Revenue Management
      Vision 2020: Ahmedabad 2005


             Peter C. Bell

     Ws                  PBELL@IVEY.CA
...
My Objective




    To introduce you to the practice and theory of
      Revenue Management

    Since this is a large an...
AGENDA:



    • Introduction
    • What is revenue management, who uses it
      and what has been the impact?
    • The ...
AGENDA:



    • Introduction
    • What is revenue management, who uses it
      and what has been the impact?
    • The ...
REVENUE MANAGEMENT: Definition




    Revenue management (RM) is the
     science and art of enhancing firm
     revenues...
REVENUE MANAGEMENT: History



    The first reference to RM is:

    Taylor, C.J. (1962) The determination of passenger
 ...
REVENUE MANAGEMENT: History



    The first major users of RM were
      American Airlines and Delta Airlines
      start...
OR developments in “revenue
    enhancement” since 1985 have led
    to innovative new methods of pricing
    and deliveri...
“MANAGEMENT SCIENTISTS
    HAVE WRECKED THE AIRLINE
           INDUSTRY”

          Joseph F. Coates
            (Californ...
However the impact of revenue
     management has been dramatic


        … and the use of RM continues to
           expa...
“We estimate that yield management has
     generated $1.4 billion in incremental revenue in
     the last three years”
  ...
“We have estimated that the yield management
     system at American Airlines generates almost
     $1 billion in annual i...
quot;Ford Motor Co. has quietly been enjoying a
       huge surge in profitability... 1995 and 1999,
       U.S. vehicle s...
“(revenue management) basically saved National
     Car Rental. And you can go from the CEO of
     National on down, and ...
and .. on the other side:


     RM used by the competition has bankrupted
     several corporations .. the clearest examp...
Donald Burr, Founder and CEO of People
       Express


     “believes that major carrier’s use of
       sophisticated co...
WHO USES RM?


     •   AIRLINES (All?)
     •   HOTELS (Hyatt, Marriott, Hilton, Sheraton, Forte, Disney ..)
     •   VAC...
AGENDA:



     • Introduction
     • What is revenue management, who uses it
       and what has been the impact?
     • ...
THE 5 PILLARS OF RM



     •   New approaches to pricing
     •   Discount allocation
     •   Trading-up
     •   Overbo...
NEW APPROACHES TO PRICING
       PRODUCTS AND SERVICES




21              w           © 2005 by Peter C. Bell
THE NEW PRICING CONCEPT




     • Use product price as a management
       control variable.
     • Set this price “optim...
THE “CONCEPTUAL LEAPS”


     • “Products” do not have a value, rather the
       value of a product depends on the point ...
DEMAND AT A POINT IN TIME BY A
     CUSTOMER CLUSTER DRIVES RM PRICING


        MARKET SEGMENTATION IS THE KEY TO
       ...
A MARKET



                        Q = F(P,……..)
     Price




                                 Quantity Sold

25       ...
SEGMENTING A MARKET

                      Q = F(P,……..)
                      becomes qi = Fi(pi,…..)
                   ...
MARKET SEGMENTATION: METHODS




     • Time of purchase
     • Customer characteristics (seniors, others)
     • Sales ch...
Example of market segmentation

     Coke price rises with heat
     Vending machine that alters price with temperature
  ...
“CLUSTERING” CUSTOMERS


     • Different groups of customers value a product
       differently
        – Example:
      ...
An example of “clusters”

     •   E-Bivalent Newbies (5% of online shoppers)
          – Newest to Net, somewhat older, s...
CHANGING PRODUCT VALUE
     OVER TIME (“time segmentation”)


     • Perishable products that age,
     • Seasonality,
   ...
CHANGING DEMAND OVER TIME
         Example: PERISHABLE PRODUCTS
Demand




            Segment 1           S2            S...
CHANGING DEMAND OVER TIME
          Example: EVENT or TRIP TICKETS
Demand




                            Time       Event...
CHANGING DEMAND OVER TIME
          Example: EVENT or TRIP TICKETS
Demand




                            Time       Event...
Common Demand Models

     Q = Quantity sold
     p = price/unit

     Linear demand:
            Q=A–Bp
        Usually m...
LINEAR APPROXIMATION OF DEMAND
             CURVE



                  Demand Curve
     Price

                          ...
MODEL CHOICE MAY NOT BE OBVIOUS

                                  DEMAND EQUATION ESTIMATION

                        70
...
General Demand Function

     In general, for any time period and cluster:

            Q = F(P, Ps, Pc, X1, X2, ….)

    ...
Estimating Demand

     Demand estimation is a craft: firms tend to keep
       this part of their RM confidential.

     ...
“LEAKAGE”




     • Demand “leakage” (from a high priced
       segment to a low priced segment)
       occurs when segme...
“FENCES”

     • Revenue will disappear unless market
       segments are kept separate to limit “leakage”
       from hig...
Pricing



     Approaches to Revenue Maximization
        – Traditional fixed pricing
        – Variable pricing
        ...
Single price: 2 market segments


                           Revenue = p (Q1 + Q2)
                           There is usu...
Two prices: 2 market segments


                               Revenue = p1Q1 + p2Q2
     Price                     If p1*...
Formal statement of deterministic ODP
     problem (time segments)

     Let:    pi be the product price in period i,
    ...
Deterministic ODP problem with forecast
     errors

     Let:    pi be the product price in period i,
             qi be ...
ACCEPT/REJECT DECISION MAKING

     RM algorithms are mostly “accept/reject” rules.

     If a customer appears and offers...
Revenue optimization drove the entry of RM into
     services.
          - non-replenishable inventories,
          - low ...
The Single-Period Stochastic Optimum
     Pricing Problem
     Define:
     •   p - the price (a decision variable),
     ...
Inventory/SC models vs. RM models




     • Most inventory and supply chain models
       assume demand (Q) is given.
   ...
56   w   © 2005 by Peter C. Bell
THE 5 PILLARS OF RM



     •   Optimum dynamic pricing
     •   Discount allocation
     •   Trading-up (or planned upgra...
Discount allocation



     • Multiple prices for the same units
        – Multi-day packages (hotels, rental cars)
      ...
Discount allocation: Solver example




59                 w                © 2005 by Peter C. Bell
Discount allocation: hotel example




60                  w               © 2005 by Peter C. Bell
DYNAMICS OF MULTIPLE DISCOUNT
     PACKAGES AND PRICE CATEGORIES



     Issue: If a customer appears and demands the
    ...
Reservation rule (Littlewood 1972)


     Issue: How many units (seats) to reserve for
        low price sale?

     Conti...
EMSR Heuristic (Expected Marginal Seat
     Revenue) Belobaba 1987

     Apply Littlewood’s rule sequentially to fare clas...
Protection levels: Expected MR curves




65                   w                  © 2005 by Peter C. Bell
Overbooking (aka overselling)


     Issue: Should you take more orders than you
        have product in the expectation t...
OVERBOOKING: EXAMPLES


     •   airline seats, and passenger train seats, are usually
         booked in advance of the d...
Managing the overbooked customer

     A key cost in all the models
     • Airlines offer cash or travel coupons to
      ...
Minimizing the “no show” rate



     If all customers with reservations showed up,
         there would be no benefit fro...
Overbooking: the basic model

     M = the amount of product
     B = the booking limit (B ≥ M)
     RN = the value of sal...
Overbooking: Determining the optimal level




71                    w                  © 2005 by Peter C. Bell
Trading up (planned upgrades)



     Issue: If a customer appears demanding a
        product that is sold out, should yo...
Re-planing



     Issue: If a plane is sold out several days before
        flight date and a customer appears prepared
 ...
Other RM tools

     • “Markdown optimization” is common in retail
       (Retek, Manugistics, Spotlight): This is really
...
AGENDA:



     • Introduction
     • What is revenue management, who uses it
       and what has been the impact?
     • ...
Integration




     • Although these tools are almost always
       discussed separately, they all function within
      ...
PRICES


     RESERVATION LEVELS




78            w           © 2005 by Peter C. Bell
CAPACITY


                PRICES


                RESERVATION LEVELS




79                       w           © 2005 by ...
CAPACITY
                         OVERBOOKING LEVEL


                PRICES


                RESERVATION LEVELS




80  ...
CAPACITY
                         OVERBOOKING LEVEL


                PRICES


                RESERVATION LEVELS

       ...
CAPACITY
                         OVERBOOKING LEVEL


                PRICES                  REPLANE
                    ...
CAPACITY
                         OVERBOOKING LEVEL


                PRICES                  REPLANE
                    ...
Update
                                         Real time
                          Database
     Historical Data         ...
REQUIREMENTS FOR SUCCESS


     • SUPERIOR INFORMATION TECHNOLOGY,


     • SUPERIOR OPERATIONS RESEARCH SKILLS,
       an...
AGENDA:



     • Introduction
     • What is revenue management, who uses it
       and what has been the impact?
     • ...
BUSINESS OPPORTUNITIES


     A great number of products seem ripe for RM.

     Some examples:
     Cinemas, golf courses...
RESEARCH OPPORTUNITIES

     Academic
     Almost every “inventory” model can be extended
       to include a demand curve...
CONCLUSIONS


     RM tools have become very important for both
       business and OR
     There are opportunities for ma...
CONCLUSIONS



     RM techniques raise many business issues:
       winning firms will be able to implement these
       ...
91   w   © 2005 by Peter C. Bell
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Revenue Management Peter C. Bell 2005

  1. 1. Revenue Management Vision 2020: Ahmedabad 2005 Peter C. Bell Ws PBELL@IVEY.CA 1 w © 2005 by Peter C. Bell
  2. 2. My Objective To introduce you to the practice and theory of Revenue Management Since this is a large and fast growing field, this will be a broad-brush survey. 2 w © 2005 by Peter C. Bell
  3. 3. AGENDA: • Introduction • What is revenue management, who uses it and what has been the impact? • The five pillars of RM – Pricing, discount allocation, overbooking, trading up and re-planing • Integrating the tools • Conclusions 3 w © 2005 by Peter C. Bell
  4. 4. AGENDA: • Introduction • What is revenue management, who uses it and what has been the impact? • The five pillars of RM – Pricing, discount allocation, overbooking, trading up and re-planing • Integrating the tools • Conclusions 4 w © 2005 by Peter C. Bell
  5. 5. REVENUE MANAGEMENT: Definition Revenue management (RM) is the science and art of enhancing firm revenues while selling essentially the same amount of product. 5 w © 2005 by Peter C. Bell
  6. 6. REVENUE MANAGEMENT: History The first reference to RM is: Taylor, C.J. (1962) The determination of passenger booking levels. Proceedings of the Second AGIFORS Symposium, American Airlines, New York. This work recognizes the value of selling more airline seats than capacity in anticipation of “no-shows.” We now call this “overbooking.” 6 w © 2005 by Peter C. Bell
  7. 7. REVENUE MANAGEMENT: History The first major users of RM were American Airlines and Delta Airlines starting about 1985. Both Tom Cook (American) and Robert Cross (Delta) have been cited as the “fathers” of corporate RM. 7 w © 2005 by Peter C. Bell
  8. 8. OR developments in “revenue enhancement” since 1985 have led to innovative new methods of pricing and delivering products. We call these methods “revenue management” tools. 8 w © 2005 by Peter C. Bell
  9. 9. “MANAGEMENT SCIENTISTS HAVE WRECKED THE AIRLINE INDUSTRY” Joseph F. Coates (California futurist) 9 w © 2005 by Peter C. Bell
  10. 10. However the impact of revenue management has been dramatic … and the use of RM continues to expand to new products. 10 w © 2005 by Peter C. Bell
  11. 11. “We estimate that yield management has generated $1.4 billion in incremental revenue in the last three years” by “creating a pricing structure that responds to demand on a flight-by-flight basis” R.L. Crandall, Chairman and CEO of AMR, 1992 11 w © 2005 by Peter C. Bell
  12. 12. “We have estimated that the yield management system at American Airlines generates almost $1 billion in annual incremental revenue” Tom Cook, President SABRE Decision Technologies, June 1998 12 w © 2005 by Peter C. Bell
  13. 13. quot;Ford Motor Co. has quietly been enjoying a huge surge in profitability... 1995 and 1999, U.S. vehicle sales rose just 6 percent, from 3.9 million units to 4.1 million units. But revenue was up 25 percent, and pretax profits soared 250 percent, from about $3 billion to $7.5 billion. Of that $4.5 billion growth, Ford's Lloyd Hansen, controller for global marketing and sales, estimates that about $3 billion came from a series of revenue management initiatives.” CFO Magazine, August, 2000 13 w © 2005 by Peter C. Bell
  14. 14. “(revenue management) basically saved National Car Rental. And you can go from the CEO of National on down, and they will all say: ‘just applying these OR models made the life or death difference for this company’” Kevin Geraghty, Aeronomics Inc. 15 w © 2005 by Peter C. Bell
  15. 15. and .. on the other side: RM used by the competition has bankrupted several corporations .. the clearest example being Peoples’ Express Airlines. 16 w © 2005 by Peter C. Bell
  16. 16. Donald Burr, Founder and CEO of People Express “believes that major carrier’s use of sophisticated computer programs to immediately match or undercut his prices ultimately killed People Express” 17 w © 2005 by Peter C. Bell
  17. 17. WHO USES RM? • AIRLINES (All?) • HOTELS (Hyatt, Marriott, Hilton, Sheraton, Forte, Disney ..) • VACATIONS (Club Med, Princess Cruises, Norwegian ..) • CAR RENTAL (National, Hertz, Avis, Europcar ..) • WASHINGTON OPERA • FREIGHT (Sea-Land, Yellow Freight, Cons. Freightways ..) • TELEVISION ADS (CBC, ABC, NBC, TVNZ, Aus7 ..) • UPS, SNCF • RETAIL (Retek, Khimetrics) • REAL ESTATE (Archstone) • NATURAL GAS • TEXAS CHILDREN’S HOSPITAL 18 w © 2005 by Peter C. Bell
  18. 18. AGENDA: • Introduction • What is revenue management, who uses it and what has been the impact? • The five pillars of RM – Pricing, discount allocation, overbooking, trading up and re-planing • Integrating the tools • Conclusions 19 w © 2005 by Peter C. Bell
  19. 19. THE 5 PILLARS OF RM • New approaches to pricing • Discount allocation • Trading-up • Overbooking • Re-planing • + markdown optimization, purchase loans, etc 20 w © 2005 by Peter C. Bell
  20. 20. NEW APPROACHES TO PRICING PRODUCTS AND SERVICES 21 w © 2005 by Peter C. Bell
  21. 21. THE NEW PRICING CONCEPT • Use product price as a management control variable. • Set this price “optimally” to various customer groups or “clusters”. • Be prepared to change prices often. 22 w © 2005 by Peter C. Bell
  22. 22. THE “CONCEPTUAL LEAPS” • “Products” do not have a value, rather the value of a product depends on the point in time of purchase. • “Products” have different values to different clusters of customers. 23 w © 2005 by Peter C. Bell
  23. 23. DEMAND AT A POINT IN TIME BY A CUSTOMER CLUSTER DRIVES RM PRICING MARKET SEGMENTATION IS THE KEY TO ENHANCING REVENUES THROUGH RM PRICING 24 w © 2005 by Peter C. Bell
  24. 24. A MARKET Q = F(P,……..) Price Quantity Sold 25 w © 2005 by Peter C. Bell
  25. 25. SEGMENTING A MARKET Q = F(P,……..) becomes qi = Fi(pi,…..) for i = 1,…N Price Market Segmentation Quantity Sold 26 w © 2005 by Peter C. Bell
  26. 26. MARKET SEGMENTATION: METHODS • Time of purchase • Customer characteristics (seniors, others) • Sales channel (“clicks” and “bricks”) • Offer a discount to large customers • Offer a discount for slow delivery ++ 27 w © 2005 by Peter C. Bell
  27. 27. Example of market segmentation Coke price rises with heat Vending machine that alters price with temperature change is possible NEW YORK (CNNfn) - It's not the New Coke, but it may be the Smart Coke. Soft-drink giant Coca-Cola Co. is working on a vending machine that automatically raises the price of a soda whenever the weather grows hot. Coke chairman Doug Ivester said the machine was designed to reconcile supply and demand by raising the price when demand increased. quot;Coca-Cola is a product whose utility varies from moment to moment,quot; he was quoted as saying. 28 w © 2005 by Peter C. Bell
  28. 28. “CLUSTERING” CUSTOMERS • Different groups of customers value a product differently – Example: • “Business class” air customers value convenience, comfort, flexibility • “Economy class” customers value low prices, (and perhaps longer stays, advance reservations) • “Clustering” means assigning customers to “clusters” or “market segments” 29 w © 2005 by Peter C. Bell
  29. 29. An example of “clusters” • E-Bivalent Newbies (5% of online shoppers) – Newest to Net, somewhat older, spends least online, likes online least • Time Sensitive Materialists (17%) – Most interested in convenience, less likely to read reviews or compare prices • Clicks and Mortar (23%) – Browse online, prefers to buy offline, more likely female, has privacy and security concerns, goes to malls often • Hooked, Online and Single (16%) – More likely young, single males with high incomes, have been on Net longest, most likely to play games, download, bank online • Hunter-Gatherers (20%) – Typically 30-49 years old, two kids, most likely to visit sites that provide information and comparison • Brand Loyalists (19%) – Most likely to bypass search engines to go directly to sites they know, most satisfied with shopping online, spend most online -- Harris Interactive study of 3,000 Internet Shoppers, 2000 30 w © 2005 by Peter C. Bell
  30. 30. CHANGING PRODUCT VALUE OVER TIME (“time segmentation”) • Perishable products that age, • Seasonality, • Some customers will pay for the security of early purchase, or for the flexibility of late purchase, • Suppliers may attach value to the security of early sales………. 31 w © 2005 by Peter C. Bell
  31. 31. CHANGING DEMAND OVER TIME Example: PERISHABLE PRODUCTS Demand Segment 1 S2 S3 Time 32 w © 2005 by Peter C. Bell
  32. 32. CHANGING DEMAND OVER TIME Example: EVENT or TRIP TICKETS Demand Time Event Date 33 w © 2005 by Peter C. Bell
  33. 33. CHANGING DEMAND OVER TIME Example: EVENT or TRIP TICKETS Demand Time Event Date 34 w © 2005 by Peter C. Bell
  34. 34. Common Demand Models Q = Quantity sold p = price/unit Linear demand: Q=A–Bp Usually maximum and minimum prices are specified Constant elasticity demand: Q = A p-e where e is the price elasticity of demand 35 w © 2005 by Peter C. Bell
  35. 35. LINEAR APPROXIMATION OF DEMAND CURVE Demand Curve Price Linear Approximation Quantity Sold 36 w © 2005 by Peter C. Bell
  36. 36. MODEL CHOICE MAY NOT BE OBVIOUS DEMAND EQUATION ESTIMATION 70 60 50 Quantity 40 30 20 10 0 $100.00 $150.00 $200.00 $250.00 Price Q = 92.1 - .37 P R2 = 0.95 Q= 2170037377 P-3.59 R2 = 0.95 37 w © 2005 by Peter C. Bell
  37. 37. General Demand Function In general, for any time period and cluster: Q = F(P, Ps, Pc, X1, X2, ….) • where: • P = price of product • Ps = price of substitute products • Pc = price of complement products • Xi are exogenous variables (weather, economic factors, advertising…etc) 39 w © 2005 by Peter C. Bell
  38. 38. Estimating Demand Demand estimation is a craft: firms tend to keep this part of their RM confidential. Two steps are required: 1. Build a demand model (off-line). Common techniques include regression, curve fitting, and cluster analysis. 2. Develop an on-line demand model updating procedure to respond immediately to unexpected observed demand. 40 w © 2005 by Peter C. Bell
  39. 39. “LEAKAGE” • Demand “leakage” (from a high priced segment to a low priced segment) occurs when segmentation is not perfect. Q1 = F1(p1…) – L(p1 – p2) Q2 = F2(p2…) + L(p1 – p2) where p1 > p2 41 w © 2005 by Peter C. Bell
  40. 40. “FENCES” • Revenue will disappear unless market segments are kept separate to limit “leakage” from high priced segments to low priced segments. • Tools to maintain segment separation are called “fences”. Examples of fences: – The fee airlines charge to modify a low fare ticket (usually $150-200). – The requirement for a Saturday night stopover for a low fare ticket. – Booking and paying 90 (or 60, or 30) days in advance. Look for examples of creative fences! 42 w © 2005 by Peter C. Bell
  41. 41. Pricing Approaches to Revenue Maximization – Traditional fixed pricing – Variable pricing – Optimum dynamic pricing • Computing optimum prices 43 w © 2005 by Peter C. Bell
  42. 42. Single price: 2 market segments Revenue = p (Q1 + Q2) There is usually a p* that Price optimizes revenue. p Q1 Q2 Quantity Sold 44 w © 2005 by Peter C. Bell
  43. 43. Two prices: 2 market segments Revenue = p1Q1 + p2Q2 Price If p1* and p2* maximize revenue then: p1 p1*Q1 + p2*Q2 ≥ p*(Q1 + Q2) p2 Q1 Q2 Quantity Sold 45 w © 2005 by Peter C. Bell
  44. 44. Formal statement of deterministic ODP problem (time segments) Let: pi be the product price in period i, qi be the quantity sold in period i, qi = fi (pi) be the demand curve for period i, and I be the inventory to be sold over N pricing periods. then: ∑ N Max Z = pi qi i =1 Subject to: qi = fi (pi) for i = 1, ......N ∑ N qi = I i =1 46 w © 2005 by Peter C. Bell
  45. 45. Deterministic ODP problem with forecast errors Let: pi be the product price in period i, qi be the quantity sold in period i, qi = fi (pi) be the demand curve for period i, and I be the inventory to be sold over N pricing periods. then: For each period, k, k = 1,2,...N ∑ N Z= piqi Max i=k Subject to: qi = fi (pi) + error for i = k, k+1, ......N ∑ ∑ k −1 N qi = I − qi i= k i =1 49 w © 2005 by Peter C. Bell
  46. 46. ACCEPT/REJECT DECISION MAKING RM algorithms are mostly “accept/reject” rules. If a customer appears and offers to buy a unit for $P, do you accept (in which case you give up the opportunity to sell the same unit to a later arriving customer who may pay more than $P), or do you reject (in which case you give up $P in the hope of selling the unit later >$P but may not sell the unit). The issue is one of balancing “yield loss” and “spoilage”. 52 w © 2005 by Peter C. Bell
  47. 47. Revenue optimization drove the entry of RM into services. - non-replenishable inventories, - low (zero?) variable cost of providing product. For restockable items, contribution optimization can be more difficult. - role of inventory and replacement policies, - need for “profitable market share”. 53 w © 2005 by Peter C. Bell
  48. 48. The Single-Period Stochastic Optimum Pricing Problem Define: • p - the price (a decision variable), • c - the variable production cost (c < p), • I - the quantity available for sale (which may be a decision variable), • h - holding cost per unit of inventory unsold at the end of the period, • u - shortage cost per unit of unsatisfied demand, • q = D(p, ξ) be the demand function where ξ is a random variable with density function f(ξ). The contribution, π, depends on the random demand: qp − cI − h ( I − q ) q<I π ( p, I ) =   I ( p − c) − u (q − I ) q≥I The firm must chose values for the decision variables (p and I) based on expected contribution, E(π), which depends on the forecast of the random demand q: 54 w © 2005 by Peter C. Bell
  49. 49. Inventory/SC models vs. RM models • Most inventory and supply chain models assume demand (Q) is given. • RM models replace given demand (Q) with a given demand curve [F(p)]. The firm must optimize p (and hence determine Q) and simultaneously optimize inventory. • Many research opportunities. 55 w © 2005 by Peter C. Bell
  50. 50. 56 w © 2005 by Peter C. Bell
  51. 51. THE 5 PILLARS OF RM • Optimum dynamic pricing • Discount allocation • Trading-up (or planned upgrades) • Overbooking • Re-planing (or short selling) • + markdown optimization, purchase loans, etc 57 w © 2005 by Peter C. Bell
  52. 52. Discount allocation • Multiple prices for the same units – Multi-day packages (hotels, rental cars) – Singles and 10-packs – A ski hill had 22 different packages covering the same ski session • Issue: how many units to allocate to each discount package price (the “reservation level”)? 58 w © 2005 by Peter C. Bell
  53. 53. Discount allocation: Solver example 59 w © 2005 by Peter C. Bell
  54. 54. Discount allocation: hotel example 60 w © 2005 by Peter C. Bell
  55. 55. DYNAMICS OF MULTIPLE DISCOUNT PACKAGES AND PRICE CATEGORIES Issue: If a customer appears and demands the low fare or discount package, when do you say “No” in order to preserve product for the higher paying customers? Example: How many “full fare economy” seats on the plane? 61 w © 2005 by Peter C. Bell
  56. 56. Reservation rule (Littlewood 1972) Issue: How many units (seats) to reserve for low price sale? Continue to sell discount product at time t until: r ≥ (1 - Pt) R or (1 - Pt) ≤ r / R Where: r = low price (marginal revenue) R = high price (marginal revenue) Pt = probability of selling at least the remaining number of units. 62 w © 2005 by Peter C. Bell
  57. 57. EMSR Heuristic (Expected Marginal Seat Revenue) Belobaba 1987 Apply Littlewood’s rule sequentially to fare classes in increasing fare order. Let µi ,σi be the estimates of mean and std. deviation of demand for product class i with price pi Set a reservation (or protection) level of Li so that pi+1 = Pi P(Xi > Li) Where Pi is the weighted average fare for classes 1,2,,,,,I And Xi is a normal random variable convoluting demand for classes 1,2,….i 64 w © 2005 by Peter C. Bell
  58. 58. Protection levels: Expected MR curves 65 w © 2005 by Peter C. Bell
  59. 59. Overbooking (aka overselling) Issue: Should you take more orders than you have product in the expectation that some customers who have ordered will not collect the product? • If so, how many extra orders should you take and when? – P{cancel order} declines as delivery date approaches 66 w © 2005 by Peter C. Bell
  60. 60. OVERBOOKING: EXAMPLES • airline seats, and passenger train seats, are usually booked in advance of the date of travel, • rental cars can be reserved ahead of the day of rental, • hotel rooms and campsite spaces, seats for stage shows, sports events, and concerts are sold in advance, • fresh turkeys can be ordered for delivery at thanksgiving, • package vacations and cruises are usually booked in advance, • tuxedos, cut flowers, some baked goods, etc. are commonly booked for future delivery 67 w © 2005 by Peter C. Bell
  61. 61. Managing the overbooked customer A key cost in all the models • Airlines offer cash or travel coupons to ticketed customers in order to persuade them to take an alternate flight when space is needed for overbooked passengers. • Hotels will trade up overbooked customers to rooms on the executive floor, • Rental car companies will substitute a higher class of car at no extra charge. In all these cases, the cost is well know. 68 w © 2005 by Peter C. Bell
  62. 62. Minimizing the “no show” rate If all customers with reservations showed up, there would be no benefit from overbooking • Require payment at the time the booking is made, perhaps offering an early payment price reduction. • Require payment in full at some prearranged time in advance of the delivery date. If payment is not received, the supplier cancels the booking. • Fees may be charged if a booking is changed. 69 w © 2005 by Peter C. Bell
  63. 63. Overbooking: the basic model M = the amount of product B = the booking limit (B ≥ M) RN = the value of sale of unit N with RN+1 ≤ RN, Ci = cost of satisfying the ith overbooked customer if no product is available, Ci+1 ≥ Ci P[Q|B] = probability that Q customers will show up if we sell B units. The expected cost of unsold product is: {(RQ+1 + RQ+2 +...+ RM) P[Q|B] } summed over all values of Q < M The expected cost of handling oversold customers is: {(C1 + C2 +...+ CQ-M) P[Q|B] } summed over all values of Q > M Find B that minimizes the sum of these two expected costs. 70 w © 2005 by Peter C. Bell
  64. 64. Overbooking: Determining the optimal level 71 w © 2005 by Peter C. Bell
  65. 65. Trading up (planned upgrades) Issue: If a customer appears demanding a product that is sold out, should you trade the customer up to a higher valued product (at your expense)? Issue B. If you adopt this as policy, what does this do to your inventory management? 73 w © 2005 by Peter C. Bell
  66. 66. Re-planing Issue: If a plane is sold out several days before flight date and a customer appears prepared to pay a “high” price for that flight, can you profitably “incentivize” a low-fare paid customer to change flights? 2001 McKinsey, CALEB Technologies, American Airlines 74 w © 2005 by Peter C. Bell
  67. 67. Other RM tools • “Markdown optimization” is common in retail (Retek, Manugistics, Spotlight): This is really price optimization with non-increasing prices. – The benefits are claimed to be very substantial • “Bottleneck optimization” (Maxager Tech.) is price optimization where “inventory” is production time on the scarce production unit. • There are others but all seem to be variations on the 5 basic tools. 75 w © 2005 by Peter C. Bell
  68. 68. AGENDA: • Introduction • What is revenue management, who uses it and what has been the impact? • The five pillars of RM – Pricing, discount allocation, overbooking, trading up and re-planing • Integrating the tools • Conclusions 76 w © 2005 by Peter C. Bell
  69. 69. Integration • Although these tools are almost always discussed separately, they all function within a highly integrated system 77 w © 2005 by Peter C. Bell
  70. 70. PRICES RESERVATION LEVELS 78 w © 2005 by Peter C. Bell
  71. 71. CAPACITY PRICES RESERVATION LEVELS 79 w © 2005 by Peter C. Bell
  72. 72. CAPACITY OVERBOOKING LEVEL PRICES RESERVATION LEVELS 80 w © 2005 by Peter C. Bell
  73. 73. CAPACITY OVERBOOKING LEVEL PRICES RESERVATION LEVELS PLANNED UPGRADES 81 w © 2005 by Peter C. Bell
  74. 74. CAPACITY OVERBOOKING LEVEL PRICES REPLANE LEVEL RESERVATION LEVELS PLANNED UPGRADES 82 w © 2005 by Peter C. Bell
  75. 75. CAPACITY OVERBOOKING LEVEL PRICES REPLANE LEVEL RESERVATION LEVELS PLANNED UPGRADES 83 w © 2005 by Peter C. Bell
  76. 76. Update Real time Database Historical Data Product Sales Sales Data Revise Demand Model Current Inventory Build The Demand Levels Demand Model Market Forecasts Off-line Support Activities Pricing Posted Prices System Revenue Management System 84 w © 2005 by Peter C. Bell
  77. 77. REQUIREMENTS FOR SUCCESS • SUPERIOR INFORMATION TECHNOLOGY, • SUPERIOR OPERATIONS RESEARCH SKILLS, and • THE ABILITY TO MANAGE DYNAMIC PRICES. 85 w © 2005 by Peter C. Bell
  78. 78. AGENDA: • Introduction • What is revenue management, who uses it and what has been the impact? • The five pillars of RM – Pricing, discount allocation, overbooking, trading up and re-planing • Integrating the tools • Conclusions 86 w © 2005 by Peter C. Bell
  79. 79. BUSINESS OPPORTUNITIES A great number of products seem ripe for RM. Some examples: Cinemas, golf courses, electricity, taxis, public transit, newspapers and magazines, advertising, fashion clothing, blue jeans, vegetables, fast food, supermarkets, sports events, theatre, pop concerts,…… 87 w © 2005 by Peter C. Bell
  80. 80. RESEARCH OPPORTUNITIES Academic Almost every “inventory” model can be extended to include a demand curve (some already have been!) Accept/reject decision heuristics (Bayesian) Application The merger of SC optimization and RM (“EPO”) Clustering New and improved “fencing” Demand modeling (how good does it need to be?) 88 w © 2005 by Peter C. Bell
  81. 81. CONCLUSIONS RM tools have become very important for both business and OR There are opportunities for many new revenue maximizing models and pricing/inventory models Heuristics to aid implementation are a priority Competitive models provide an opportunity The competitive customer Competition among RM firms 89 w © 2005 by Peter C. Bell
  82. 82. CONCLUSIONS RM techniques raise many business issues: winning firms will be able to implement these ideas while keeping customers (and regulators) happy. Everyone gains from the efficiencies that RM produces, but some individuals lose. Successful implementation usually requires taking good care of the few who lose. 90 w © 2005 by Peter C. Bell
  83. 83. 91 w © 2005 by Peter C. Bell

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