Key Topics: Seasonality and exponential smoothing in time-series forecasting.

MARRIOTT ROOMS FORECASTING "A hotel room is aperishable good. If it is vacant for one night, the revenue is lost forever.\" Linda Snow was commenting on the issue of capacity utilization in the hotel business. "On the other hand, the customer is king with us. We go to great pains to avoid telling a customer with a reservation at the front desk that we don't have a room for him in the hotel." As reservation manager of one of Marriott's hotels, Snow faced this tradeoff constantly. To complicate the matter, customers often booked reservations and then failed in show, or cancelled reservations just before their expected arrival. In addition, some guests stayed over in the hotel extra days beyond their original reservation and others checked out early. A key aspect of dealing with the capacityemanagement problem was having a good forecast ofhow many rooms would be needed on any future date. It was Snow's responsibility to prepare a forecast on Tuesday aftemoon of the number ofrooms that would be occupied each day of the next week (Saturday through Friday). This forecast was used by almost every department within the hotel for avariety of purposes; now she needed the forecast for a decision in her own department Hamilton Hotel The Hamilton Hotel was a large downtown business hotel with 1,877 rooms and abundant meeting space for groups and conventions. It had been built and was operated by Marriott Hotels, a company that operated more than 180 hotels and resorts worldwide and was expanding rapidly into other lodgingemarket segments. Management at the Hamilton reported regularly to Marriott Corporation on both occupancy and revenue performance. .2- Hotel managers were rewarded for their ability to meet targets for occupancy and revenue. Snow could not remember a time when the targets went down, but she had seen them goup in the two years since she took the job asreservation manager. The hotel managers were continuously comparing forecasts of performance against those targets. In addition to overseeing the reservations ofce with eight reservationists, Snow prepared the following week's forecast and on Tuesday aemoon, she presented it to other department managers in the hotel. The forecast was used toschedule, for example, daily work assignments for housekeeping personnel, the clerks at the front desk, restaurant personnel, and others. It also played a role inpurchasing and revenue, and cost planning. Overbooking At the moment, however, Snow needed her forecast to know how to treat an opportunity that was developing for next Saturday. It was Tuesday, August 18, 1987, and Snow's forecasts were due by midaftemoon for Saturday, August 22 through Friday, August 28. Although 1,839 rooms were already reserved for Saturday, Snow had just received a request om a tour company for as many as 60more rooms for that night. The tour company would take any number of rooms less than 60that Snow would provide, but no more than 60. Normally Snow would be ecstatic about such a request: selling out the house for a business hotel on a Saturday would be a real coup. The request, in its entirety, put reservations above the capacity of the hotel, however. True, a reservation on the books Tuesday was not the same asa "head in the bed" on Saturday, especially when weekend nights produced a lot of "no- show" reservations. \"Chances are good we still wouldn't have a ll house onSaturday," Snow thought aloud. "But if everybody came and someone was denied a room due to overbooking, I would certainly hear about it, and perhaps Bill Marriott would also! " Snow considered the tradeoff between a vacant room and denying a customer a room. The contribution margin om a room was about $90, since the low variable costs arose primarily om cleaning the room and check-in/check-out. Onthe other side, if a guest with a reservation was denied a room at the Hamilton, the front desk would nd a comparable room somewhere in the city, transport the guest there, and provide some gratuity, such as a fruit basket, in consideration for the inconvenience. If the customer was a Marquis cardholder (a frequent guest staying more than 45nights a year in the hotel), they would receive $200 cash plus the next two stays at Marriott ee. Snow was not sure how to put a cost gure on a denied room. In her judgment, it should be valued- good will and all - at about twice the contribution gure. Forecasting Snow focused on getting a good forecast for Saturday, August 22, and making a decision on whether toaccept the additional reservations for that day. She had historical data ondemand for rooms in the hotel. Exhibit 1 shows demand for dates starting with Saturday, May 23, 1987. (Saturday, August 22, was the beginning of week 14in this database.) Demand gures included the number of turned-down requests for a reservation on a night when the hotel had stopped taking