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The Role of RM in SCsRevenue management is the use of pricing to increase the profit generated from alimited supply of supply chain assets SCs are about matching demand and capacity Prices affect demands
Yield management similar to RM but deals more with quantities rather than pricesSupply assets exist in two forms Capacity: expiring Inventory: often preserved
Revenue management may also be defined as offering different prices based oncustomer segment, time of use and product or capacity availability to increasesupply chain profitsMost commonly known example is probably in airline ticket pricing Pricing according to customer segmentation at any time Pricing according to reading days for any customer segment
Reading days : Number of days until departure
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Conditions for RM to Work
The value of the product varies in different market segments Airline seats: Leisure vs. Business travel Films: Movie theater goers, DVD buyers, Cheap movie theater goers, TV watchers.
The product is highly perishable or product waste occurs Fashion and seasonal apparel High tech products
Demand has seasonal and other peaks Products ordered at Amazon.com, peaking in December Supply Chain textbook orders peaking in August and January.
The product is sold both in bulk and on the spot market O wner of warehouse who can decide whether to lease the entire warehouse through
long-term contracts or save a portion of the warehouse for use in the spot market Truck capacities for a transportation company
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RM for Multiple Customer Segments
If a supplier serves multiple customer segments with a fixed asset,the supplier can improve revenues by setting different prices for each segment
Must figure out customer segmentsPrices must be set with b arriers such that the segment willing to
pay more is not able to pay the lower price Barriers : Time, location, prestige, inconvenience, extra service
In the case of time barrier, The amount of the asset reserved for the higher price segment is such that
quantities below are equal the expected marginal revenue from the higher priced segment the price of the lower price segment
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Customer Segmentation by extra serviceExample: Cruise ship
A cruise ship with C= 400 identical cabinsWhat is the price to maximize revenue?
Price
No. Seats
2000
1000
P =2000-2Q
D emand Curve
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Example: Cruise ship
Price
No. seatsQ 1
=400
P 1 =1200
Q 2 =200
P 2 =1600Revenue=1600(200) + 1200(400-200)=560,000
ff er additional services todiff erentiate products and pricing
Increase revenue more?
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Barrier: T ime which implies Customer SegmentRM for Multiple Customer Segments
pL = the price charged to the lower price segment pH = the price charged to the higher price segmentDH = mean demand for the higher price segment
WH = standard deviation of demand for the higher price segmentCH = capacity reserved for the higher price segmentR H(CH) = expected marginal revenue from reserving more capacity
= Prob(Demand from higher price segment > C H) x p H
O ptimality by equivalance of marginal revenues: R H(CH) = p Lwhich leads to
Prob(Demand from higher price segment > C H) = p L / pH
CH = F-1
(1- p L/pH, DH,WH) = Norminv(1- p L/pH, DH,WH)
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Example 15.1: ToFrom Trucking
Revenue from segment A = p A = $3.50 per cubic ftRevenue from segment B = p B = $2 .00 per cubic ftMean demand for segment A = D A = 3,000 cubic ft
Std dev of segment A demand = WA = 1,000 cubic ftCA = Norminv(1- p B/pA, DA,WA)
= Norminv(1- ( 2 .00 /3.50), 3000 , 1000 )= 2 ,8 2 0 cubic ft
If pA increases to $5. 00 per cubic foot, thenCA = Norminv(1- p B/pA, DA,WA)
= Norminv(1- ( 2 .00 /5.00 ), 3000 , 1000 )= 3,2 53 cubic ft
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Two questions:
What happens to the capacity reserved for the high paying segment, when the high paying segmentstarts paying about the low paying segment? How much does the high paying segment value quick
service?
We never consider the distribution of the demand for low paying segment when computing the reservedcapacity for the high paying segment. Can this becorrect, why?
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RM in the Service Industries
Airline Industry uses RM the most.Evidence of airline revenue increases of 4 to 6 percent: With effectively no increase in flight operating costs
RM allows for tactical matching of demand vs. supply: Booking limits can direct low-fare demand to empty flights Protect seats for highest fare passengers on forecast full flights
Hotel, Restaurant, Car rental, O verseas shipping, Cruise
travel, Transportation capacity providers, Computationcapacity providers (computer farms) and sometimesHealth care industries show similarities to airline industryin using RM.
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What are the barriers among customer segmentsin the airline industry?
L eisure
Travelers
BusinessTravelers
No
Offer
No
D emand
Sensitivityto
P rice
Sensitivity t o D urati o nSensitivity t o Flexibility
High L ow
L ow
High
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A RM ModelExpected Revenue = Expected Revenue from Business Class +Expected Revenue from Leisure ClassAssume demand distribution for the business class is known andthe demand for leisure class is C
L B r QC dx x f Qdx x xf r Q )()()()( 0
!
g
0)](1[)(
!! L B r Q F r dQQd
Marginal revenue of business class = Marginal revenue of leisure class
B
L B
r r r
Q F !)( * SL: Service Level
capacityirplane passenger,isurerevenue/le passenger,sinessrevenue/bu !!! L B r r
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Example: Airline seat classes
There are only two price classes Leisure: (f 2 ) $100 per ticket Business: (f1) $ 2 50 per ticket
Total available capacity= 8 0 seatsDistribution of demand for business class is knownAssume enough demand for the leisure class
H ow many seats t o all o cate t o the business class t o maximize expected revenue?
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Business Class Demand Distribution
0%
20%
40%
60%
80%
100%
Business Class Seat Allocation
P r o
b a b
i l i t y
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
P robabilitycd f
P robability 5% 11% 28% 22% 18% 10% 6%
cd f 5% 16% 44% 66% 84% 94% 100
0 5 10 15 20 25 30
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Identifying O ptimal Allocation
0%
20%
40%
60%
80%
100%
Bus i ss l ss t ll ti
r
i l i t
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
P r ilitf
P r ilit 5% 11% 28% 22% 18% 10% 6%
cd f 5% 16% 44% 66% 84% 94% 100
0 5 10 15 20 25 30
SL= 0.60SL= 0.60
Opt imal Alloca t ion Qu an t it y = 15
No te:r B: 2 50,r L: 100
SL = (r B - r L )/ r B= (2 50-100 )/2 50 = 60%
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Expected Revenue
Expected Revenue
8000
8688
92389438 9363
9063
8638
78008000
8200
8400
86008800
900092009400
9600
0 5 10 15 20 25 30 35
Business Class
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O ptimality Condition
Marginal Revenue Business
0
50
100
150
200
250
0 5 10 15 20 25 30 35
MarginalRevenue
L eisure
Optimality C o nditi o n : Choose the number of seats for the business class such that marginal revenue from business class isthe same as the marginal revenue from the leisure class.
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RM for Perishable Assets
Any asset that loses value over time is perishableExamples: high-tech products such as computers and cell
phones, high fashion apparel, underutilized capacity, fruits andvegetablesTwo basic approaches: Dynamic Pricing: Vary price over time to maximize expected revenue O verbooking: O verbook sales of the asset to account for cancellations
Airlines use the overbooking most Passengers are offloaded to other routes O ffloaded passengers are given flight coupons This practice is legal
Dynamic pricing belongs to RM while overbooking can be said to morewithin the domain of Yield management.
But concepts are more important than the names!
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RM for Perishable Assets
O verbooking or overselling of a supply chain asset is valuable if order cancellations occur and the asset is perishable
The level of overbooking is based on the trade-off between the costof wasting the asset if too many cancellations lead to unused assets( s poilage ) and the cost of arranging a backup ( offload ) if too fewcancellations lead to committed orders being larger than theavailable capacitySpoilage and offload are actually terms used in the airline industry
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RM for Perishable Assets
p = price at which each unit of the asset is soldc = cost of using or producing each unit of the asset
b = cost per unit at which a backup can be used in the case of shortageCw = p c = marginal cost of wasted capacity = O verage costCs = b c = marginal cost of a capacity shortage = Underage costO * = optimal overbooking level
P (D emand=Capacity)= C o / (C u + C o )
P (Order cancellati o ns < O *) = C o / (C u + C o )
s* := P r o bability( o rder cancellati o ns < O*) = C w / (C w + C s)
Beware:T
his is the newsvendor formula in disguise.
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RM for Perishable Assets
If the distribution of cancellations is known to be normal withmean Qc and standard deviation Wc then
O * = F -1(s*, Qc, Wc) = Norminv(s*, Qc, Wc)
If the distribution of cancellations is known only as a function of the booking level (capacity L + overbooking O ) to have a meanof Q(L+O ) and std deviation of W(L+O ), the optimal
overbooking level is the solution to the following equation:O * = F -1(s*,Q L+O ),W(L+O ))
= Norminv(s*, Q L+O ),W(L+O ))
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Example 15. 2Cost of wasted capacity = C w = $10 per dressCost of capacity shortage = C s = $5 per dresss* = C w / (Cw + C s) = 10/(10+5) = 0.667
Qc =8
00; W
c = 400O * = Norminv(s*, Qc,Wc)= Norminv( 0.667 ,8 00 ,400 ) = 9 73
If the mean is 15 % of the booking level and the coefficient of variation is 0.5, then the optimal overbooking level is thesolution of the following equation:
O * = Norminv( 0.667 ,0.15(5 000 +O * ),0.07 5(5000 +O * ))Using Excel Solver, O * = 1,115
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RM for Seasonal Demand
Seasonal peaks of demand are common in many SCs\ Most retailers achieve a large portion of total annual demand in
December
Amazon.comO ff-peak discounting can shift demand from peak to non-
peak periodsCharge higher price during peak periods and a lower price
during off-peak periodsRead Section 9 .3: Managing Demand [with discounts] of the textbook.
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RM for Bulk and Spot CustomersMost consumers of production, warehousing, and transportationassets in a supply chain face the problem of constructing a
portfolio of long-term bulk contracts and short-term spot marketcontracts
Long-term contracts for low cost Short-term contracts for flexibilityThe basic decision is the size of the bulk contractThe fundamental trade-off is between wasting a portion of the low-cost bulk contract and paying more for the asset on the spot market
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RM for Bulk and Spot Customers
For the simple case where the spot market price is known butdemand is uncertain, a formula can be used
cB = bulk rate
cS = spot market priceQ* = optimal amount of the asset to be purchased in bulk
p* = probability that the demand for the asset does not exceed Q*
Marginal cost of purchasing another unit in bulk is c B.
The expected marginal cost of not purchasing another unit in bulk and then purchasing it in the spot market is (1-p*)c S.
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Revenue Management for Bulk and Spot Customers
If the optimal amount of the asset is purchased in bulk, themarginal cost of the bulk purchase should equal the expectedmarginal cost of the spot market purchase, or c B = (1-p*)c S
Solving for p* yields p* = (c S cB) / c S
If demand is normal with mean Q and std deviation W, the optimal
amount Q* to be purchased in bulk isQ* = F -1(p*, Q,W) = Norminv(p*, Q,W)
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Example 15. 3: Buying transportation capacityto bring goods from China
Bulk contract cost = c B = $1 0,000 per million unitsSpot market cost = c S = $1 2 ,500 per million unitsDemand for transportation: Q = 10 million units
W= 4 million units p* = (c S cB) / cS = (1 2 ,500 10,000 ) / 12 ,500 = 0.2Q* = Norminv(p*, Q,W) = Norminv( 0.2 ,10,4) = 6.63The manufacturer should sign a long-term bulk contract for 6.63
million units per month and purchase any transportationcapacity beyond that on the spot market
If the demand is exactly 1 0 million units without any variability,how much long-term bulk contract with the transporter?
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Using RM in Practice
Evaluate your market carefully Understand customer requirements for services and products Price, flexibility (time, specs), value-added services, etc. Based on requirements identify customer segments (groups) Differentiate products/services and their pricing according to
customer segments Dell: Same product is sold at a different price to different consumers
(private/small or large business/government/academia/health care) Price of the same product for the same industry varies
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Using RM in Practice
Quantify the benefits of revenue managementImplement a forecasting process
Apply optimization to obtain the revenue managementdecisionInvolve both sales and operationsUnderstand and inform the customer
Integrate supply planning with revenue management
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Summary of Learning O bjectives
What is the role of revenue management in asupply chain?Under what conditions are revenue managementtactics effective?What are the trade-offs that must be consideredwhen making revenue management decisions?
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Smart Pricing Through Rebates
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Rebate Examples
Nikon Coolpix digital camera is sold either on-lineor in stores for $ 600 . the manufacturer provides arebate of $1 00 independently of where the camerais purchased.
Sharp VL-WD 2 55U digital camcorder is sold for
about $5 00 at retail or virtual stores. Sharp provides a rebate to the customer of $1 00 independently of where the product is purchased.
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Mail-in-Rebate
What is the manufacturer trying to achieve withthe rebate? Why the manufacturer and not the retailer?
Should the manufacturer reduce the wholesale price instead of the rebate?
Are there other strategies that can be used toachieve the same effect?
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Example
A Retailer and amanufacturer. Retailer faces customer
demand. Retailer orders from
manufacturer.
S elling P rice=?
Wholesale P rice=$ 900
Retailer Manu f acturer
Variable P roduction Cost=$ 200
Demand
Price
10000
2000
P =2000-0.22Q
D emandCurve
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Example
Retailer profit=(P R -PM)(1/0.22 )(2 ,000 - PR )
Manufacturer profit=(P M-CM) (1/ 0.22 )(2 ,000 - PR )
Retailer takes P M=$9 00 Sets P R =$1450 to maximize (P R -9 00 ) (1/ 0.22 )(2 ,000 - PR ) Q = (1/ 0.22 )(2 ,000 1,450) = 2 ,500 units Retailer Profit = (1, 450-9 00 )2 ,500 = $1, 37 5,000
Manufacturer takes CM=variable cost Manufacturer profit=( 9 00 -2 00 )2 ,500 = $1, 750,000
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Retailer Expected Profit (No Rebate)
0
200,000
400,000
600,000
800,000
1,000 ,000
1,200 ,000
1,400 ,000
1,600 ,000
5 00 1 ,0 00 1 ,5 00 2 ,0 00 2 ,50 0 3 ,00 0 3 ,50 0 3 ,65 4 4 ,11 0 4 ,56 7 4 ,547
Order
R e
t a i l e r
E x p e c
t e d
P r o
f i t
$1,37 5,000
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Manufacturer Profit (No Rebate)
0
1 000 000
2 000 000
3 000 000
4 000 000
5 000 000
6 000 000
5 0 0
10 0 0
15 0 0
20 0 0
25 0 0
30 0 0
35 0 0
36 5
4
41 1 0
45 6 7
45 4 7
49 6
1
53 7
4
57 8 8
62 0
1
66 1
4
70 2 8
74 4
1
78 5 5
r de r
M a n u a c
t u r e r
P r o
i t
$1,750,000
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Example: Customer Mail-in Rebate
What happens with $1 00 customer mail-in rebate? Note that it is a discount for the customer so the demand should
go up!!! Q = (1/0.22 ) [2 ,000 (PR -Rebate)] = (1/ 0.22 ) [2 ,000 (1450-100 )] =
2 9 54
Retailer Profit = (1, 450-9 00 )2 ,9 55 = $1, 62 5,2 50 Manufacturer profit=( 9 00 -2 00 -100 )2 ,9 55 = $1, 773 ,000
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Retailer Expected Profit ($1 00 Rebate)
0
200,000
400,000
600,000
800,000
1,000,000
1,200,000
1,400,000
1,600,000
1,800,000
1,000 1,500 2,000 2,500 3,000 3,500 4,000 4,110 4,567 4,547 4,961
O rder
R e
t a i l e r
E x p e c
t e d P r o
f i t
$1,62 5,2 50
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Manufacturer Profit ($1 00 Rebate)
0
1,000,000
2,000,000
3,000,000
4,000,000
5,000,000
6,000,000
1 , 0 0 0
1 , 5 0 0
2 , 0 0 0
2 , 5 0 0
3 , 0 0 0
3 , 5 0 0
4 , 0 0 0
4 , 1 1 0
4 , 5 6 7
4 , 5 4 7
4 , 9 6 1
5 , 3 7 4
5 , 7 8 8
6 , 2 0 1
6 , 6 1 4
7 , 0 2 8
7 , 4 4 1
7 , 8 5 5
8 , 2 6 8
O rder
a n u
f a c
t u r e r
P r o
f i t
$1,773 ,000
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Example: Wholesale discount
What happens with $1 00 wholesale discount to retailer?
Retailer takes P M=$8 00
Sets P R =$1400 to maximize (P R -8 00 ) (1/ 0.22 )(2 ,000 - PR ) Q = (1/ 0.22 )(2 ,000 1,400 ) = 2 ,72 7 units Retailer Profit = (1, 400 -8 00 )2 ,72 7 = $1, 499 ,8 50
Manufacturer takes P R =$8 00 and CM=variable cost Manufacturer profit=( 8 00 -2 00 )2 ,72 7 = $1, 499 ,8 50
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Example: Global O ptimization
What happens if manufacturer sells directly or optimizesfor the whole system globally? Manufacturer sets P R =$1,1 00 to maximize (P M -2 00 )
(1/0.22 )(2 ,000 - PM
) Q = (1/ 0.22 )(2 ,000 1,100 ) = 4,09 1 units Manufacturer profit=(11 00 -2 00 ) 4,09 1 = $ 3,68 1,9 00
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Strategy Comparison
Strategy Retailer Manufacturer Total
No Rebate 1,370,096 1,750,000 3,120,096 With Rebate ($100) 1,625,250 1,773,000 3,398,250 Reduce Wholesale P ($100) 1,499,850 1,499,850 2,999,700 Global Optimization 3,681,900
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Managerial Insights
Mail in Rebate allows supply chain partners tomove away from sequential strategies towardglo bal o ptimizati o n
Provides retailers with upside incentive
Mail in Rebate o utperf o rms wholesale pricediscount for manufacturer
O ther advantages of rebates: Not all customers will remember to mail them in Gives manufacturer better control of pricing
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Smart Pricing
Customized Pricing Revenue Management Techniques
Distinguish between customers according to their price
sensitivity Influence retailer pricing strategies Move supply chain partners toward global optimization
Dynamic Pricing Changing prices over time without necessarily
distinguishing between different customers Find the optimal trade-off between high price and low
demand versus low price and high demand
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When does Dynamic Pricing Provide Significant ProfitBenefit?
Limited CapacityDemand VariabilitySeasonality in Demand PatternShort Planning Horizon
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The Internet makes Smart Pricing Possible
Low Menu CostLow Buyer Search CostVisibility To the back-end of the supply chain allows to
coordinate pricing, production and distribution
Customer Segmentation
Difficult in conventional stores and easier on theInternet
Testing Capability
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A Word of Caution
Amazon.com experimented with dynamic pricing customers responded negatively
Coca-Cola distributors rebelled against a seasonal pricing scheme
O paque fares (priceline.com, hotwire.com) Determining the correct mix of opaque and regular
fares is difficult.