1IIE/RA CONTEST PROBLEMSCONTEST PROBLEM 6IIE/RA Contest ProblemsSixth Annual Contest: SM Theme ParksSM Theme Parks is the parent company for a series of theme amusement parks locatedprimarily in the southern part of the United States. Most of these parks are small to mid-size. However, we are currently completing plans for a major theme park to be calledBayou Adventure World. This complex will actually contain four distinct parks: FrogPond, Skunk Hollow, Gator Island, and Raccoon Corner. Customers can enter BayouAdventure World at any of the four parks and use the provided transportation to travelbetween them.There will be several forms of transportation, including boats, a steam railroad, horseand wagon, and open-air buses. These transportation options are mostly theme-orientedand will only carry a small proportion of the people who will want to move betweenparks. The major transportation option is to be a people-mover system. The people-movers (which are basically trains) will be on a continuous loop: Frog Pond to SkunkHollow to Gator Island to Raccoon Corner and back to Frog Pond. Although the type ofpeople-mover has been selected and the track designed, the system still needs to be sizedto meet the needs of Bayou Adventure World.This system can accommodate up to eight trains. Each train consists of one or morecars, with each car having a capacity of approximately 25 people. The objective is to sizethe system so that it minimizes the number of times that waiting customers are not able toboard the people-mover because it is full. Ideally, there would always be room for anywaiting customers. However, it is understood that a design that always meets demandmay result in a very expensive system.In designing similar types of systems, we have chosen not to look at the amount oftime that a customer has to wait for a people-mover, but to look at the proportion of timethat a people-mover leaves a station when people are unable to board. So in comparingdifferent designs, you should consider the following performance categories:1. Train leaves a stop with no people waiting to board,2. Train leaves with 1 to 24 people still waiting,3. Train leaves with 25 to 49 people still waiting, and4. Train leaves with 50 or more people still waiting.We believe that a properly designed system would have very few, if any, Type 4occurrences. We would also like to minimize the number of Type 2 and 3 occurrences. Atthe same time, we would like to keep our investment at a minimum. We have requestedand received cost figures from the people-mover manufacturers. These costs includedinitial capital, operating, and maintenance costs for the projected life of each unit. TheIIE_RA_6.pmd5/30/2006, 12:10 PM1
2IIE/RA CONTEST PROBLEMScost for the first car of each train is $800 per day. The cost for additional cars is $500 perday per car.The trains are computer-controlled and fully automatic. Although there can be slightvariations in travel time between parks, you can probably assume that the times (inminutes) given below are accurate enough for this study.Travel TimeFromTo(in min.)Frog PondSkunk Hollow5Skunk HollowGator Island8Gator IslandRaccoon Corner7Raccoon CornerFrog Pond6There are two possible modes to consider for customer loading and unloading. Thefirst option requires that customers board from one side and exit from the other. When atrain stops at a station, the unload doors open for 30 seconds to allow passengers to exit.Then the load doors open for 45 seconds to allow new customers to board. The doorsclose and the train leaves the station. The second option uses a single side for bothunloading and loading. When the train stops at a station, the doors open and customersare allowed to both board and exit at the same time. This option normally allows for thedoors to be open for 2 minutes. Since these times are computer-controlled, the onlyvariation results when a customer does not allow a door to close. This usually results in a10-second delay.The first option is the most desirable as it allows for a more orderly and controlledboarding and exiting process. However, this option costs an additional $20 per day percar. It is also possible that the second option might require additional cars. We would liketo know the relative merits of these options.Since Bayou Adventure World is not yet operational, demand data for this systemhave been based on our experiences with other parks. We plan to design the system tomeet an above-average (but not peak) day of expected attendance. Customers may haveto wait longer on busier days, but we feel that this is not a problem. We will takeadvantage of well-below-average attendance days to conduct preventive maintenanceon selected trains.Bayou Adventure World is scheduled to be open between 10 AM and 10 PM daily. Ourprojected customer arrivals (arrivals per hour) to each station are given below. Althoughthere will probably be more variations, we can only provide hourly rates at this time.These are customers who arrive at a station (e.g., Frog Pond station) and want transporta-tion to another station. The people-mover manufacturer recommends that we start thetrains a few minutes before we open the gates each day so that the system is fully func-tional when the first customers arrive. The trains will also continue to run after the closingtime for approximately one-half hour, or until all customers have departed the park.IIE_RA_6.pmd5/30/2006, 12:10 PM2