Dennis F.X. Mathaisel

Software Development Models


Dennis F.X. Mathaisel
Professor of Management Science
Babson Hall
Babson Park, MA 02457
Tel: (781) 239-4994
Fax: (781) 239-6416

This page provides brief descriptions of models/computer software for airline planning and airline operations control available through the author. The models cover a range of strategic and tactical planning activities, as well as operational activities within an airline operator.




• Fleet planning

• Airline schedule development

• Aircraft routing to maintenance

• Fleet assignment

• Passenger allocation and schedule evaluation

• Simulation of aircraft motion on an airport surface


• Timetable construction



• Aircraft routing




Fleet Planning (CELL, FA-4)

Fleet planning models are concerned with determining an optimal program of aircraft acquisition for the airline system and the optimal utilization of these aircraft in the system for a future multiple-period planning horizon of 3 years or more. There may also be the need to include financial constraints, which can be set to limit the airline's ability to borrow money and purchase new equipment. Such fleet planning models are strategic models by nature. There are two approaches and, therefore, two models for this problem.


The Cell Model is a macro approach which reduces the size of the multiple-period problem by clustering individual routes into classes or "cells", such as short-haul, medium-haul, or long-haul. The Cell Model finds the optimum combination of aircraft types and frequencies for all of the cells in this aggregate network. The reduced size of the problem permits a rapid evaluation of the fleet requirement for multiple years into the future. Financial constraints (such as debt/equity limits) are also available in the Cell Model. The Cell Model assists the airline firm in optimizing:
1. the market structure for the airline, in terms of these cells;
2. the assignment of aircraft types for each cell; and
3. the frequency of service in each cell.

It is an economics-based model which consists of a series of equations which can be solved to find a profit (or contribution to profit) maximizing set of decisions on cell structure, aircraft types and frequency. The decisions are made simultaneously, using techniques from mathematical programming.  The model allows an airline manager to select the most appropriate aircraft for a given cell structure, or select the optimal cells and frequencies for a given set of aircraft, or select aircraft, cells, and frequencies simultaneously. The results are useful for fleet planning, the acquisition of new aircraft, and the retirement of old aircraft. These decisions are made for multiple periods of time.

Fleet Assignment and Network Optimization (FA-4)

The second approach to fleet assignment is the use of the Fleet Assignment model FA-4, which makes optimal decisions on routes, aircraft types and frequencies for a single-period in time, over all periods in the planning horizon. FA-4 assists the airline firm in optimizing:

1. the route network design for the airline;
2. the assignment of aircraft for each route; and
3. the frequency of service on each route.

It is an economics-based model which consists of a series of equations which can be solved to find a profit (or contribution to profit) maximizing set of decisions on routes, aircraft and frequency. The decisions are made simultaneously, using techniques from mathematical programming.

The model allows an airline manager to select the most appropriate aircraft for a given set of routes, or select the optimal routes and frequencies for a given set of aircraft, or select aircraft, routes, and frequencies simultaneously. The results are useful for fleet planning, the acquisition of new aircraft, and the retirement of old aircraft. The results also provide valuable insight into the profit impact of a specific route upon a network, and into how the addition of new stations/services or the deletion of existing ones affect optimal routings. These decisions are made for a single period in time.

FA-4 requires inputs on costs, fares, and maximum desirable load factors. It also uses detailed input describing the aircraft, the routes and demand information for every city pair in the network (passengers and/or cargo).
The main output of the model is the optimal assignment of aircraft types and frequencies along routes of the network. The output is detailed in showing the frequencies of service and traffic volumes for each market of the system, and also for each segment of the network. Activities in terms of passengers, cargo, and aircraft operations are also shown by airport. Overall system data in the form of total passengers enplaned, total revenue passenger miles, total aircraft departure and miles by type, system revenues, costs, contribution to fixed costs, etc., is an additional feature.

Airline Schedule Development (ISS)

The Interactive Scheduling System (ISS) is designed for the development of future schedules. ISS incorporates numerous graphical representations of a schedule plan with validation and error checking routines and printed summary reports. The system automates the schedule development and distribution processes in an airline.   The implementation of the system's more intuitive toolset, which includes a graphical editor for both routing and schedule manipulation and the capability to handle fully-dated schedules, streamlines many manual work processes.  Supporting the toolset with a comprehensive database structure will greatly enhance the feed of schedule data within and without the airline. These tools enable schedulers to meet market and operational changes, as well as other internal and external (industry and government) directives, in a more timely manner with a more finely tuned schedule.

Some of the basic functions provided in the Interactive Scheduling System include:

1.   Standalone or client-server architecture
2.   Multiple users, record locking, security codes
3.   Interactive graphics editor
4.   Unlimited number of aircraft, segments, rotations, stations
5.   Filtering and sorting
6.   Multiple schedule views
    6.1  Station activity
    6.2  Lines of flying for one day
    6.3  Weekly rotations
    6.4  Fully-dated schedule display
    6.5  Gate assignment
    6.6  Timetable (O-D display)
    6.7  Geographic map projection of routings
7.   Rule-based constraint checker
    7.1  Crew requirements
    7.2  Maintenance requirements
    7.3  Operations (ground times, station continuity, curfews)
8.   Librarian: merging and splitting schedules
9.   Interfaces to existing systems
10.   Automatic flight numbering
11.   Import and export functions: read and write data files to mainframe
12.   Internal database
13.   Printed summary reports

All displays use color icons, menu features, and a graphical editing capability. ISS interfaces with airline-specific schedule planning algorithms as well as with optimization routines and fast heuristics to assist schedulers with various scheduling subproblems. ISS runs on a UNIX workstation in a stand-alone or client-server architecture, allowing multiple users to work on the same schedule.

Passenger/Cargo Allocation and Schedule Evaluation


Given a schedule plan for an airline or for the industry (the airline's competition) and given a set of origin-destination markets, PATH finds all possible non-stop and multi-stop paths for each O-D pair. PATH also generates all feasible single-connecting and double-connecting paths for each O-D. The connecting paths are constructed according to specified circuity rules.


The ALLOC (Traffic Allocation) Model simulates the allocation of origin to destination traffic to flights within a given schedule. The schedule can include an individual airline and the airline's competitors schedule or a schedule for the entire industry. The two major inputs to the system are:
• Total origin - destination market demand.
• Schedule files, including aircraft type, times, frequency, etc.

The output from the ALLOC model is the number of passengers traveling on each flight segment in the schedule. The allocation is based on the level (quality) of service and fares provided in the market. The process is divided into two steps:

1. The determination of the basic ("behavioral") passenger preference for each competitive service offered in the market.
2. The incremental allocation of demand, such that segment loads build up gradually, and demand not finding space on the preferred flight is diverted (spilled) to less-loaded service offerings.

The Thru-Flight Optimization module analyzes the marginal profit gained by changing a connecting flight into a thru-flight.

Timetable Construction (INSERT, REDUCTA)
The timetable construction models INSERT and REDUCTA find an optimal assignment of departure and arrival times for a set of flights in an airline's route network. There are two approaches and, therefore, two models for this problem.


INSERT is an "insertion-based" algorithm for building aircraft itineraries based on the demand for service, aircraft routing requirements, and operational constraints. The algorithm builds up aircraft routes and schedules through a sequential insertion of origin to destination (O-D) demands into the system. The demand is characterized by a level of priority (e.g., revenue) and a "window" defined by its earliest departure time and latest arrival time. These times can be loosely defined, but the algorithm does have the capability to distinguish between "high-priority" or "high-revenue" service and "low-priority/revenue" service. There are a set of structured decision rules which complement the INSERT algorithm. These rules are grouped into three categories:

• Aircraft choice rules
• Hubbing decision rules
• Hub choice

The aircraft choice rules can be used as an option to affect the choice of aircraft type to be assigned to the demand. The attributes that affect the decision are: distance, volume, and "delivery time". These rules can be used, for instance, to assign turbo-prop or commuter aircraft to short-haul, low-density markets. The hubbing decision rules can be used to force hub construction into the routing patterns. The final set of rules, hub choice, concerns where to hub, if hubbing is appropriate.


Given an existing timetable, the REDUCTA algorithm will shift flights within a specified "time window" with the objective of increasing the efficiency of the timetable by reducing the number of aircraft needed to satisfy the schedule. If an existing timetable is not given, REDUCTA will begin assigning departure and arrival times, and then it will shift these times within a specified window to reduce the requirements for aircraft. REDUCTA can be modified to accept departure and arrival time preference curves, that can then be used in the construction of the initial timetable. Curfew times, maximum gates available, and other operational constraints can be added in to REDUCTA.

Aircraft Routing / Fleet Routing

Aircraft Routing

The aircraft routing models find a cyclic routing pattern for individual aircraft in the fleet. These models develop a FIFO (first-in-first-out) or LIFO (last-in-first-out) routing pattern on selected aircraft or fleets, or for the entire schedule plan.

Maintenance Routing

Operational changes in aircraft routings are often necessary due to flight cancellations or delays. It is desirable to make these changes whenever possible without altering maintenance schedules.  The Maintenance Routing Model provides a rapid means of assuring that proposed aircraft routings accommodate a specified maintenance schedule. The program routes each tail number to its maintenance station at the proper time without exceeding the hours remaining on the aircraft.

The program can be used in several ways:

• To reroute the fleet after disruption of the schedule
• To create an initial maintenance routing with the fewest wasted hours on each aircraft
• To consider a wide range of feasible routings and alternative maintenance schedules.

Simulation of Aircraft in Motion on the Airport Surface (GMS)

This system is a real-time simulation of aircraft motion on the ground at airports. The aircraft Ground Motion Simulator (GMS) is designed to realistically simulate tower, ground, and apron aircraft control. The simulation includes high-fidelity graphic views, in color, of airport ground activity. It simulates air traffic operations in real time for all stages of flight from take-off to landing as well as all phases of ground movement of aircraft including landing roll, taxiing, yielding, platooning, parking, pushback, and takeoff roll.  The capability to simulate aircraft movement on airport taxiways and runways provides a realistic environment for testing the planning processes regarding the management of departing traffic and its interactions with aircraft landing at an airport. The GMS simulates the environment at any arbitrary airport and interfaces through a fast, two way data communications link to an existing Air Traffic Control simulation facility. The GMS consists of a host computer workstation, an experimenter's station, one or more traffic controller stations, and one or more pseudopilot stations. The graphical user interface and the graphical displays were developed in object-oriented C on the X/Windows graphics system on UNIX workstations.








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