Determining Optimal Level of Availability in a Supply Chain

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					Determining Optimal Level of Availability in a Supply Chain

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Outline
 Determining

optimal level of product

availability
– Single order in a season – Continuously stocked items

under capacity constraints  Levers to improve supply chain profitability  Contracts

 Ordering

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Mattel, Inc. & Toys “R” Us
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
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Key Questions
much should Toys R Us order given demand uncertainty?  How much should Mattel order?  Will Mattel’s action help or hurt profitability?  What actions can improve supply chain profitability?
 How

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How much to order? Parkas at L.L. Bean
Demand 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Probabability .01 .02 .04 .08 .09 .11 .16 .20 .11 .10 .04 .02 .01 .01 Cumulative Probability of demand being this size or less .01 .03 .07 .15 .24 .35 .51 .71 .82 .92 .96 .98 .99 1.00 Probability of demand greater than this size .99 .97 .93 .85 .76 .65 .49 .29 .18 .08 .04 .02 .01 .00

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Parkas at L.L. Bean
Cost per parka = $45 Sale price per parka = $100 Discount price per parka = $50 Holding and transportation cost = $10 from selling parka = $100-$45 = $55  Cost of overstocking = $45+$10-$50 = $5
 Profit

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Parkas at L.L. Bean
demand = 10 (‘00) parkas  Expected profit from ordering 10 (‘00) parkas = $499
 Expected

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Parkas at L.L. Bean
Additional Expected Expected Expected Marginal 100s Marginal Benefit Marginal Cost Contribution 11th 5500.49 = 2695 500.51 = 255 2695-255 = 2440 12th 13th 14th 15th 16th 17th 5500.29 = 1595 500.71 = 355 1595-355 = 1240 5500.18 = 990 5500.08 = 440 5500.04 = 220 5500.02 = 110 5500.01 = 55 500.82 = 410 990-410 = 580 500.92 = 460 440-460 = -20 500.96 = 480 220-480 = -260 500.98 = 490 110-490 = -380 500.99 = 495 55-495 = -440

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Optimal level of service
r = sale price; s = outlet or salvage price; c = purchase price CSL = Probability that demand will be at or below reorder point At optimal order size, Expected Marginal Benefit from raising order size = (1-CSL*)(r - c) = Expected Marginal Cost = CSL*(c - s). (1-CSL*)Cu = CSL* Co, CSL* = Cu / (Cu + Co)
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Order Quantity for a Single Order
Co = Cost of overstocking = $5 Cu = Profit from sale =Cost of understocking = $55 R* = Optimal order size

CSL  Pr ob( Demand  R*)  55 Cu   0.917 C u  C o 55  5

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Optimal Order Quantity
1.2
0.917

1 0.8 0.6 0.4 0.2 0
10 12 14 16 4 6 8

Probability

Optimal Order Quantity = 13
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How to Estimate Demand Distribution?
 Historical

data: Time series forecasting factors: Regression, causal

 Dependent

forecasting
 Expert

opinion: Buying committee

Key: Forecast must include estimated demand and uncertainty (standard deviation) of demand

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Continuously Stocked Items: Optimal Safety Inventory Levels
For each order cycle
– Benefit of increasing safety stock by one unit = (1-CSL)Cu – Cost of increasing safety stock by one unit = HQ*/R

where
– CSL = probability of not stocking out in a cycle with current level of safety stock = Cycle Service Level – H = cost of holding one unit for one year – R = Annual demand – Q* = Economic order quantity
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Optimal Safety Inventory Levels
CSL = 1-HQ*/CuR
R = 100 gallons/week; R= 20; H = $0.6/gal./year L = 2 weeks; Q = 400; ROP = 300.

What is the imputed cost of stocking out?

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Ordering Under Capacity Constraints
Autumn Leaves Ruffle Retail price $150 $200 $250 Purchase price $75 $90 $110 Salvage price $40 $50 $90 Mean Demand 1000 500 250 Standard deviation 250 175 125 of demand

Available Capacity = 1,500.
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Assuming No Capacity Constraints
Autumn Leaves Ruffle ri-ci $150$200$250$75=$75 $90=$1 $110=$1 10 40 ri-si $150$200 - $250-$90 $40=$110 $50 = = $160 $150 Critical 75/110 = 110/150 140/160= Fractile 0.68 = 0.73 0.875 zi 0.47 0.61 1.15 Q 1118 607 394
* i

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Ordering Under Capacity Constraints
0: Set Qi = 0 for all products i.  Step 1: Compute the marginal contribution for all products i.  Step 2: Increase Qj, for the product j with the largest marginal contribution, by 1.  Step 3: If all the capacity is not used up and there is some product with a positive marginal contribution, return to Step 1, else stop.
 Step

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Marginal Contribution Calculations
Order Quantity Capacity left Autumn Leaves Ruffle 1500 0 0 0 1490 0 0 10 1360 1350 1340 1330 1320 1310 890 880 870 290 280 1 0
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Marginal Contribution Autumn Leaves Ruffle 74.997 109.679 136.360 74.997 109.679 135.611 74.997 74.997 74.997 74.997 74.997 74.997 74.997 74.996 74.995 69.887 69.887 53.196 53.073 109.679 109.679 109.617 109.543 109.457 109.357 73.033 73.033 73.033 67.422 67.422 53.176 53.176 109.691 106.103 106.103 106.103 106.103 106.103 70.170 70.170 70.170 70.170 65.101 52.359 52.359
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0 0 0 0 0 0 0 10 20 580 580 788 789

0 0 10 20 30 40 380 380 380 400 400 446 446

140 150 150 150 150 150 230 230 230 230 240 265 265

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Ordering Under Capacity Constraints
N products for i = 1, ..., N, all produced using the same capacity  Total available capacity = B  ri = sale price; si = outlet or salvage price; ci = purchase price. All are for product i  Marginal contribution of raising order size of product i from Qi to Qi + 1 = (1-pi)(ri - ci) - pi(ri si) where pi is the probability that demand for product i will be Qi or less.
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 Assume

Levers for Increasing Supply Chain Profitability
salvage value or decrease margin lost from stockout  Improved forecasting to lower uncertainty  Quick response to increase number of orders per season  Postponement of product differentiation  Tailored sourcing
 Increase

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Impact of Improving Forecasts
Demand: Normally distributed with a mean of R = 350 and standard deviation of R = 100 Purchase price = $100 Retail price = $250 Disposal value = $85 Holding cost for season = $5

How many units should be ordered as R changes?
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Impact of Improving Forecasts O* Expected Expected Expected R
150 120 90 60 30 0
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526 491 456 420 385 350

Overstock Understock Profit 186.7 8.6 $47,469 149.3 112.0 74.7 37.3 0
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6.9 5.2 3.5 1.7 0

$48,476 $49,482 $50,488 $51,494 $52,500
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Quick Response: Multiple Orders per Season
 Ordering

shawls at a department store

– – – – –

Selling season = 14 weeks Cost per handbag = $40 Sale price = $150 Disposal price = $30 Holding cost = $2 per week

weekly demand = 20  SD of weekly demand = 15

 Expected

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Impact of Quick Response
Single Order Two Orders in Season
Average Ending Expect. Total Invent. Profit Order 349 69 $26,590 342 332 319 313 302 60 52 43 36 32 $27,085 $27,154 $26,944 $27,413 $26,916 Service Order Ending Expect. Initial OUL Level Size Invent. Profit Order for 2nd Order 0.96 378 97 $23,624 209 209 0.94 0.91 0.87 0.81 0.75 367 355 343 329 317 86 73 66 55 41 $24,034 201 $24,617 193 $24,386 184 $24,609 174 $25,205 166 201 193 184 174 166

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Forecast Improves for Second Order (SD=3 instead of 15)
Single Order Two Orders in Season
Average Ending Expect. Total Invent. Profit Order 292 19 $27,007 293 288 288 283 282 18 17 14 14 14 $27,371 $26,946 $27,583 $27,162 $27,268 Service Order Ending Expect. Initial OUL Level Size Invent. Profit Order for 2nd Order 0.96 378 96 $23,707 209 153 0.94 0.91 0.87 0.81 0.75 367 355 343 329 317 84 76 63 52 44 $24,303 201 $24,154 193 $24,807 184 $24,998 174 $24,887 166 152 150 148 146 145

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Value of Postponement: Benetton
 For  For

each color each garment

– Mean demand = 1,000; SD = 500
– – – – Sale price = $50 Salvage value = $10 Production cost using option 1 (long lead time) = $20 Production cost using option 1 (greige thread) = $22

 What

is the value of postponement?

– Expected profit increases from $94,576 to $98,092
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Value of Postponement with Dominant Product
 Color

with dominant demand: Mean = 3,100, SD

= 800  Other three colors: Mean = 300, SD = 200
 Expected

profit without postponement = $102,205  Expected profit with postponement = $99,872

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Tailored Postponement: Benetton
Q1 units for each color using Option 1 and QA units (aggregate) using Option 2  Results:
– Q1 = 800 – QA = 1,550 – Profit = $104,603
 Produce

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Tailored Sourcing
 Sourcing

alternatives

– Low cost, long lead time supplier
» Cost = $245, Lead time = 9 weeks

– High cost, short lead time supplier
» Cost = $250, Lead time = 1 week

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Tailored Sourcing Strategies
Fraction of demand from overseas supplier 0% 50% 60% 100% Annual Profit $37,250 $51,613 $53,027 $48,875

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Tailored Sourcing: Multiple Sourcing Sites
Characteristic Primary Site Secondary Site Low Low Low Low
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Manufacturing High Cost Flexibility High (Volume/Mix) Responsiveness High Engineering Support
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Dual Sourcing Strategies
Strategy Primary Site Secondary Site Stable demand Predictable, large batch products Older stable products
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Volume based Fluctuation dual sourcing Product based Unpredictable dual sourcing products, Small batch Model based Newer dual sourcing products
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Impact of Supply Chain Contracts on Profitability: Buyback Contracts
by publishers  Tech Fiber produces jacket at v = $10 and charges a wholesale price of c = $100. Ski Adventure sells jacket for p = $200. Unsold jackets have no salvage value. Should TF be willing to buy back unsold jackets? Why?
 Buybacks

Buyback
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Buyback Contracts
Wholesale Price c Buy Back Price b Optimal Order size for SA Expected Profit for SA Expected Returns to TF Expected Profit for TF Expected Supply Chain Profit

$100 $100 $100 $100 $110 $110 $120 $120

$0 $30 $60 $95 $78 $105 $96 $116

1,000 1,067 1,170 1,501 1,191 1,486 1,221 1,501

$76,063 $80,154 $85,724 $96,875 $78,074 $86,938 $70,508 $77,500

120 156 223 506 239 493 261 506

$90,000 $91,338 $91,886 $86,935 $100,480 $96,872 $109,225 $106,310

$166,063 $171,492 $177,610 $183,810 $178,555 $183,810 $179,733 $183,810

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Quantity Flexibility Contracts
a retailer order O units the manufacturer commits to supplying up to (1+)O and the retailer commits to buying (1-)O  How can quantity flexibility contracts help increase profitability?
 If

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Quantity Flexibility Contracts
 
Wholesale price c Order size O Expected purchase by SA Expected sale by SA Expected profits for SA Expected profits for TF Expected supply chain profit

0.00 0.20 0.40 0.00 0.15 0.42 0.00 0.2 0.5

0.00 0.20 0.40 0.00 0.15 0.42 0.00 0.2 0.5

$100 $100 $100 $110 $110 $110 $120 $120 $120

1,000 1,050 1,070 962 1,014 1,048 924 1,000 1,040

1,000 1,024 1,011 962 1,009 1,007 924 1,000 1,003

880 968 994 860 945 993 838 955 996

$76,063 $91,167 $97,689 $66,252 $78,153 $87,932 $56,819 $70,933 $78,874

$90,000 $89,830 $86,122 $96,200 $99,282 $95,879 $101,640 $108,000 $104,803

$166,063 $180,997 $183,811 $162,452 $177,435 $183,811 $158,459 $178,933 $183,677

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Learning Objectives
Optimal order quantities are obtained by trading off cost of lost sales and cost of excess stock  Levers for improving profitability


– – – – –


Increase salvage value and decrease cost of stockout Improved forecasting Quick response with multiple orders Postponement Tailored sourcing

Contracts: Buyback, quantity flexibility
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