48,878$ 200 15 33,846$ 5,000$ 38,846$ 250 12 27,077$ 6,250$ 33,327$ 300 10 22,564$ 7,500$ 30,064$ 350 9 19,341$ 8,750$ 28,091$ 400 8 16,923$ 10,000$ 26,923$ 450 7 15,043$ 11,250$ 26,293$ 500 6 13,538$ 12,500$ 26,038$ 510 6 13,273$ 12,750$ 26,023$ 520 6 13,018$ 13,000$ 26,018$ 530 6 12,772$ 13,250$ 26,022$ 540 6 12,536$ 13,500$ 26,036$ 550 6 12,308$ 13,750$ 26,058$ 600 5 11,282$ 15,000$ 26,282$ 650 5 10,414$ 16,250$ 26,664$ 700 4 9,670$ 17,500$ 27,170$ 750 4 9,026$ 18,750$ 27,776$ 800 4 8,462$ 20,000$ 28,462$ 850 4 7,964$ 21,250$ 29,214$ 900 3 7,521$ 22,500$ 30,021$

1000 3 6,769$ 25,000$ 31,769$

$-

$20,000

$40,000

$60,000

$80,000

$100,000

$120,000

$140,000

$160,000

0 100 200 300 400 500 600 700 800 900 1000

Order (batch) size Q

Setup Cost

Holding Cost

Total Cost


Economies of Scale: Economic Order Quantity EOQ

R : Demand per year,

S : Setup or Order Cost ($/setup; $/order),

H : Marginal annual holding cost ($/per unit per year),

Q : Order quantity.

C : Cost per unit ($/unit),

r+h: Holding cost % (%/yr),

H = (r+h) C.

H

SRQEOQ

2

Batch Size Q

Total annual costs

H Q/2: Annual holding cost

S R /Q:Annual setup cost

EOQ

SRH2


Optimal Economies of Scale: For a Palü Gear retailer

R = 3077 units/ year C = $ 250 / unit

r = 0.20/year S = $ 2,200 / order

Unit annual holding cost = H =

Optimal order quantity = Q =

Number of orders per year = R/Q =

Time between orders = Q/R =

Annual order cost = (R/Q)S = $13,008.87/yr

Average inventory I = Q/2 =

Annual holding cost = (Q/2)H =$13,008.87/yr

Average flow time T = I/R =


Learning Objectives: Batching & Economies of Scale

Average inventory for a batch size of Q is Q/2. Increasing batch size of production (or purchase) increases average

inventories (and thus cycle times). The optimal batch size trades off setup cost and holding cost. To reduce batch size, one has to reduce setup cost (time). Square-root relationship between Q and (R, S):

– If demand increases by a factor of 4, it is optimal to increase batch size by a factor of 2 and produce (order) twice as often.

– To reduce batch size by a factor of 2, setup cost has to be reduced by a factor of 4.


Role of Leadtime L: Palü Gear cont.

The lead time from when a Palü Gear retailer places an order to when the order is received is two weeks. If demand is stable as before, when should the retailer place an order?

I-Diagram:

The two key decisions in inventory management are:– How much to order?– When to order?


Demand uncertainty and forecasting

Forecasts are usually (always?) wrong.

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

The forecast horizon must at least be as large as the lead time. The longer the forecast horizon, the less accurate the forecast.

Aggregate forecasts tend to be more accurate.

J.A. Van Mieghem/Operations/Supply Chain Mgt 20

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

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


Safety Stocks

Q

Time t

ROP

L

R

L

order order order

mean demand during supply lead time:

= R L

safety stock Is

Inventory on hand

I(t)

Q

Is

0

L


1. How to find service level (given ROP)?2. How to find re-order point (given SL)?

L = Supply lead time, D =N(RR) = Demand per unit time is normally distributed

with mean R and standard deviation R ,

DL =N() = Demand during the lead time

where = RL and RL

1. Given ROP, find SL = Cycle service level = P(no stock out)

= P(demand during lead time < ROP)

= F(z*= (ROP- )/) [use table]

= NORMDIST(ROP, , , True) [or Excel]

2. Given SL, find ROP = + Is

= + z* [use table to get z* ]

= + NORMSINV(SL)* [or Excel]

Safety stock Is = z* Reorder point ROP = + Is


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 0.09

0.0 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*.


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

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. Determine lead time demand =

2. Required # of standard deviations z* =

3. Answer: Safety stock Is =


Comprehensive Financial Evaluation:Inventory Costs of Palü Gear

1. Cycle Stock (Economies of Scale)

1.1 Optimal order quantity =

1.2 # of orders/year =

1.3 Annual ordering cost per store = $13,009

1.4 Annual cycle stock holding cost. = $13,0092. 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

Levers to decrease safety stock without hurting level of service:

Decrease demand variability or forecast error,

Decrease delivery lead time,

Decrease delivery lead time variability.

LzI Rs *


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

H = $ 50 / jacket, yearS = $ 2,200 / orderSupply lead time L = 2 weeksDesired cycle service level F(z*) = 95%.

Palü Gear now is considering restructuring to an Internet store.

= =


Palü Gear’s Internet restructuring: comprehensive financial inventory evaluation

1. Cycle Stock (Economies of Scale)1.1 Optimal order quantity =1.2 # of orders/year =

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 =

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

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

= $65,980.


Improving Supply Chain Performance: 2. Postponement & Commonality (HP Laserjet)

Generic PowerProduction

Unique PowerProduction

Process I: UniquePower Supply

Europe

N. America

Europe

N. America

Transportation

Process II: UniversalPower Supply

Make-to-Stock Push-Pull Boundary Make-to-Order


Learning Objectives:Supply Chain Performance

Pooling of stock reduces the amount of inventory

– physical

– information

– specialization

– substitution

– commonality/postponement

Benetton: Tailored response (e.g., partial postponement) can be used to better match supply and demand

Single product

Multi product


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 order?

1%1%

3%

6%

10%

13%

16% 16%

13%

10%

6%

3%

1%1%

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

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

Demand forecast for Christmas jackets

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


In reality, you do not know demand for sure…Impact of uncertainty if you order the expected Q = 2000

Stock: 2000

DemandProbability of Demand

units sold

units overstock

units understock Profit

800 1% 800 1200 0 940001000 1% 1000 1000 0 1450001200 3% 1200 800 0 1960001400 6% 1400 600 0 2470001600 10% 1600 400 0 2980001800 13% 1800 200 0 3490002000 16% 2000 0 0 4000002200 16% 2000 0 200 4000002400 13% 2000 0 400 4000002600 10% 2000 0 600 4000002800 6% 2000 0 800 4000003000 3% 2000 0 1000 4000003200 1% 2000 0 1200 400000

Expected: 1825.6 141.6 240.0 357331


What happens if you change your order level to hedge against uncertainty? Performance for all possible Q using Excel

200

-55

= F(Q)

Order Probability Cumulative Expected Expected Expected Expected

size Q Demand = Q P (Demand < Q ) units sold units overstock units understock Profit

1000 2% 2% 983.6 0.0 1082.0 196,721$ 1001 984.6 0.0 1081.0 196,914$ 1200 3% 5% 1177.4 2.9 888.2 235,323$ 1400 6% 12% 1364.8 12.2 700.8 272,291$ 1600 10% 21% 1540.2 33.6 525.4 306,184$ 1800 13% 34% 1696.2 74.3 369.4 335,142$ 2000 16% 50% 1825.6 141.6 240.0 357,331$ 2200 16% 66% 1924.0 240.0 141.6 371,593$ 2400 13% 79% 1991.2 369.4 74.3 377,929$ 2600 10% 88% 2032.0 525.4 33.6 377,496$ 2800 6% 95% 2053.3 700.8 12.2 372,126$ 2999 2062.6 887.2 3.0 363,726$ 3000 3% 98% 2062.7 888.2 2.9 363,683$


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


Accurate response:Find optimal Q from newsboy model

Cost of overstocking by one unit = Co

– the out-of-pocket cost per unit stocked but not demanded

– “Say demand is one unit below my stock level. How much did the one unit overstocking cost me?” E.g.: purchase price - salvage price.

Cost of understocking by one unit = Cu

– The opportunity cost per unit demanded in excess of the stock level provided

– “Say demand is one unit above my stock level. How much could I have saved (or gained) if I had stocked one unit more?” E.g.: retail price - purchase 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.

Marginal Analysis: Order more as long as F(Q) < Cu / (Co + Cu)

= smallest Q such that service level F(Q) > critical fractile Cu / (Co + Cu)


Where else do you find newsboys?

Deciding on economic service level Benefits: Flexible Spending Account decision ATM

Capacity Mgt


Goal of a Supply ChainMatch Demand with Supply

It is hard … Why?

Hard to Anticipate DemandForecasts are wrong… why?

There is lead time… why there is lead time?

Lead time (flow time) = Activity time+ Waiting Time

Because there is waiting time..Why there is waiting time? There is inventory in the SC

(Little’s Law)

Why there is Inventory?

Economies of ScaleThere are fixed costs

of ordering/production

Q*=

UncertaintyForecast Error

Safety Stock Is= zR

Seasonality

H

SR2

Implications:

How fast cycle inventory grows if demand grows.

How much to invest in fixed cost reduction to reduce batch size.

L

Implications:

Is z (service level appropriate)

Reduce Lead time

Reduce R


Implications:

Is z (service level appropriate)

Reduce Lead time

Reduce R

Where does R come from?

Customer Demand UncertaintyNormal Variations…

How do we deal with it?

Aggregation•Physical•Information•Specialization•Component Commonality•Postponement

Information Uncertainty

Balance overstocking and understockingNewsboy Problem … Critical Fractile = 1- P(stockout)

s. chopra/operations/supply chain mgt1 operations management: supply chain management module u...

Documents

safety stock u

supply chain key

supply cost

matching supply

assets u net present

supply system

u average logistics

u cost of understocking