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Mathematical Hotel Revenue Optimization

Mathematical Hotel Revenue Optimization. Robert Hernandez, Hotel Data Science. Origin World Labs. robert@originworld.com. Mathematical Reasoning for Hotel Revenue Management Decision Making. Robert Hernandez, Hotel Data Science. Origin World Labs. robert@originworld.com. Randomness in RM.

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Mathematical Hotel Revenue Optimization

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  1. Mathematical Hotel Revenue Optimization Robert Hernandez, Hotel Data Science Origin World Labs robert@originworld.com Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

  2. Mathematical Reasoning for Hotel Revenue Management Decision Making Robert Hernandez, Hotel Data Science Origin World Labs robert@originworld.com Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

  3. Randomness in RM Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization • Every problem in RM involves uncertainty. • Uncertainty means that a process is random. • Website visits • Conversions • Calls to reservations • Booking a room • Group sales • Restaurant visits • Check-in • No shows • Cancellations • We need to count how often we can expect a random event to occur. • How often an event occurs if the FREQUENCY.

  4. Counting Frequency 5 1 2 3 4 6 7 Day 10 8 5 8 9 8 5 Reserv 5 8 9 10 Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

  5. Probability 5 8 9 10 Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

  6. How spread out is the data Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization Two Parameters Average Standard Deviation

  7. Normal Distribution Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

  8. Normal Distribution Excel 1 - NORM.DIST(number of rooms, average, standard deviation, TRUE) Given an average and a standard deviation, you can get the # of rooms that will be sold with a certain probability. NORM.INV(1-specific probability, average, standard deviation) Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization Given an average and a standard deviation, you can get the probability that any # of rooms will be sold.

  9. How we describe our data file Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization Two Parameters Average Standard Deviation

  10. Segment(i.e. Slice and Dice) Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization by Month by Period by Market by Channel by Days Out

  11. Expected Value Reward x Chance of Reward = Rational, Long term Expected Value (Law of Very Large Numbers) Core Assumption of all Decision Sciences The Blue Pill Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization If the scenario plays out many times.

  12. The Lottery Costs $2 to play ($150MM) * .000000578% = $.86 - $2 * 99.9999994% = - $2 Rational Expected Value -$1.14 Lottery – Tax on people that don’t know math. Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization Powerball odds 1/173,000,000 = .000000578% chance of winning.

  13. History of Capacity Control Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization Inherited from Airline Yielding. Accommodate business people. Fill up with economy. Marketing delivered the rates Operations Research calculated controls. Published on paper.

  14. Capacity Control Top 30@$500 Frequent 20@$300 Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

  15. Littlewood’s Rule I will switch to selling to my better class when the EV for that rate is higher than my lower class rate. > Rate2 Prob1 Rate1 x > Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

  16. Expected Marginal Seat Revenue > Rate(w.avg lower classes) Rate1 Prob1 x > Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

  17. Expected Marginal Seat Revenue > Rate(w.avg lower classes) Rate2 Prob2 x > Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

  18. Fundamental Model of Demand How many units can I sell at each price point? High We’d like to put this relationship into a mathematical model. Demand Curve Quantity (Q) Low Prices (P) Low High Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

  19. Fundamental Model of RM How many rooms can I sell at each rate? High Hotel Demand Curve Rooms (Q) Low Rate (P) Low High Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

  20. Fundamental Model of RM Data Point 2. How many rooms sold when we charge a high rate? (H,L) (L,H) Data Point 1 High Rooms (Q) (H,L) Data Point 2 Low Low Rate (P) High Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization Data Point 1. How many rooms sold when we charge a low rate? (L,H)

  21. Core Assumption of Demand Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

  22. Core Assumption of Demand Those that paid a higher price will pay a lower price. The Blue Pill Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

  23. Core Assumption of Demand 8 5 3 1 Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

  24. Demand Estimate Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

  25. Equation of a Line Y = SLOPE. X + INTERCEPT Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

  26. Equation of a Line Y = SLOPE. X + INTERCEPT INTERCEPT SLOPE Rooms = SLOPE. Rate + INTERCEPT Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

  27. The SLOPE Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

  28. The SLOPE High Rooms Sold – Low Rooms Sold Slope = Low Rate – High Rate Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

  29. Intercept Rooms = SLOPE. Rate + INTERCEPT Rooms - SLOPE. Rate = INTERCEPT Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

  30. Demand Example 8 5 3 1 Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

  31. Demand Formula Rooms = SLOPE. Rate + INTERCEPT (1,400) , (8,100) Rooms = -.023. Rate + 10.33 Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

  32. Revenue Formula Rooms = SLOPE. Rate + INTERCEPT Revenue = Rate . Rooms Revenue = Rate . (SLOPE. Rate + INTERCEPT) Revenue = SLOPE. Rate2+ Rate.INTERCEPT Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

  33. Revenue Formula Revenue = Rate . (-.023. Rate + 10.33) Revenue = -.023. Rate2+ Rate.10.33 Revenue = -.023. 1002+ 100 .10.33 Revenue = -.023. 10,000 + 100 .10.3 Revenue = -.023. 10,000 + 1030 = 800 Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

  34. Revenue Formula Graph Revenue = -.023. Rate2+ Rate.10.33 Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

  35. Derivative of Revenue Formula Der of Revenue = SLOPE. Rate2+ Rate.INTERCEPT Der of Revenue = 2 .SLOPE. Rate + INTERCEPT Marginal Revenue = 2 .SLOPE. Rate + INTERCEPT Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

  36. Marginal Revenue Formula Mar Revenue = -.023. Rate2+ Rate.10.33 Mar Revenue = 2 .-.023. Rate + 10.33 Mar Revenue = -.046 . Rate + 10.33 Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

  37. Derivative of Revenue Graph Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

  38. Optimal Rate Mar Revenue = -.046 . Rate + 10.3 0= -.046 . Rate + 10.3 10.3/ .046 = Rate 223.91 = Opt Rate Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

  39. Rate Formula Rooms = SLOPE. Rate + INTERCEPT Rooms - INTERCEPT= Rate SLOPE Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

  40. Micro Optimization Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization Recognition of Multiple Simultaneous Demand Patterns. Isolate data for each demand. Utilize Dimensions to Micro-Segment Event | Market | Room Type | Source | VIP | Package | Promo

  41. Micro Optimization Market Channel Room Type Bed Type Period Date Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

  42. Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization Thank You robert@originworld.com 786.704.2277

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