AIRLINE CONNECTION POINT ANALYSIS D. W. Baird, Trans World Airlines, Inc. ABSTRACT This paper describes a SAS Institute, Inc. based system for computing connection cities to be used for Trans World Airlines', Inc. World Wide Availability System. This system utilizes the worlds airline schedules to compute roughly 35,000 markets that contain direct (no plane change) flight service. The direct markets are then processed to find all combinations of connection points, by utilizing spherical trigonometry (with world latitudes and longitudes), market and trip mileages may be used as a base for elliptical analysis. This program will aid us in identifying the best connect points and routings for our airlines' construction of trips in markets that may have no direct service or due to traffic "flow", require connection trips as well as direct trips. DESCRIPTION The foundation for this program is an input file consisting of the worlds airline schedules. This data is initially received from Official Airline Guide, Inc., a company who distributes all airline schedules to those carriers who purchase this information. This data is sent via a Standard Schedule Input Manual (SSIM) tape. The data on this tape contains all of the single legs of travel that carriers fly. TWA takes this schedule data, and transforms it into city pair information as described below: CHICAGO / ~. --(~O~~O_) -J. LOS ANGELES () ATLANTA (ATL) NEW YORK (NYC) The above represents an airline schedule for one flight, from Los Angeles to New York, with stops in Chicago and Atlanta. This is a 3 leg flight. From a single flight schedule, resultant city pairs are produced, in numbers, according to the following algorithm: Number of City Pairs = [(Number of Legs) (Number of Legs + l)j 2 In transposing the above schedule data into city pairs, the following results: From the contents of approximately 35,000 records are created. seasonal schedules, slightly. DIRECT CITY PAIRS BOARD OFF 1. 2. ATL 3. NYC 4. ATL 5. NYC 6. ATL NYC the SSIM file, direct city pair Depending upon this number may vary After all the direct city pair records have been created, the mileage between the board point, and the off point (for each city pair) must be calculated. This is done by merging an ATLAS file (containing the latitude and longitude of the worlds airports) by the board point of the city pair records, then merging again by the off point. Now by utilizing the algorithm shown in Figure 3, the mileage for each city pair is computed. This resultant file is then shown in Figure 2 as DATA = READ2. This file will contain approximately 35,000 "observations". Only one other file is required, and that is the "market", or "markets" over which connect points are to be computed. This is shown in Figure 2 as: DATA = READ!. The general SAS program flow is now described, and follows the flow depicted in Figure 2, and utilized the data given in Figure 1. STEP 1 The markets that the connect points are to be computed for, are placed into the "market" file. This is data set READ1. 392
STEP 2 STEP 3 STEP 4 STEP 5 After reading the Worlds Airline Schedule tape (SSlM), a world wide direct data file is created, as described previously. These direct city pairs with mileages, are read into data set READ2. This done in a previous merge with the ATLAS file. The program now creates data set READ3, as an exact copy of READ2. The effect of Step 2, and Step 3 is to create READ2 for the first segment possibilities of all connections, and READ3 will be the second segment possibilities. This data set, called BRD, is a merge of data sets READ! and READ2, by board point. NOTE: The program is written as a rj1acro. So, if data set READ1 has multiple observations, the entire program acts on each observation via a call to the MACRO. Hence, to the program it always "appears" as though data set READ! has only one observations - as shown in the example. The effect of this step is to retain only those segments that depart from the board point of interest. This data set, called OFF, is a merge of data sets READ! and READ3, by off points. This step will retain only those segments that arrive into the point of interest. Now in data set BRD (Step 4), variable name OFF is changed to CONNECT. In data set OFF (Step 5), variable name BOARD is changed to CONNECT. STEP 6 This data set is now a merge of data sets BRD and OFF, by CONNECT keeping an observation only if it existed in BOTH data sets. This resultant data set is exactly the file that is needed. Since this file contains mileages, and other carrier related information regarding the associated city pairs, several calculations and sorts may now be made. For TWA's purposes, this file may be analized by several factors in order to determine which connect points are indeed the "best". Some of these factors are: Segment 1 vs Segment 2 mileage. That is, which segment is the longest. How does the connection point compare to the markets direct mileage. This is our "Ellipse". Which of the listed connect points have TWA service, as Segment 1 or Segment 2. CONCLUSION As airlines change their schedules, approximately once each month, TWA needs to have a dynamic method of determining what connect points are "best", based upon new schedule information. Since the SAS program is CLIST driven, our analysts are able to gain knowledge regarding a specific market, and its connect point possibilities in a interactive mode. 393
FIGURE 1 SAMPLE PROBLEM This example contains data for the program flow shown in Figure 2 given the following file: DIRECT CITY PAIRS (MARKETS) ------ BOARD POINT ----- OFF POINT.. -------_... DAB ~ ORD ~===============:: _ ORD----------i",. BaS =====-=: - DAB - BOS - Los Angeles Daytona Beach Boston ORD - Chicago O-Hare - New York - St. Louis John F. Kennedy Utilizing the above, we need to compute the following: points and routings MARKET ROUTINGS Board s Off Routing CONNECTION MARKETS JI,. ~ORD~ #1 #2 BOS ----...,... -------;..;) BaS #1 394
FIGURE 2 Step 1 DATA READ 1 ; MARKET FILE Sort by OFF Sort by BRD Step 2 DATA READ2; WORLD WIDE DIRECTS Step 3 DATA READ3; WORLD WIDE DIRECTS ~Qil. OAB BOS DUPLICATE ~ Sort by OFF Sort by BRO Step 4 DATA BRD MERGE READl (IN=A) READ2; IF A; BY BRD; Step 5 DATA OFF MERGE READl ~d ~ Off OAB Step 6 DATA CONN: MERGE BRD (IN=A) OFF (IN=B); IF A & B; by CONNECT POINT; BOARO CONNECT POINT OFF 395
! FIGURE 3 SPHERICAL TRIANGLE TRIGONOMETRY REFERENCES FORMULAS: Suppose A, B, C ilre the three angles of 8 spherical triangle and a, b, c are the Opposite sides. 1. SAS Institute (1982) SAS USER'S GUIDE: BASICS, If A, b, c a,e given, then... ----~'c ~.A <,,' -' b, a B 8 = cos 1 [cos b cos c + sm b sin c cosaj c= cos 1 [COS C - COS.8 cos b] sin 8 SIn b 2. SAS Institute (1980) SAS APPLICATIONS GUIDE, 3. SAS Institute (1983) SAS VIEWS: PROCESSING, 4. Hewlett Packard (1974) HP-45 APPLICATIONS, Cupertino, California NAVIGATtONAL COURSE: This routine can be used to find the grnt circle route and the true course C if the coordinates of the source (Ills- "s) and destination (GO' 9 0 )8,e known. 5. SAS sample program library: Member COMBO NOTE: SAS is a registered trademark of SAS Institute, Inc. Further Information May Be Obtained From: NOTES: IS" Latitude S" Source 9 " Longitude 0= OestinatiOl'l 1. A=Os 90,1II=9O"-If$'c=9O"-80 2. Nonhern hemisphere latitudes ami Western hemisphere longitudes 8,e indicated 8S positive numbers. Southern and Eastern coordinates are indicated 811 negative numbers. 3. 1 (spherical coordinate) = 60 naulical miles 4. True course = 36()o - C If sin A < 0 Ii. e going _st). D. W. Baird Trans World Airlines, Inc. Administrative Center - Level 5 11500 Ambassador Drive Kansas City, Missouri 64195 (816) 464-7701, I. 396