product availability inventory scm chopra3 ppt ch12.complete

© Chopra / OPNS 455 / Optimal Availability 1

Chapter 12: Determining the Optimal Level of Product Availability

Part IV: Planning and Managing

Inventories in A Supply Chain


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


Key Questions

How 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?


Drivers of Supply Chain PerformanceEfficiency Responsiveness

Inventory

Facilities Transportation

Supply chain structure

•Seasonal Inventory•Cycle Inventory •Safety Inventory

•Level of Product Availability•Newsboy tradeoff for Seasonal items; continuously stocked

items; multiple products under capacity constraints•Levers to improve supply chain profits and decrease seasonal inventory


Estimating Optimal Level of Product Availability Buyers’ Estimate of Demand Distribution at L.L. Bean

Demand [100s]

Probabability Probability of demand being this much or less

Probability of demand being greater than this much

4 .01 .01 .99 5 .02 .03 .97 6 .04 .07 .93 7 .08 .15 .85 8 .09 .24 .76 9 .11 .35 .65

10 .16 .51 .49 11 .20 .71 .29 12 .11 .82 .18 13 .10 .92 .08 14 .04 .96 .04 15 .02 .98 .02 16 .01 .99 .01 17 .01 1.00 .00

Expected Demand = 1,026 Parkas


Estimating Optimal Level of Product Availability Cost of Over- and Understocking at L.L Bean

Cost per parka = c = $45

Sale price per parka = p = $100

Discount price per parka = $50

Holding and transportation cost = $10

Salvage value = s = $50-$10 = $40

Profit from selling parka = Cu = p-c = $100-$45 = $55

Cost of overstocking = Co = c-s = $45+$10-$50 = $5


Estimating Optimal Level of Product Availability Profit from Ordering the Expected Demand at L.L. Bean

Order Quantity = 1000 Parkas (Expected Demand = 1,026)

Probability Demand Sold Overstocked Understocked Profit0.01 400 400 600 0 $ 19,000 0.02 500 500 500 0 $ 25,000 0.04 600 600 400 0 $ 31,000 0.08 700 700 300 0 $ 37,000 0.09 800 800 200 0 $ 43,000 0.11 900 900 100 0 $ 49,000 0.16 1,000 1,000 0 0 $ 55,000 0.20 1,100 1,000 0 100 $ 55,000 0.11 1,200 1,000 0 200 $ 55,000 0.10 1,300 1,000 0 300 $ 55,000 0.04 1,400 1,000 0 400 $ 55,000 0.02 1,500 1,000 0 500 $ 55,000 0.01 1,600 1,000 0 600 $ 55,000 0.01 1,700 1,000 0 700 $ 55,000

Expected: 1,026 915 85 111 $ 49,900


If we order 1,000, the CSL=probability(demand ≤ 1,000) = 0.51

Expected marginal contribution of an additional 100 units =

0.49 x 100 x $55 - 0. 51 x 100 x $5 = $2,440

Additional 100 units sell with probability 1-CSL = 0.49. We earn margin Cu=p-c = $55 / unit.

Estimating Optimal Level of Product Availability Expected Marginal Contribution of Increasing Order Size by 100 units at L.L. Bean

Additional 100 units do not sell with probability CSL = 0.51.We lose Co= c-s = $5 per unit.


Estimating Optimal Level of Product Availability Expected Marginal Contributions as Availability is Increased

Additional100s

ExpectedMarginal Benefit

ExpectedMarginal Cost

Expected MarginalContribution

11th 5500.49 = 2695 500.51 = 255 2695-255 = 2440

12th 5500.29 = 1595 500.71 = 355 1595-355 = 1240

13th 5500.18 = 990 500.82 = 410 990-410 = 580

14th 5500.08 = 440 500.92 = 460 440-460 = -20

15th 5500.04 = 220 500.96 = 480 220-480 = -260

16th 5500.02 = 110 500.98 = 490 110-490 = -380

17th 5500.01 = 55 500.99 = 495 55-495 = -440

Optimal Order Quantity = 1,300 ParkasExpected Profit = $ 54,160Service level = 92%


Estimating Optimal Level of Product Availability Seasonal Items with a Single Order in a Season: Summary

p = sale prices = outlet or salvage pricec = purchase priceO* = optimal order sizeCSL* = optimal cycle service level = probability (demand ≤ O*)

At the optimal cycle service level CSL* and order size O*:Expected marginal profit from raising the order size by one unit to O*+ 1 ≤ 0Expected Marginal Revenue = probability the unit sells Cu = (1-CSL*) Cu

Expected Marginal Cost = probability the unit does not sell Co = CSL* Co

Therefore: (1-CSL*) Cu ≤ CSL* Co

Optimal Cycle Service Level: CSL* ≥ Cu / (Cu + Co ) = (p-c) / (p-s)

Cu = p-c

Co = c-s

Critical fractile


Product Availability for Continuous Distributions: Example

Motown studios is deciding on the number of copies of a CD to

have manufactured. The manufacturer currently charges $2 for

each CD. Motown sells each CD for $12 and currently places

only one order for the CD before its release. Unsold CDs must

be trashed. Demand for the CD has been forecast to be

normally distributed with a mean of 30,000 and a standard

deviation of 15,000.

How many CDs should Motown order?


Evaluating Expected Profits, Overstock, and Understock

Expected profits = (p-s) NORMDIST((O - )/, 0, 1, 1)

- (p-s) NORMDIST((O- )/, 0, 1, 0) – O(c-s) NORMDIST(O, , , 1)

+ O (p-c) [1 - NORMDIST(O, , , 1)] (12.3)

Expected overstock = (O - )NORMDIST((O - )/, 0, 1, 1)+ NORMDIST((O - )/, 0, 1, 0) (12.4)

Expected understock = ( - O)[1- NORMDIST((O - )/, 0, 1, 1)] + NORMDIST((O - )/, 0, 1, 0) (12.5)


Product Availability for Continuous Distributions Under Quantity Discounts

Motown studios is deciding on the number of copies of a CD to have manufactured. The manufacturer currently charges $2 for each CD. Motown sells each CD for $12 and currently places only one order for the CD before its release. Demand for the CD has been forecast to be normally distributed with a mean of 30,000 and a standard deviation of 15,000. How many CDs should Motown order?What is the expected profit?What is the expected overstock?What is the expected understock?

The manufacturer now offers a price of $1.95 for orders of at least 50,000 CDs and a price of $1.90 for orders of at least 60,000 CDs.

How should Motown respond?



Inventory





items


Given– 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

– D = Annual demand

– Q = Replenishment lot size

Basic tradeoff– Benefit from increasing safety inventory (additional sales if

demand is high) versus cost of increasing safety inventory (holding cost of one unit)

Estimating Optimal Level of Product Availability Continuously Stocked Items


Estimating Optimal Level of Product Availability Continuously Stocked Items

Benefit from increasing safety inventory by one unit = (1- CSL*) Cu

Cost of increasing safety inventory by one unit = HQ/D

Equating the two gives optimal level of product availability

CSL* = 1-HQ/(CuD)


Estimating Cost of Understocking for Continuously Stocked Items

Data

D = 100 gallons/week; D= 20; H = $0.6/gal./yearL = 2 weeks; Q = 400; ROP = 300.

What is the implied cost of stocking out?– Safety Inventory = ROP – D*L = 100– Standard deviation of lead time demand: 20*sqrt(2)=28.3– With given policy, CSL=NORMSDIST(100/28.3)=0.9998– Implied cost of stocking out:

Cu= HQ / (1-CSL) / D = 0.6*400/ 0.0002 / 5,200 = $230.8

Source: Example 12.3 in C & M



Inventory





items; multiple products under capacity constraints


Optimal Availability for Multiple Products Under Capacity Constraint

High End Mid Range Retail price pi $150 $100 Purchase price ci $50 $40 Salvage price si $35 $25 Mean Demand 1000 2000 Standard deviation of demand

300 400

Available Capacity = 3,000.


Optimal Availability Assuming No Capacity Constraint

High End Mid Range Cu = pi - ci $150-

$50=$100 $100-$40=$60

Co + Cu =pi - si $150-$35=$115

$100 – $25 =$75

Critical Fractile

100/115 = 0.87

60/75= 0.80

Optimal

Order *iO

1,337 2,337

Total Order Quantity = 3,674 > 3,000


Optimal Availability Under Capacity Constraint Optimal Ordering Policy

At optimality, expected marginal contribution of each item ordered is equal

Order qty, O 1089 1911Exp. Mar. Profit 29.10$ 29.10$ Expected Profit 89,416$ 105,736$ Total Expected Profit 195,152$

High End Mid Range


Optimal Availability Under Capacity Constraint Optimal Ordering Policy

Step 1: Set order quantity Qi = 0 for all products i.

Step 2: For all products i, compute/update the expected marginal contribution at the current order quantity

Step 3: For the product j with the largest positive expected marginal contribution, increase order quantity Qj by the minimum increment. This is equivalent to auctioning off capacity one unit at a time and assigning it to the highest bidder (the one with the largest expected marginal contribution)

Step 4: If there is still capacity available and there is some product with a positive expected marginal contribution, return to Step 2, else stop.



Inventory





items; multiple products under capacity constraints

•Levers to improve supply chain profits and decrease seasonal inventory


Levers to Improve SC profits and decrease Seasonal Inventory

Increase salvage value (over stock outlets) Decrease cost of under stocking (substitution) Improve forecasts Multiple orders in a season Postponement

What happens to profits, understock, and overstock in each case?


Supply Chain Flows Without Postponement

Supply Chain Flows With Component Commonality and Postponement

Levers to Improve SC profits and decrease Seasonal Inventory: Postponement of Product Differentiation


Value of Postponement: BenettonData Demands (uncorrelated)

– Each color: Mean = 1,000; SD = 500– Aggregate: Mean = 4,000, SD = 1000

For each garment– 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 effect of postponement?– Expected overstock and under stock reduced

What is the value of postponement?– Expected profit increases from $94,576 to $98,092


Value of Postponement: Benetton

How does the value of postponement change as the demand uncertainty increases/decreases?

Which components are better postponed – most or least expensive? Short or long lead times?

How does value change as number of colors postponed increases/decreases?

With a process that allows postponement do you want to sell more or fewer colors?


Value of Postponement with Dominant Product

Demand– Color with dominant demand: Mean = 3,100, SD = 800

– Other three colors: Mean = 300, SD = 200

– Aggregate: Mean = 4,000, SD = 872

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

Why is postponement not valuable with a dominant product?

How should we react?

CV=0.26CV=0.67CV=0.22


Tailored Postponement: Benetton

Q1 (colored) QA(neutral) Total Aver. Profit

Aver. Overstock

Aver. Understock

0 4,524 4,524 $ 98,092 715 190

1337 0 5,348 $ 94,576 1648 300

700 1,850 4,650 $ 102,730 308 168

800 1,550 4,750 $ 104,603 427 170

900 950 4,550 $ 101,326 607 266

900 1,050 4,650 $ 101,647 664 230

1000 850 4,850 $ 100,312 815 195

1000 950 4,950 $ 100,951 803 149

1100 550 4,950 $ 99,180 1026 211

1100 650 5,050 $ 100,510 1008 185

4 colors, for each: mean demand = 1,000, SD=500Produce Q1 units for each color, and QA units undyed


Cautions in Implementing Postponement

The cost of postponement– Postponement often increases the manufacturing cost

– Design and production costs can only be justified over a family of products

Value of postponement is larger the more uncertain and the less correlated the individual product demands

Cautions– End products must look suitably different to the consumer

– Do a small set of products provide most of the sales?

– Do products have low uncertainty?

Tailored postponement– Higher manufacturing cost is justified only for uncertain portion of demand.

– Consider more efficient process for stable portion of demand.


Push Pull

Cycle Inventory Safety Inventory Seasonal Inventory

• Aggregation• Volume baseddiscounts over rolling horizon• EDLP, promoteto limit forwardbuy

• Quick response•Reduce uncertainty•Reduce lead time•Reduce lead time variability•Increase reorder frequency

• Accurate response by pooling•Tailored pooling based on

•Demand correlation•Coefficient of variation•Value of product•Level of service•Holding cost

•Increase salvage value anddecrease lost margin•Shorten lead time to reduceuncertainty•Multiple orders in season.•Tailored postponement

Managing Inventories and Uncertainty in the Supply Chain: Summary of Lessons

product availability inventory scm chopra3 ppt ch12.complete

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