Determine optimal level of product availability.ppt

Vendor selection strategy

1. Determining Optimal Level of
Product Availability
Supply Chain Management

2. 2
Learning Objectives
Importance of level of product availability
Factors to consider when setting availability levels
Newsvendor model
Managerial “levers” for improving supply chain
profitability
Value of postponement in a supply chain
Setting optimal levels of product availability in
practice
Double marginalisation; contracts

3. 3
Product Availability: Tradeoffs
High availability =>
responsive to customers
attract increased sales
higher revenue
High availability =>
larger inventory
higher costs
risk of obsolescence
Nordstrom, Marks & Spencer, Escada
Bossini, supermarket, Fa Yuen Street
E-commerce
customer can find alternate source easily
pressure on manufacturers to increase availability

4. 4
Newsboy Model
single period model (one selling season)
(one-time order, e.g. for quantity
discount)
demand uncertainty
order placed (and delivered) before demand is known
unmet demand is lost
unsold inventory at the end of the period is discard (or
salvaged at lower value)
How much to order?
Newsvendor Model

5. 5
Factors affecting availability
Demand uncertainty

Overstocking cost C
0
= loss incurred when a unit unsold at end of selling
season

Understocking cost C
u
= profit margin lost due to lost sale (because no
inventory on hand)
Customer/Cycle service level CSL
=level of product availability
= Prob(Demand < stock level)

6. 13-6Copyright ©2013 Pearson Education.
Determining Optimal Level of
Product Availability
•Single period
•Possible scenarios
–Seasonal items with a single order in a
season
–One-time orders in the presence of quantity
discounts
–Continuously stocked items
–Demand during stockout is backlogged
–Demand during stockout is lost

7. 7
Example: Selling parkas at LL Bean
Cost per parka = c = $45
Sale price per parka = p = $100
Inventory holding (until season end) and transportation cost
(to outlet store) per parka = $10
Discount price per parka (season end sales) = $50
Salvage value per parka = $50 -$10 = $40 = s
Cost of overstocking = C
o
= $45 + $10 - $50 = c - s = $ 5
Marginal profit from selling parka = cost of understocking =
C
u = $100 - $45 = p - c = $55

8. 13-8Copyright ©2013 Pearson Education.
L.L. Bean Example – Demand Distribution
Demand D
i
(in hundreds)Probability p
i
Cumulative Probability of
Demand Being D
i
or Less (P
i
)
Probability of Demand
Being Greater than D
i
4 0.01 0.01 0.99
5 0.02 0.03 0.97
6 0.04 0.07 0.93
7 0.08 0.15 0.85
8 0.09 0.24 0.76
9 0.11 0.35 0.65
10 0.16 0.51 0.49
11 0.20 0.71 0.29
12 0.11 0.82 0.18
13 0.10 0.92 0.08
14 0.04 0.96 0.04
15 0.02 0.98 0.02
16 0.01 0.99 0.01
17 0.01 1.00 0.00
Table 13-1

9. 9
LLBean: Expected Profit
Expected demand
Expected profit if order 10
Expected profit if order k

))(10](1[)])(10()([
10
10
4
cpPscicpip
i
i


10
17
4

j
jpj
))(](1[)])(()([
4
cpkPscikcpip
k
k
i
i 


10. 10
LLBean: Expected profit
Demand ProbabilitySum(d(i)xp(i)) Cumulative Prob.Prob. demand greaterExpected profit
d(i) p(i) P(i) = Pr( D < d(i) )1 - P(i) = Pr( D > d(i) )if stock d(i)
4 0.01 0.04 0.01 0.99 220.00
5 0.02 0.14 0.03 0.97 274.40
6 0.04 0.38 0.07 0.93 327.60
7 0.08 0.94 0.15 0.85 378.40
8 0.09 1.66 0.24 0.76 424.40
9 0.11 2.65 0.35 0.65 465.00
10 0.16 4.25 0.51 0.49 499.00
11 0.20 6.45 0.71 0.29 523.40
12 0.11 7.77 0.82 0.18 535.80
13 0.10 9.07 0.92 0.08 541.60
14 0.04 9.63 0.96 0.04 541.40
15 0.02 9.93 0.98 0.02 538.80
16 0.01 10.09 0.99 0.01 535.00

11. 11
Newsvendor : Marginal Analysis
Stock one unit if …
Stock 2 units (instead of 1 unit) if ...
Stock 1 Stock 2 Stock 3
D = 0
D = 1
D = 2
D = 3

12. 12
Increase order from k to k+1 if
Prob(Demand < k) < C
u
C
o
+ C
u
Order k+1 instead of k if
Pr(D>k) C
u Pr(D<k) (C
o) > 0
orPr(D< k ) (C
o
) + [1-Pr(D<k)] C
u
> 0
order k+1
keep order size at k
instead of k
1 more unsold
1 fewer lost sale
0
C
u
P
k
1-P
k
C
o
Additional
contribution

13. 13
LL Bean
13
917.0
555
55
54045
5545100
orderso
CC
C
ratiocritical
scC
cpC
uo
u
o
u







Demand Probability Cumulative Prob.
d(i) p(i)P(i) = Pr( D < d(i) )
4 0.01 0.01
5 0.02 0.03
6 0.04 0.07
7 0.08 0.15
8 0.09 0.24
9 0.11 0.35
10 0.16 0.51
11 0.20 0.71
12 0.11 0.82
13 0.10 0.92
14 0.04 0.96
15 0.02 0.98
16 0.01 0.99

14. 13-14Copyright ©2013 Pearson Education.
L.L. Bean Example
Additional
Hundreds
Expected Marginal
Benefit
Expected Marginal
Cost
Expected Marginal
Contribution
11th 5,500 x 0.49 = 2,695500 x 0.51 = 2552,695 – 255 = 2,440
12th 5,500 x 0.29 = 1,595500 x 0.71 = 3551,595 – 355 = 1,240
13th 5,500 x 0.18 = 990500 x 0.82 = 410 990 – 410 = 580
14th 5,500 x 0.08 = 440500 x 0.92 = 460 440 – 460 = –20
15th 5,500 x 0.04 = 220500 x 0.96 = 480 220 – 480 = –260
16th 5,500 x 0.02 = 110500 x 0.98 = 490 110 – 490 = –380
17th 5,500 x 0.01 = 55 500 x 0.99 = 495 55 – 495 = –440
Table 13-2

15. 13-15Copyright ©2013 Pearson Education.
L.L. Bean Example
Figure 13-1

16. 16
EXAMPLE A product is priced to sell at $100 per unit, and its cost is
constant at $70 per unit. Each unsold unit has a salvage value of $30.
Demand is expected to range between 35 and 40 units for the period: 35
units definitely can be sold and no units over 40 will be sold. The demand
probabilities and the associated cumulative probability distribution (P) for
this situation are shown on next slide.
The marginal profit if a unit is sold is the selling price less the cost, or C
u =
$100 − $70 = $30.
The marginal loss incurred if the unit is not sold is the cost of the unit less
the salvage value, or C
o
= $70 − $30 = $40.
How many units should be ordered?
SOLUTION The optimal probability of the last unit being sold is
43.0
4030
30





ou
u
n
CC
C
CP

17. 17
According to the cumulative probability table (the last column in table
below, 37 units should be stocked. The net benefit from stocking the 37th
unit is the expected marginal profit minus the expected marginal loss.
Demand and Cumulative Probabilities
(p) CP
n
Number of Units Probability of Cumulative
Demanded This Demand Probability
35 0.10 1 to 35 0.10
36 0.15 36 0.25
37 0.25 37 0.50
38 0.25 38 0.75
39 0.15 39 0.90
40 0.10 40 1.00
41 0 41 or more 1.00

18. 18
Marginal Inventory Analysis for Units Having Salvage Value
(N) (p) (P) (MP) (ML)
Units of Probability CP
n Expected Marginal Expected Marginal
Demand of Demand Profit of n-th Unit Loss of n-th Unit (Net)
(100-70)(1- CP
n-1) (70-30)CP
n-1 (MP)-(ML)
35 0.10 0.10 $30 $0 $30.00
36 0.15 0.25 27 4 23.00
37 0.25 0.50 22.50 10 12.50
38 0.25 0.75 15 20 (5.00)
39 0.15 0.90 7.50 30 (22.50)
40 0.10 1.00 3 36 (33.00)
41 0 1.00 (40.00)
Note: Expected marginal profit is the selling price of $100 less the unit cost of $70 times the
probability the unit will be sold.
Expected marginal loss is the unit cost of $70 less the salvage value of $30 times the
probability the unit will not be sold.
Net = (MP)(1 - CP
n-1
) - (ML) CP
n-1
= (1 - 0.25)($100 - $70) - (0.75) ($70 - $30)
= $22.50 - $10.00 = $12.50
For the sake of illustration, all possible decisions are shown. From the last column, we can
confirm that the optimum decision is 37 units.

19. 19
Newsvendor Model-
Demand Distribution Continuous
Order y such that
CSL* = Prob(Demand < y) = C
u
C
o + C
u
y
Critical ratio
Critical fractile
Optimal Cycle
Service level

20. 20
Newsvendor model:
normally distributed demand
Demand D ~ N(
Order y such that CSL* = Prob(Demand < y*) = C
u
C
o + C
u
Let y* = +z*
*)](1[**)(*
*)()(*)()(
)(*)()]*((
0
*
*
zFCyzFCy
zfCCzFCC
dxxfCydxxfxyCxCprofitExpected
sus
sousou
y
uo
y
u


 



2
2
1
2
2
1
2
2
)(
)(
t
s
zt
s
etf
dzetF








21. 13-21Copyright ©2013 Pearson Education.
Optimal Cycle Service Level for
Seasonal Items – Single Order
C
o:Cost of overstocking by one unit, C
o = c – s
C
u:Cost of understocking by one unit, C
u = p – c
CSL*:Optimal cycle service level
O*:Corresponding optimal order size
Expected benefit of purchasing extra unit = (1 – CSL*)(p – c)
Expected cost of purchasing extra unit = CSL*(c – s)
Expected marginal
contribution of raising = (1 – CSL*)(p – c) – CSL*(c – s)
order size

22. 13-22Copyright ©2013 Pearson Education.
Optimal Cycle Service Level for
Seasonal Items – Single Order

23. 13-23Copyright ©2013 Pearson Education.
Optimal Cycle Service Level for
Seasonal Items – Single Order

24. 13-24Copyright ©2013 Pearson Education.
Evaluating the Optimal Service
Level for Seasonal Items
Demand  = 350,  = 100, c = $100, p = $250,
disposal value = $85, holding cost = $5
Salvage value= $85 – $5 = $80
Cost of understocking= C
u
= p – c = $250 – $100 = $150
Cost of overstocking= C
o = c – s = $100 – $80 = $20

25. 13-25Copyright ©2013 Pearson Education.
Evaluating the Optimal Service
Level for Seasonal Items

26. 13-26Copyright ©2013 Pearson Education.
Evaluating the Optimal Service
Level for Seasonal Items
Expected
overstock
Expected
overstock
Expected
understock
Expected
understock

27. 13-27Copyright ©2013 Pearson Education.
Evaluating Expected Overstock
and Understock
μ = 350, σ = 100, O = 450
Expected
overstock
Expected
understock

28. 13-28Copyright ©2013 Pearson Education.
One-Time Orders in the Presence
of Quantity Discounts
1.Using C
o
= c – s and C
u
= p – c, evaluate the optimal cycle
service level CSL
*
and order size O
*
without a discount
1.Evaluate the expected profit from ordering O
*
2.Using C
o = c
d – s and C
u = p – c
d, evaluate the optimal
cycle service level CSL
*
d and order size O
*
d with a discount
1.If O
*
d ≥ K, evaluate the expected profit from ordering O
*
d
2.If O
*
d < K, evaluate the expected profit from ordering K units
3.Order O
*
units if the profit in step 1 is higher
1.If the profit in step 2 is higher, order O
*
d units if O
*
d ≥ K or K units if
O
*
d < K

29. 13-29Copyright ©2013 Pearson Education.
Evaluating Service Level with
Quantity Discounts
•Step 1, c = $50
Cost of understocking= C
u
= p – c = $200 – $50 = $150
Cost of overstocking= C
o
= c – s = $50 – $0 = $50
Expected profit from ordering 177 units = $19,958

30. 13-30Copyright ©2013 Pearson Education.
Evaluating Service Level with
Quantity Discounts
•Step 2, c = $45
Cost of understocking= C
u
= p – c = $200 – $45 = $155
Cost of overstocking= C
o
= c – s = $45 – $0 = $45
Expected profit from ordering 200 units = $20,595

31. 13-31Copyright ©2013 Pearson Education.
Desired Cycle Service Level for
Continuously Stocked Items
•Two extreme scenarios
1.All demand that arises when the product
is out of stock is backlogged and filled
later, when inventories are replenished
2.All demand arising when the product is
out of stock is lost

32. 13-32Copyright ©2013 Pearson Education.
Desired Cycle Service Level for
Continuously Stocked Items
Q:Replenishment lot size
S:Fixed cost associated with each order
ROP:Reorder point
D:Average demand per unit time
σ:Standard deviation of demand per unit time
ss:Safety inventory (ss = ROP – D
L)
CSL:Cycle service level
C:Unit cost
h:Holding cost as a fraction of product cost per unit time
H:Cost of holding one unit for one unit of time. H = hC

33. 13-33Copyright ©2013 Pearson Education.
Demand During Stockout is
Backlogged
Increased cost per replenishment cycle
of additional safety inventory of 1 unit = (Q > D)H
Benefit per replenishment cycle of
additional safety inventory of 1 unit = (1 – CSL)C
u

34. 13-34Copyright ©2013 Pearson Education.
Demand During Stockout is
Backlogged
Lot size, Q= 400 gallons
Reorder point, ROP= 300 gallons
Average demand per year, D = 100 x 52 = 5,200
Standard deviation of demand per week, 
D
= 20
Unit cost, C= $3
Holding cost as a fraction of product cost per year, h= 0.2
Cost of holding one unit for one year, H= hC = $0.6
Lead time, L= 2 weeks
Mean demand over lead time, D
L= 200 gallons
Standard deviation of demand over lead time, 
L

35. 13-35Copyright ©2013 Pearson Education.
Demand During Stockout is
Backlogged

36. 13-36Copyright ©2013 Pearson Education.
Evaluating Optimal Service Level
When Unmet Demand Is Lost
Lot size, Q= 400 gallons
Average demand per year, D= 100 x 52 = 5,200
Cost of holding one unit for one year, H= $0.6
Cost of understocking, C
u
= $2

37. 37
Yield Management
Airline, hotel bookings
2 classes of customers
high fare/revenue
low fare/revenue
Suppose there are infinite demand for low-fares
Model: How many seats Q to allocate for high
fares?
C
0
= LR
C
u= HR - LR
Overbooking?Overbooking?

38. 38
Managerial levers for increased profitability
Increase salvage value
Sell to outlet stores, overseas
Decrease margin lost from stockout
Backup sourcing (e.g. competitor?)
Rain-check, discount coupon for future purchase
Reduction of demand uncertainty
Improve forecasting
Quick response
Postponement
Tailored sourcing

39. 39
Improved Forecasts
Improved forecasts result in reduced uncertainty
Less uncertainty (lower 
R) results in either:
Lower levels of safety inventory (and costs) for the same
level of product availability, or
Higher product availability for the same level of safety
inventory, or
Both lower levels of safety inventory and higher levels
of product availability
An increase in forecast accuracy decreases both the overstocked and
understocked quantity and increases a firm’s profits.

40. 40
Impact of improved forecasts
Demand ~ N(350, 
R
),
c=$100, p=$250, s=$85-$5= $80
Cost of understocking = Cu = p-c = $250-$100 = $150
Cost of overstocking = Co = c-s = $100 - $80 = $20
CSL* = Pr(D < y*) = (250-100)/(150+20)=0.88
y*=350+1.185 
R
Sigma Optimal orderExp. OverstockExp. UnderstockExp. Profit
150 526 186.7 8.6 $47,469
120 491 149.3 6.9 $48,476
90 456 112 5.2 $49,482
60 420 74.7 3.5 $50,488
30 385 37.3 1.7 $51,494
0 350 0 0 $52,500

41. 41
Impact of Improved forecasts
y
y

Expected understockE
xpected overstock
Expected profit

42. 42
Quick Response
Reduction of replenishment leadtime
Allows for multiple orders during selling season
Only if lead-time reduced sufficiently for additional orders to be
executed before season ends
Increased forecast accuracy
Forecasts more accurate closer to selling season
Forecast based on initial demand more accurate than pre-season
forecasts
Consequences of multiple replenishments:
Expected total quantity less for same service level
Average overstock (for disposal) is less
Profits are higher

43. 43
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
Expected weekly demand = 20
SD of weekly demand = 
D
= 15

44. 13-44Copyright ©2013 Pearson Education.
Quick Response: Multiple
Orders Per Season
•Two ordering policies
1.Supply lead time is more than 15 weeks
•Single order placed at the beginning of the
season
•Supply lead time is reduced to six weeks
2.Two orders are placed for the season
•One for delivery at the beginning of the season
•One at the end of week 1 for delivery in week 8

45. 13-45Copyright ©2013 Pearson Education.
Single Order Policy

46. 13-46Copyright ©2013 Pearson Education.
Single Order Policy
Expected profit with a single order= $29,767
Expected overstock= 79.8
Expected understock= 2.14
Cost of overstocking= $10
Cost of understocking= $110
Expected cost of overstocking= 79.8 x $10 = $798
Expected cost of understocking= 2.14 x $110 = $235

47. 13-47Copyright ©2013 Pearson Education.
Two Order Policy
Expected profit from seven weeks= $14,670
Expected overstock= 56.4
Expected understock= 1.51
Expected profit from season= $14,670 + 56.4
x $10 + $14,670
= $29,904

48. 48
Impact of Quick Response
Single Order Two Orders in Season
Service
Level
Order
Size
Ending
Invent.
Expect.
Profit
Initial
Order
OUL
for 2
nd
Order
Average
Total
Order
Ending
Invent.
Expect.
Profit
0.9637897 $23,624209209349 69 $26,590
0.9436786 $24,034201201342 60 $27,085
0.9135573 $24,617193193332 52 $27,154
0.8734366 $24,386184184319 43 $26,944
0.8132955 $24,609174174313 36 $27,413
0.7531741 $25,205166166302 32 $26,916

49. 13-49Copyright ©2013 Pearson Education.
Quick Response: Multiple
Orders Per Season
•Three important consequences
1.The expected total quantity ordered during the
season with two orders is less than that with a
single order for the same cycle service level
2.The average overstock to be disposed of at the
end of the sales season is less if a follow-up
order is allowed after observing some sales
3.The profits are higher when a follow-up order is
allowed during the sales season

50. 13-50Copyright ©2013 Pearson Education.
Quick Response: Multiple
Orders Per Season
Figure 13-4

51. 13-51Copyright ©2013 Pearson Education.
Quick Response: Multiple
Orders Per Season
Figure 13-5

52. 13-52Copyright ©2013 Pearson Education.
Two Order Policy with Improved
Forecast Accuracy
Expected profit from second order= $15,254
Expected overstock= 11.3
Expected understock= 0.30
Expected profit from season= $14,670 + 56.4
x $10 + $15,254
= $30,488

53. 53
Forecast Improves for Second Order
(SD=3 Instead of 15)
Single Order Two Orders in Season
Service
Level
Order
Size
Ending
Invent.
Expect.
Profit
Initial
Order
OUL
for 2
nd
Order
Average
Total
Order
Ending
Invent.
Expect.
Profit
0.9637896 $23,707209153292 19 $27,007
0.9436784 $24,303201152293 18 $27,371
0.9135576 $24,154193150288 17 $26,946
0.8734363 $24,807184148288 14 $27,583
0.8132952 $24,998174146283 14 $27,162
0.7531744 $24,887166145282 14 $27,268

54. 54
Postponement
Delay of product differentiation closer to time of sale.
Prior to point of postponement, only aggregate
forecast needed (more accurate than individual
product forecasts)
Individual forecasts more accurate close to time of
sale
Better match of supply to demand, higher profits
E.g. Benetton: dye  knit
Valuable for on-line sales
Costs?

55. 55
Benetton
Retail price p=$50, Salvage value s=$10
4 colours: demand for each ~ N(


Option 1 (dye  knit): cost c=$20
Individual forecast 20 weeks ahead
Option 2 (knit  dye): cost c=$22
Aggregate forecasts 20 weeks ahead
Dye after individual demand known

56. 56
Benetton
Option 1:
CSL* = 30/40 = 0.75
y* = 1000 + (0.674)500 =1337
Total production = 4(1337) = 5348
Expected overstock =1648, Expected understock =300
Expected profit = $94,576
Option 2:
CSL* = 28/40 = 0.7
y* = 4000 + (0.524)[2(500)] =4524 =total produced
Expected overstock =715, Expected understock =190
Expected profit = $98,092

57. 13-57Copyright ©2013 Pearson Education.
Value of Postponement: Benetton
•Postponement is not very effective if a large
fraction of demand comes from a single product
•Option 1
Red sweaters demand 
red = 3,100, 
red = 800
Other colors  = 300,  = 200
Expected profits
red
= $82,831
Expected overstock= 659
Expected understock= 119

58. 13-58Copyright ©2013 Pearson Education.
Value of Postponement: Benetton
Other colors  = 300,  = 200
Expected profits
other= $6,458
Expected overstock= 165
Expected understock= 30
Total production = 3,640 + 3 x 435 = 4,945
Expected profit = $82,831 + 3 x $6,458 = $102,205
Expected overstock = 659 + 3 x 165 = 1,154
Expected understock = 119 + 3 x 30 = 209

59. 13-59Copyright ©2013 Pearson Education.
Value of Postponement: Benetton
•Option 2
Total production = 4,475
Expected profit = $99,872
Expected overstock = 623
Expected understock = 166
Postponement may not be effective with Dominant Product

60. 60
Value of Postponement
Better match supply and demand
Increase profits, especially if firm produce large
variety of products with similar demand level that is
NOT positively correlated
!! May reduce profits if there is major single product,
especially if postponement increases manufacturing
costs
Tailored postponement
Use postponement on uncertain demand
Use lower-cost production on certain demand
Segregate by product or by quantity

61. 13-61Copyright ©2013 Pearson Education.
Tailored Postponement: Benetton
•Use production with postponement to satisfy
a part of demand, the rest without
postponement
•Produce red sweaters without postponement,
postpone all others
Profit = $103,213
•Tailored postponement allows a firm to
increase profits by postponing differentiation
only for products with uncertain demand

62. 13-62Copyright ©2013 Pearson Education.
Tailored Postponement: Benetton
•Separate all demand into base load and
variation
–Base load manufactured without postponement
–Variation is postponed
Four colors
Demand mean = 1,000, = 500
–Identify base load and variation for each color

63. 13-63Copyright ©2013 Pearson Education.
Tailored Postponement: Benetton
Manufacturing Policy
Q
1
Q
2
Average
Profit
Average
Overstock
Average
Understock
0 4,524 $97,847 510 210
1,337 0 $94,377 1,369 282
700 1,850 $102,730 308 168
800 1,550 $104,603 427 170
900 950 $101,326 607 266
900 1,050 $101,647 664 230
1,000 850 $100,312 815 195
1,000 950 $100,951 803 149
1,100 550 $99,180 1,026 211
1,100 650 $100,510 1,008 185
Table 13-4

64. 64
Tailored Sourcing
Use a combination of two supply source:
One focused on lower cost, less able to handle
uncertainty,
One focused on flexibility but higher cost.
Focus on different capabilities
Better match supply to demand; increase profits
 Volume based:
E.g. Benetton, firms with overseas suppliers
Product based:
E.g. Levi, traditional vs. custom jeans

65. 65
Tailored Sourcing Strategies
Fraction of demand from
overseas supplier
Annual Profit
0% $37,250
50% $51,613
60% $53,027
100% $48,875

66. 66
Tailored Sourcing: Multiple
Sourcing Sites
CharacteristicPrimary SiteSecondary Site
Manufacturing
Cost
High Low
Flexibility
(Volume/Mix)
High Low
ResponsivenessHigh Low
Engineering
Support
High Low

67. 67
Dual Sourcing Strategies
Strategy Primary SiteSecondary Site
Volume based
dual sourcing
FluctuationStable demand
Product based
dual sourcing
Unpredictable
products,
Small batch
Predictable,
large batch
products
Model based
dual sourcing
Newer
products
Older stable
products

68. 68
Setting Product Availability for Multiple
Products under Capacity Constraints
Single product order
Multiple product order
Decrease the order size
Allocating the products
When ordering multiple products under a limited supply capacity,
the allocation of capacity to products should be based on their
expected marginal contribution to profits. This approach allocates a
relatively higher fraction of capacity to products that have a high
margin relative to their cost of overstocking.

69. 13-69Copyright ©2013 Pearson Education.
Setting Product Availability for Multiple
Products Under Capacity Constraints
•Two styles of sweaters from Italian supplier
High end Mid-range

1 = 1,000 
2 = 2,000

1
= 300 
2
= 400
p
1
= $150 p
2
= $100
c
1 = $50 c
2 = $40
s
1
= $35 s
2
= $25
CSL = 0.87 CSL = 0.80
O = 1,337 O = 2,337

70. 13-70Copyright ©2013 Pearson Education.
Setting Product Availability for Multiple
Products Under Capacity Constraints
•Supplier capacity constraint, 3,000 units
Expected marginal
contribution high-end
Expected marginal
contribution mid-range

71. 13-71Copyright ©2013 Pearson Education.
Setting Product Availability for Multiple
Products Under Capacity Constraints
1.Set quantity Q
i = 0 for all products i
2.Compute the expected marginal contribution MC
i(Q
i) for each
product i
3.If positive, stop, otherwise, let j be the product with the highest
expected marginal contribution and increase Q
j by one unit
4.If the total quantity is less than B, return to step 2, otherwise
capacity constraint are met and quantities are optimal
subject to:

72. 13-72Copyright ©2013 Pearson Education.
Setting Product Availability for Multiple
Products Under Capacity Constraints
Expected Marginal Contribution Order Quantity
Capacity Left High End Mid Range High End Mid Range
3,000 99.95 60.00 0 0
2,900 99.84 60.00 100 0
2,100 57.51 60.00 900 0
2,000 57.51 60.00 900 100
800 57.51 57.00 900 1,300
780 54.59 57.00 920 1,300
300 42.50 43.00 1,000 1,700
200 42.50 36.86 1,000 1,800
180 39.44 36.86 1,020 1,800
40 31.89 30.63 1,070 1,890
30 30.41 30.63 1,080 1,890
10 29.67 29.54 1,085 1,905
1 29.23 29.10 1,088 1,911
0 29.09 29.10 1,089 1,911
Table 13-5

73. 73
Setting Optimal Levels of
Product Availability in Practice
Use an analytical framework to increase profits
Beware of preset levels of availability
Use approximate costs because profit-
maximizing solutions are very robust
Estimate a range for the cost of stocking out
Ensure levels of product availability fit with
the strategy

74. 74
Summary
Newsvendor model
Tradeoff cost of over-stock
and lost sales
Managerial levers for
increasing supply chain
profitability
Adjust costs
Improve forecasting
Quick response
Postponement
Tailored sourcing
Allocate limited supply
capacity among multiple
products to maximise
expected profits
Making supply meet demand!Making supply meet demand!