Forecasting and Aggregate Planning

Forecasting and Aggregate Planning

Revenue Management Chapter 13 1 Learning Goals Yield management (with protection levels) and overbooking give demand flexibility where supply flexibility is not possible. The Newsvendor model can be used: Single decision in the face of uncertainty. Underage and overage costs. 2 Revenue (Yield) Management 3 Some U.S. airline industry observations

Since deregulation in 78, 137 carriers have filed for bankruptcy until 2006. From 95-99 (the industrys best 5 years ever) airlines earned 3.5 cents on each dollar of sales: The US average for all industries is around 6 cents. From 90-99 the industry earned 1 cent per $ of sales. Carriers typically fill 72.4% of seats while the break-even load is 70.4%. - Utilization is about 3% higher in 2007-08 perhaps due to flight cancellations. Gas prices are high and will remain so. Downsize airlines Merge. Domestic/international Alternate transportation means High speed train 4

Matching supply to demand when supply is fixed Examples of fixed supply: Travel industries (fixed number of seats, rooms, cars, etc). Advertising time (limited number of time slots). Telecommunications bandwidth. Size of the MBA program. Doctors availability for appointments. Revenue management is a solution: If adjusting supply is impossible adjust the demand! Segment customers into High willingness to pay Low willingness to pay. Limit the number of tickets sold at a low price, i.e., control the average price by changing the mix of customers.

5 Environments suitable for revenue management The same unit of capacity (e.g., airline seat) can be used to deliver services to different customer segments (e.g., business and leisure customers) at different prices. High gross margins (so the variable cost of additional sales is low). Perishable capacity (it cannot be stored) and limited capacity (all possible customers cannot always be served). Capacity is sold in advance of demand: Costly adjustment of sold capacity. There is an opportunity to segment customers (so that different prices can be charged) and different segments are willing to pay different prices. It is not illegal or morally irresponsible to discriminate the customers. Is Revenue management for incoming MBA class possible? 6 Revenue Management: Booking limits and protection levels 7 The Park Hyatt Philadelphia 118 King/Queen rooms. Hyatt offers a rL= $159 (low fare) discount fare for a mid-week stay, targeting leisure travelers. Regular fare is rH= $225 (high fare) targeting business travelers.

Demand for low fare rooms is abundant. Let D be uncertain demand for high fare rooms. Suppose D has Poisson distribution with mean 27.3. Assume most of the high fare (business) demand occurs only within a few days of the actual stay. Objective: Maximize expected revenues by controlling the number of low fare rooms sold. 8 Yield management decisions 1.

The booking limit is the number of rooms to sell in a fare class or lower. The protection level is the number of rooms you reserve for a fare class or higher. Let Q be the protection level for the high fare class. Q is in effect while selling low fare tickets. Since there are only two fare classes, the booking limit on the low fare class is 118 Q: You will sell no more than 118-Q low fare tickets because you are protecting (or reserving) Q seats for high fare passengers. 0 Sell no more than the low fare booking limit, 118 - Q 118 Q seats protected for high fare passengers 9 The connection to the newsvendor

A single decision is made before uncertain demand is realized. There is an overage cost: D: Demand for high fare class; Q: Protection level for high fare class If D < Q then you protected too many rooms (you over protected) ... so some rooms are empty which could have been sold to a low fare traveler. There is an underage cost: If D > Q then you protected too few rooms (you under protected) so some rooms could have been sold at the high fare instead of the low fare. Choose Q to balance the overage and underage costs. 10 Optimal protection level Overage cost: If D < Q we protected too many rooms and earn nothing on Q - D rooms.

We could have sold those empty rooms at the low fare, so Co = rL. Underage cost: If D > Q we protected too few rooms. D Q rooms could have been sold at the high fare but were sold instead at the low fare, so Cu = rH rL Optimal high fare protection level: F (Q* ) Cu r r H L C o Cu rH Optimal low fare booking limit = 118 Q* Choosing the optimal high fare protection level is a Newsvendor problem with properly chosen underage and overage costs. 11

Hyatt example Critical ratio: Poisson distribution with mean 27.3 Cu r r 225 159 66 h l 0.2933 Co Cu rh 225 225 Q F (Q ) L (Q ) Q F (Q ) L (Q ) Q F (Q ) L (Q ) 10 0.0001 17.30 20 0.0920 7.45 30 0.7365 1.03 11 0.0004 16.30 21 0.1314 6.55 31 0.7927 0.77

12 0.0009 15.30 22 0.1802 5.68 32 0.8406 0.56 13 0.0019 14.30 23 0.2381 4.86 33 0.8803 0.40 14 0.0039 13.30 24 0.3040 4.10 34 0.9121 0.28 15 0.0077 12.31 25 0.3760 3.40 35 0.9370 0.19 16 0.0140 11.31 26 0.4516 2.78 36 0.9558 0.13 17 0.0242 10.33 27 0.5280 2.23 37 0.9697 0.09 You can also use poisson(Q,mean=27.3,1)=0.29 Excel function to solve 18 0.0396 9.35 28 0.6025 1.76 38 0.9797 0.06 for Q. 19 0.0618 8.39 29 0.6726 1.36 39 0.9867 0.04 Answer: 24 rooms should be protected for high fare travelers. Similarly, a booking limit of 118-24 = 94 rooms should be applied to low fare reservations. 12

Related performance measure calculations How many high-fare travelers will be refused a reservation? Expected lost sales = 4.10, From Table 13.2 How many high-fare travelers will be accommodated? Expected sales = Expected demand - Lost sales = 27.3 - 4.1 = 23.2 How many seats will remain empty? Expected left over inventory = Q - Expected sales = 24 - 23.2 = 0.8. What is the expected revenue assuming all low fare rooms are sold $225 x Exp. Sales(=23.2) + $159 x Booking limit(=118-24=94) = $20,166. Without yield management worst case scenario is selling all the rooms at the low fare and making $159 x 118 = $18,762. With revenue management revenue increases by (20,166-18,762)/18,762=7.5% 13

Example: Bulk Contracts Most consumers of production, warehousing, and transportation assets face the problem of constructing a portfolio of long-term bulk contracts and short-term spot market contracts Long-term contracts for low cost Short-term contracts for flexibility The basic decision is the size of the bulk contract The fundamental trade-off is between wasting a portion of the lowcost bulk contract and paying more for the asset on the spot market 14 Example: Bulk Contracts For the simple case where the spot market price is known but demand is uncertain, a formula can be used cB = bulk rate cS = spot market price Q* = optimal amount of the asset to be purchased in bulk Overage cost of buying too much in bulk: cB. Underage cost of buying too little in bulk: cS- cB. F (Q * ) Cu c c S B C o Cu cS 15 Numerical Example for Bulk Contracts: Buying transportation capacity to bring goods from China Bulk contract cost = cB = $10,000 per million units Spot market cost = cS = $12,500 per million units Normal monthly Demand for transportation: = 10 million units, = 4 million units Q* = Norminv((12.5-10/12.5),10,4) million units The manufacturer should sign a long-term bulk contract for Q* million units per month and purchase any transportation capacity beyond that on the spot market. 16 Revenue Management: Overbooking 17

Ugly reality: cancellations and no-shows Approximately 50% of reservations get cancelled at some point in time. In many cases (car rentals, hotels, full fare airline passengers) there is no penalty for cancellations. Problem: the company may fail to fill the seat (room, car) if the passenger cancels at the very last minute or does not show up. Solution: sell more seats (rooms, cars) than capacity. Danger: some customers may have to be denied a seat even though they have a confirmed reservation. Passengers who get bumped off overbooked domestic flights to receive Up-to $400 if arrive <= 2 hours after their original arrival time Up-to $800 if arrive >= 2 hours after their original arrival time According to April 16, 2008 decision of the Transportation Department 18 Hyatts Problem The forecast for the number of customers that do not show up ( X ) is Poisson with mean 8.5. The cost of denying a room to the customer with a confirmed reservation is $350 in ill-will (loss of goodwill) and penalties. How many rooms (y) should be overbooked (sold in excess of capacity)? Newsvendor setup: Single decision when the number of no-shows in uncertain. Insufficient overbooking: Overbooking demand=X >y=Overbooked capacity. Excessive overbooking: Overbooking demand=X

Underage cost when insufficient overbooking if X >y then we could have sold X-y more rooms to be conservative, we could have sold those rooms at the low fare, Cu = rL. Overage cost when excessive overbooking if X 20 Optimal overbooking level Poisson distribution with mean 8.5 Q 0 1 2 3 4 5 6 7 8 9 F (Q ) 0.0002 0.0019 0.0093

0.0301 0.0744 0.1496 0.2562 0.3856 0.5231 0.6530 Q 10 11 12 13 14 15 16 17 18 19 F (Q ) 0.7634 0.8487 0.9091 0.9486 0.9726 0.9862 0.9934

0.9970 0.9987 0.9995 Optimal number of overbooked rooms is y=7. Hyatt should allow up to 118+7 reservations. There is about F(6)=25.62% chance that Hyatt will find itself turning down travelers with reservations. 21 Revenue Management: Complications 22 Revenue management challenges Demand forecasting. Wealth of information from reservation systems but there is seasonality, special events, changing fares and truncation of demand data.

Dynamic decisions. Variable capacity: Different aircrafts, ability to move rental cars around. Group reservations; Cargo overbooking. How to construct good fences to differentiate among customers? One-way vs round-trip tickets. Saturday-night stay requirement. Non-refundability. Advanced purchase requirements. Multi-leg passengers/multi-day reservations for cars and hotels: 23

A solution to the multi-leg customer: buckets Heathrow OHare JFK With segment control there are only three booking limits for the OHare-JFK leg, one for each fare class. But an OHare-Heathrow customer may be more valuable, so you could have six booking limits, one for each fare-itinerary combination. But that leads to many booking limits, so group similar fare-itineraries into buckets: Fare class Y M Q

O'Hare to JFK $724 $475 $275 Bucket Itinerary 0 1 2 3 O'Hare to Heathrow O'Hare to Heathrow O'Hare to JFK O'Hare to Heathrow O'Hare to JFK O'Hare to JFK O'Hare to Heathrow $1,610 $829 $525 Fare class Y

M Y Q M Q 24 Another solution to multi-legs: bid prices Heathrow Fare class Y M Q OHare JFK Bid price O'Hare to JFK $724 $475 $275

O'Hare to JFK $290 O'Hare to Heathrow $1,610 $829 $525 JFK to Heathrow $170 Assign a bid price to each segment: A fare is accepted if it exceeds the sum of the bid prices on the segments it uses: For example, an OHare-JFK fare is accepted if it exceeds $290 A OHare-Heathrow fare is accepted if it exceeds $290+$170 = $460 The trick is to choose good bid-prices. 25 Summary

Yield management (with protection levels) and overbooking give demand flexibility where supply flexibility is not possible. The Newsvendor model can be used: Single decision in the face of uncertainty. Underage and overage costs. These are powerful tools to improve revenue: American Airlines estimated a benefit of $1.5B over 3 years. National Car Rental faced liquidation in 1993 but improved via yield management techniques. Delta Airlines credits yield management with $300M in additional revenue annually (about 2% of year 2000 revenue.) 26 Summary of the Course Modules

1. Flow analysis 2. Formulations 3. Queues 4. Quality 5. Inventory 6. Revenue management The efficient transformation of inputs into outputs to suitably satisfy customers. 27 The End My teaching is over Your learning is forever Towards better Do not give up ever


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