Revenue Management - Cours complet PDF

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Summary

Cours complet de Revenue Management

1. Introduction
2. Static control for a single resource
3. Static control for multiple Resources
4. Revenue Management at Harrah’s
5. Randomize linear
6. Dynamic control for a single resource
7. Pricing, fund...

Description

Revenue Management Table of Contents Revenue Management...................................................................................................................1 1.

2.

Introduction...........................................................................................................................3 1.1.

RM instruments for matching supply and demand........................................................................3

1.2.

The Newsvendor Model................................................................................................................3

1.3.

The expected profit maximizing order quantity.............................................................................4

1.4.

Easy profit simulation...................................................................................................................4

1.5.

Booking Limits and Protection Levels............................................................................................4

1.6.

Littlewood’s Rule – Two classes model (1972)...............................................................................5

Static control for a single resource..........................................................................................6 2.1.1. 2.1.2. 2.1.3. 2.1.4. 2.1.5. 2.1.6. 2.2.1.

3.

Newsvendor Model Performance Measures...................................................................................................6 Expected lost sales (Graphical explanation)....................................................................................................6 Multiple booking classes.................................................................................................................................7 Nesting.............................................................................................................................................................7 n-Class model..................................................................................................................................................7 Heuristic Solution to the n-Class Model: EMSR-a...........................................................................................8 Poisson distribution.........................................................................................................................................9

Static control for multiple Resources.....................................................................................10 3.1.1. 3.1.2. 3.1.3. 3.1.4. 3.1.5.

Multiple resources – Motivation...................................................................................................................10 A Stochastic Static Network RM Model - SSNRM..........................................................................................10 The Deterministic Static Network Revenue Management (DSNRM)............................................................10 Example.........................................................................................................................................................11 Bid price controls for network RM................................................................................................................11

4.

Lecture 4 – Revenue Management at Harrah’s.....................................................................12

5.

Lecture 5 – Randomize linear program.................................................................................15

6.

5.1.

The Randomized Linear Programming (RLP) Model.....................................................................15

5.2.

RLP-based bid prices...................................................................................................................15

Lecture 6 and 7 – Dynamic control for a single resource........................................................16 6.1.

Dynamic programming................................................................................................................16

6.2.

Stochastic Dynamic Programming (SDP)......................................................................................17

6.2.1. 6.2.2.

6.3. 6.3.1. 6.3.2. 6.3.3.

6.4. 6.4.1. 6.4.2.

Total reward and policy.................................................................................................................................17 Bellman equation..........................................................................................................................................17

Stochastic Dynamic Capacity Control with Independent Demand...............................................18 Bellman Equation..........................................................................................................................................18 Structural properties.....................................................................................................................................18 Alternative model formulation......................................................................................................................18

Stochastic Dynamic Capacity Control with Customer Choice Behaviour......................................19 Discrete Choice Model of Consumer Behavior (RMDC)................................................................................19 Efficient points (subsets)...............................................................................................................................20

6.4.3. 6.4.4. 6.4.5. 6.4.6. 6.4.7. 6.4.8.

7.

Lecture 8 – Pricing, fundamental concepts............................................................................24 7.1. 7.1.1. 7.1.2.

7.2. 7.2.1. 7.2.2. 7.2.3. 7.2.4. 7.2.5.

7.3. 7.3.1.

7.4. 7.4.1.

8.

9.

Efficient points: definition.............................................................................................................................21 Summary of the Largest Marginal Revenue Procedure.................................................................................21 The reduced RMDC Model............................................................................................................................21 Selected Choice Models I: Independent Demand Model.............................................................................22 Selected Choice Models II: Attraction Choice (MNL Model).........................................................................22 Consumer‘s Choice: Viewing Products as a Bundle of Attributes.................................................................23

Fundamental concepts................................................................................................................24 Quantity-based Price Differentiation – Nonlinear Pricing.............................................................................25 Price Differentiation by Time and Customers: Dynamic Pricing....................................................................25

Deterministic Dynamic pricing.....................................................................................................26 Single-Product Single-Resource Pricing: Intuitive Modeling Approach.........................................................26 Deterministic Single-Product Dynamic Pricing Model (DSPDP) – Intuitive Approach..................................26 Optimization..................................................................................................................................................27 Solving optimization problem.......................................................................................................................28 Convex Optimization Problem.......................................................................................................................28

Single-Product Single-Resource Pricing: Smart Modeling Approach............................................29 Deterministic Single-Product Dynamic Pricing Model (DSPDP) – Smarter Approach...................................29

Multi-Product Multi-Resource Pricing in Networks.....................................................................29 Deterministic Multi-Product Dynamic Pricing Model (DMPDP)....................................................................29

Lecture 9 – Pricing and Product Line Design..........................................................................30 8.1.

Optimal Product Line design: A basic model...............................................................................30

8.2.

Linearization...............................................................................................................................32

8.3.

Linearization of Mixed-binary Bilinear Terms..............................................................................33

8.4.

Linearilized Probem Formulation................................................................................................33

8.5.

PLD Model Extension: Fixed cost for ressources..........................................................................34

Guest Lectures – Simon Kucher & Partners............................................................................35

1. Introduction 1.1.

RM instruments for matching supply and demand

-

Dynamic pricing: matching demand to supply o Price differentiation by segment o Dynamic price adjustments over time to cope with fluctuating and stochastic demand

-

Capacity control: allocate supply to demand o Reservation of portion of capacity for higher value customers at a later date o Restrictions on the amount of capacity made available to a lower value segment of customers o “seat inventory control”

1.2.

The Newsvendor Model

Notations p unit sale price, p > 0 c unit cost price, 0 < c < p v salvage value, v < c (book value of the asset after depreciation of lifetime, valeur résiduelle) D unit demand in the period, d >= 0, continuous random variable  cumulative distribution function of demand  mean demand standard deviation of demand  Q order size Co = Overage cost, the cost of ordering one more unit than necessary to answer the demand. This is the loss profit due to a leftover unit when D < Q. => too much of something Co=c −v Expected loss=Co∗(Q ) Cu = Underage cost, the cost of ordering one fewer unit than necessary to answer the demand. This is the loss profit due to lost sales unit when D > Q => too little of something Cu= p− c Expected gain=Cu∗(1 − ( Q )) To maximize expected profit, order Q units so that the expected loss on the Qth unit equals the expected gain on the Qth unit: Exepected loss=Expected gain

Co∗(Q)=Cu∗(1−( Q ) ) Cu Co+ Cu Thus, to maximize contribution, choose Q such that we don’t have lost sales (i.e., demand is Q or lower) with a probability that equals the critical ratio Critical ratio=(Q )=

1.3.

The expected profit maximizing order quantity

Assume demand is normally distributed with : - mean =  = 3192 - standard deviation =  = 1181 And that critical ratio = 0.777, the Standard Normal Distribution Function Tables gives z = 0.77 (If critical ratio falls between two values in the table, choose greater z-statistic) Then the best order quantity Q=μ+z∗σ =3192+ 0.77∗1181= 4101

1.4.

Easy profit simulation

Underage cost (spoil) = Cu = Business class price – Leisure class price = 120 – 80 = 40 Overage cost (spill) = Co = Leisure class price = 80 P (Q) = Critical ratio = Cu / (Co + Cu) = 40 / 120 = 0.33 Assume demand follows a Poisson distribution with mean 36, POISSON (x;36;1), 1 = True = cumulative Pr (D p2 >...> pn bj: Nested booking limit for class j – max number of capacity units for sale to class j and lower (in terms of revenue order, i.e. j, j+1, ..., n) yj: Nested protection level for class j – number of capacity units reserved for class j and higher (in terms of revenue order, i.e. j, j – 1, ..., 1) C: Total capacity of the single resource with Sj uj = C.

1.6.5. n-Class model Static, single leg setting with n booking classes j = 1..n Let classes be indexed such that p1 >..> pn with pj: revenue per seat in class j Classes book sequentially with low-before-high arrival pattern, i.e., demand for the n classes arrives in n stages, in increasing order of revenue values Total number Dj of reservation requests for seats in class j by the close of the booking process is stochastic with cumulative distribution function j(Dj) Given: Available capacity C (assumed to be continuous) Decision variable uj for capacity allocation to class j This problem can be formulated as a dynamic program with classes j as stages, i.e. at stage j a realization of demand Dj occurs (TvR Section 2.2.2.1) Problem can be easily solved exactly but in practice the heuristics are widely used to compute booking limits and protection levels instead (e.g., EMSR heuristic)

Opportunity costs represent the potential benefits an individual, investor, or business misses out on when choosing one alternative over another 1.6.6. Heuristic Solution to the n-Class Model: EMSR-a EMSR (= Expected Marginal Seat Revenue)

FCFS = First Comes First Served policy

1.7.

1.7.1. Poisson distribution

-

Defined only by its mean (standard deviation = square root(mean)) Does not always have a “bell” shape, especially for low demand. Discrete distribution function: only non-negative integers Good for modeling demands with low means (e.g., less than 20) If inter-arrival times of customers are exponentially distributed, the number of customers that arrive in a given interval of time has a Poisson distribution

The Poisson distribution is a discrete probability distribution that expresses the probability of a number of events occurring during a time-interval of given length if these events occur with a known average rate and independently of the time since the last event. If the expected number of occurrences in this interval is λ, then the probability that there are exactly x occurrences (x being a non-negative integer, x = 0, 1, 2, ...) is equal to x −λ

ϕ( x )= λ e x!

 Loss function for the Poisson Distribution The expected amount that a discrete random variable X with probability density x), x = 0,1,2,... exceeds a given threshold y is given by the Loss function ∞

(x) L ( y )=∑ ( y−x )ϕ x= y

The Loss Function is: y−1

L ( y )= λ− y + ∑ ( y−x (x ) ϕ) x=0

It can also be expressed as: ∞

L ( y +1 ) =L ( y ) −( 1−ϕ( y )) where L (O )=∑ x ϕ( x )=λ x=0

3. Static control for multiple Resources

1.7.2. Multiple resources – Motivation Whenever customers buy bundles of resources in combination under various terms and conditions, network revenue management problems arise. Interdependence among resources requires to jointly manage the capacity controls on all resources. 1.7.3. A Stochastic Static Network RM Model - SSNRM An extension to Littlewood’s two-class model with a single resource:

1.7.4. The Deterministic Static Network Revenue Management (DSNRM) This is the Deterministic version of the SSRNM – DSNRM To reduce complexity, we consider the deterministic approximation of the above model

A shadow price is an estimated price for something that is not normally priced in the market or sold in the market. It is often used in cost-benefit accounting to value intangible assets, but can also be used to reveal the true price of a money market share

1.7.5. Example

Max 200y1 + 150y2 + 250y3 + 190y4 + 400y5 + 310y6 Subject to y1 + y2 + y5 + y6...