Supply Chain Management

Lecture 22

Outline

• Today– Finish Chapter 12

• Sections 1, 2, 3– Section 2 up to and including Example 12.2

• Thursday– Homework 5 due before class– Start with Chapter 14

• Sections 1, 2, 3, 4, 6, 7, 8, 9– Section 6 buyback and revenue sharing contracts only

• Next week– Guest speaker: Paul Dodge

• SVP Supply Chain, ProBuild

Guest Lecture

• Date– Tuesday April 13

• Speaker– Paul Dodge (Senior Vice President – Supply

Chain)

• Subject– Today’s Supply Chain

Semester Outline

• Tuesday April 6 Chap 12• Thursday April 8 Chap 14• Tuesday April 13 Paul Dodge guest lecture• Thursday April 15 Chap 14, 15• Tuesday April 20 Chap 15• Thursday April 22 Simulation Game briefing• Tuesday April 27 Review, buffer• Thursday April 29 Simulation Game

The Newsboy/Newsvendor Problem

The Newsboy/Newsvendor Problem• Order quantity (O) • Uncertain demand (D)

• Cost of overstocking (Co = c – s)– The loss incurred by a firm for each unsold unit at the end of the

selling season

• Cost of understocking (Cu = p – c)– The margin lost by a firm for each lost sale because there is no

inventory on hand• Includes the margin lost from current as well as future sales

if the customer does not return

O’Neill PsychoFreak 3347

• The “too much/too little problem”– Order too much and inventory is left

over at the end of the season– Order too little and sales are lost

Nov Dec Jan Feb Mar Apr May Jun Jul Aug

Submit order to Manufacturer

Receive order from Manufacturer

Discount leftovers

Selling seaon

O’Neill PsychoFreak 3347

• Gather economic data– Selling price (p = $180)– Procurement cost (c = $110)– Discount price (s = $90)

• Forecast demand– Empirical demand distribution– Normal demand distribution

• Order quantity (so as to maximize profits)

Example: Parkas at L.L. Bean

Demand ProbD_i p_i

400 0.01500 0.02600 0.04700 0.08800 0.09900 0.11

1000 0.161100 0.201200 0.111300 0.101400 0.041500 0.021600 0.011700 0.01

Expected demand = ∑Dipi = 1,026 parkas

What is the expected demand?

Example: Parkas at L.L. Bean

Expected overstock = ∑Overstockipi = 85 parkas

Expected understock = ∑Understockipi = 111 parkas

Demand ProbD_i p_i

400 0.01500 0.02600 0.04700 0.08800 0.09900 0.11

1000 0.161100 0.201200 0.111300 0.101400 0.041500 0.021600 0.011700 0.01

Over- Under-stock stock

600 0500 0400 0300 0200 0100 0

0 00 1000 2000 3000 4000 5000 6000 700

What is the expected overstock?

What is the expected understock?

Example: Parkas at L.L. Bean

Expected profit = ∑Profitipi = $49,900

Demand ProbD_i p_i

400 0.01500 0.02600 0.04700 0.08800 0.09900 0.11

1000 0.161100 0.201200 0.111300 0.101400 0.041500 0.021600 0.011700 0.01

Sold Unsold Profitunits units

400 600 19000500 500 25000600 400 31000700 300 37000800 200 43000900 100 49000

1000 0 550001000 0 550001000 0 550001000 0 550001000 0 550001000 0 550001000 0 550001000 0 55000

Cost c = $45

Price p = $100

Salvage value s = $40

What is the expected profit?

Example: Parkas at L.L. Bean

Demand ProbD_i p_i

400 0.01500 0.02600 0.04700 0.08800 0.09900 0.11

1000 0.161100 0.201200 0.111300 0.101400 0.041500 0.021600 0.011700 0.01

CSL 1 - CSL

0.01 0.990.03 0.970.07 0.930.15 0.850.24 0.760.35 0.650.51 0.490.71 0.290.82 0.180.92 0.080.96 0.040.98 0.020.99 0.011.00 0.00

Expected Expected Expected Marg. benefit Marg. cost Marg. profit

1100 5500 x 0.49 = 2695 500 x 0.51 = 255 2440

Expected Expected Expected Marg. benefit Marg. cost Marg. profit

1100 5500 x 0.49 = 2695 500 x 0.51 = 255 24401200 5500 x 0.29 = 1595 500 x 0.71 = 355 1240

Expected Expected Expected Marg. benefit Marg. cost Marg. profit

1100 5500 x 0.49 = 2695 500 x 0.51 = 255 24401200 5500 x 0.29 = 1595 500 x 0.71 = 355 12401300 5500 x 0.18 = 990 500 x 0.82 = 410 5801400 5500 x 0.08 = 440 500 x 0.92 = 460 -201500 5500 x 0.04 = 220 500 x 0.96 = 480 -2601600 5500 x 0.02 = 110 500 x 0.98 = 490 -3801700 5500 x 0.01 = 55 500 x 0.99 = 495 -440

What is the optimal order quantity?

(1 – CSL)(p – c) CSL(c – s)

Cost of overstocking c – s = $5

Cost of understockingp – c = $55

Example: Parkas at L.L. Bean

Demand ProbD_i p_i

400 0.01500 0.02600 0.04700 0.08800 0.09900 0.11

1000 0.161100 0.201200 0.111300 0.101400 0.041500 0.021600 0.011700 0.01

CSL 1 - CSL

0.01 0.990.03 0.970.07 0.930.15 0.850.24 0.760.35 0.650.51 0.490.71 0.290.82 0.180.92 0.080.96 0.040.98 0.020.99 0.011.00 0.00

Expected Expected Expected Marg. benefit Marg. cost Marg. profit

1100 5500 x 0.49 = 2695 500 x 0.51 = 255 24401200 5500 x 0.29 = 1595 500 x 0.71 = 355 12401300 5500 x 0.18 = 990 500 x 0.82 = 410 5801400 5500 x 0.08 = 440 500 x 0.92 = 460 -201500 5500 x 0.04 = 220 500 x 0.96 = 480 -2601600 5500 x 0.02 = 110 500 x 0.98 = 490 -3801700 5500 x 0.01 = 55 500 x 0.99 = 495 -440

What is the safety stock?

(1 – CSL)(p – c) CSL(c – s)

Safety stock = Order quantity – Expected Demand

Optimal Level of Product Availability• Expected marginal contribution of raising the

order size from O* to O*+1(1 – CSL*)(p – c) – CSL*(c – s)

CSL* = Prob(Demand O*) = =p – c

p – s

O* = F-1(CSL*, , ) = NORMINV(CSL*, , )

Cu

Cu + Co

Example 12-1: Evaluating the optimal service level for seasonal items• The manager at Sportmart, a sporting goods store, has

to decide on the number of skis to purchase for the winter season. Based on past demand data and weather forecasts for the year, management has forecast demand to be normally distributed, with a mean 350 and a standard deviation of 100. Each pair of skis costs $100 and retails for $250. Any unsold skis at the end of the season are disposed of for $85. Assume that it costs $5 to hold a pair of skis in inventory for the season. How many skis should the manager order to maximize expected profits?

Example 12-1: Evaluating the optimal service level for seasonal itemsAverage demand (mean) =Standard deviation of demand (stdev)

=

Material cost c =Price p =Salvage value s =Cost of understocking Cu =

Cost of overstocking Co =

Optimal cycle service level CSL* =

Optimal order size O* =

350

100

$100

$250

85 – 5 = $80

p – c = 250 – 100 = $150

c – s = 100 – 80 = $20

Cu/(Cu + Co) = 150/170 = 0.88NORMINV(CSL*, , ) = 468

When Demand is Normally Distributed

• Expected profits =(p – s)Fs((O – )/) – (p – s)fs((O – )/) – O(c – s)F(O, , ) + O(p – c)[1 – F(O, , )]

Expected overstock = (O – )Fs((O – )/) + fs((O – )/)

• Expected understock = ( – O)[1 – Fs((O – )/)] + fs((O – )/)

Example 12-1: Evaluating the optimal service level for seasonal items• Expected profits =

(p – s)Fs((O – )/) – (p – s)fs((O – )/) – O(c – s)F(O, , ) + O(p – c)(1 – F(O, , ))

59,500*NORMDIST(1.18,0,1,1) – 17,000*NORMDIST(1.18,0,1,0) – 9,360*NORMDIST(468,350,100,1) + 70,200(1 – NORMDIST(468,350,100, 1))= $49,146

• Expected overstock = (O – )Fs((O – )/) + fs((O – )/) =

(450 – 350)*NORMDIST((450 – 350)/100,0,1,1) + 100*NORMDIST((450 – 350)/100,0,1,0) = 108

• Expected understock =( – O)[1 – Fs((O – )/)] + fs((O – )/) =

(350 – 450)*[1 – NORMDIST(((450 – 350)/100,0,1,1)]+ 100*NORMDIST((450 – 350)/100,0,1,0) = 8

Factors Affecting the Optimal Level of Product Availability

Consider two products with the same margin. Any leftover units of one product are worthless. Leftover

units of the other product can be sold to outlet stores. Which product should have a higher level of product

availability?

Intermezzo

1

0

CSL*

Co/Cu

Higher salvage value leads to

lower Co

Factors Affecting the Optimal Level of Product Availability

Consider two products with the same cost but different margins. Which product should have a

higher level of product availability?

Consider two products with the same margin. Any leftover units of one product are worthless. Leftover

units of the other product can be sold to outlet stores. Which product should have a higher level of product

availability?

Intermezzo

1

0

CSL*

Co/Cu

Nordstrom

Discount store

Maximizing Expected Profits

• Cost of over- and understocking have a direct impact on both the optimal cycle service level and profitability

How could one improve profitability?

Improving Supply Chain Profitability• Two obvious ways to improve profitability

1. Increase salvage value of each unit• Sport Obermeyer sells winter clothing in south America

during the summer.• Buyback contracts with manufacturer

2. Decrease the margin lost from a stock out• Arrange for backup sourcing or provide substitute product• Car part suppliers, McMaster-Carr and W.W.Grainger, are

competitors but they buy from each other to satisfy the customer demand during a stockout

Improving Supply Chain Profitability• Another way to improve profitability

3. Reduce demand uncertainty– Improved forecasting: Use better market intelligence

and collaboration to reduce demand uncertainty– Quick response: Reduce replenishment lead time so that

multiple orders may be placed in a selling season– Postponement: In a multiproduct setting, postpone

product differentiation until closer to point of sale– Tailored sourcing: Use a low lead time, but perhaps an

expansive supplier as a backup for a low-cost, but perhaps long lead time supplier

Example: Impact of Improved Forecasting• Demand is Normally distributed with a mean of

= 350 and standard deviation of = 150• Purchase price c = $100• Retail price p = $250• Salvage value s = $80

How many units should be ordered as changes?

Example: Impact of Improved Forecasting

Expected Expected Expected O* overstock understock profit150 526 186.7 8.6 $47,469

Expected Expected Expected O* overstock understock profit150 526 186.7 8.6 $47,469120 491 149.3 6.9 $48,476

Expected Expected Expected O* overstock understock profit150 526 186.7 8.6 $47,469120 491 149.3 6.9 $48,47690 456 112.0 5.2 $49,48260 420 74.7 3.5 $50,48830 385 37.3 1.7 $51,4940 350 0 0 $52,500

Increase in forecast accuracy increases a firm’s profits

Impact of Improved Forecasting• Better forecasts leads to reduced uncertainty

– Decreases both the overstocked and understocked quantity

– Increases a firm’s profits

Impact of Quick Response

• Quick response is a set of actions a supply chain takes to reduce replenishment lead time

Selling season~14 weeks

Lead time~30 weeks

Selling season~14 weeks

Lead time~14 weeks

Selling season~14 weeks

Lead time~4 weeks

Impact of Quick Response

• If quick response (reduction in replenishment lead time) allows multiple orders in the season – A buyer can usually improve forecast accuracy after

observing demand– Less overstock, less understock– Higher profits

Example: Impact of Quick Response• Mattel was hurt last year by inventory cutbacks at Toys

“R” Us, and officials are also eager to avoid a repeat of the 1998 Thanksgiving weekend. Mattel had expected to ship a lot of merchandise after the weekend, but retailers, wary of excess inventory, stopped ordering from Mattel. That led the company to report a $500 million sales shortfall in the last weeks of the year ... For the crucial holiday selling season this year, Mattel said it will require retailers to place their full orders before Thanksgiving. And, for the first time, the company will no longer take reorders in December, Ms. Barad said. This will enable Mattel to tailor production more closely to demand and avoid building inventory for orders that don't come.

Wall Street Journal, Feb. 18, 1999

Mattel Inc. & Toys “R” Us

• Decreasing replenishment lead times requires tremendous effort from the manufacturer, yet seems to benefit the retailer at the expense of the manufacturer

• Hence, the benefits resulting from quick response should be shared appropriately across the supply chain

Did Mattel’s action help or hurt profitability at Toys “R” Us?

Impact of Postponement

• Postponement is delaying product differentiation (customization) until closer to the time of the sale of the product– Delaying the commitment of the work-in-process inventory to a

particular product

• Examples– Dell delivers customized PC in a few days after customer order– HP printer places power supply modules, labels in appropriate

language on to printers after the demand is observed– Motorola cell phones are customized for different service

providers after demand is materialized– McDonalds assembles meal menus after customer order

Example: Impact of Postponement• Benetton sells knit sweaters in four colors at a retail price

p = $50– Option 1: (Long lead time) Dye the threat then knit the garment.

Results in manufacturing cost c = $20. – Option 2: (Short lead time). Knit the garment then dye the

garment. Results in manufacturing cost c = $22

• Benetton disposes any unsold sweaters at the end of the season in clearance for s = $10.

• For each color 20 weeks in advance demand forecast– Normally distributed with a mean of = 1000 and a standard

deviation of = 500

Example: Impact of Postponement

p = 50c = 20s = 10

CSL = (p – c)/(c – s)

O* = NORMINV(CSL*,,)

CSL = 0.75

O* = 1,337*4 = 5,348

p = 50c = 22s = 10

CSL = (p – c)/(c – s)

O* = NORMINV(CSL*,,)

CSL = 0.70

O* = 4,524

Expected profits$94,576

Expected profits$98,092

= 1000, = 500 = 4000, = 1000

Tailored Postponement

• By postponing all garment types, production cost of each product goes up– When this increase is substantial or a single product’s demand

dominates all other’s (causing limited uncertainty reduction via aggregation), a partial postponement scheme is preferable to full postponement.

• Tailored postponement allows a firm to increase profits by postponing differentiation only for products with the most uncertain demand; products with more predictable demand are produced at lower cost without postponement

Tailored (Dual) Sourcing

• Tailored sourcing is a business strategy where a firm uses a combination of two supply sources– The two sources must focus on different capabilities

Characteristic Efficient FlexibleManufacturing cost High LowFlexibilility (volume/mix) High LowResponsiveness High LowEngineering support High Low

Strategy Efficient FlexibleVolume based Predictable demand Unpredictable demandProduct based Predictable demand Unpredictable demandModel based Older products Newer product