Publications

SELECTIVE Publications and Contributions

“Exploiting Consecutive Ones Structure in the Set Partitioning Problem (SPP),” author Ayik, M.

Book published by Storming Media, 2000 ISBN 1423531779, 9781423531777

SPP is one of the most extensively researched models in integer optimization, and is widely applied in operations research. SPP is used for crew scheduling, vehicle routing, stock cutting, production scheduling, and many other combinatorial problems. The power and generality of SPP come at a price: an SPP can be very difficult to solve.

A real-world SPP often has columns, or rows, with long strings of consecutive ones.

• Exploited the consecutive ones structure in an SPP with a new preprocessing reduction that can eliminate some variables.
• Introduced a column-splitting technique to render a model that can be solved directly or used to bound SPP with Lagrangian relaxation or an exterior penalty method.
• Developed an SPP row-splitting method that yields a special model that Bender's decomposition may then solve faster than the monolithic SPP.
• Demonstrated these techniques with well-known test problems from airlines and other researchers.

Also, contributed a new deployment scheduling model for the US Navy’s fleet of aircraft carriers, applying the new techniques to plan with weekly fidelity over a ten-year planning horizon. This improved planned deployment coverage of areas of responsibility by about ten carrier weeks.

“Optimal Long-Term Aircraft Carrier Deployment Planning with Synchronous Depot Level Maintenance Scheduling,” author Ayik, M.

Book published by Storming Media, 1998 ISBN 1423562046, 9781423562047

Forward deployment of Navy aircraft carrier battle groups is a primary means for the United States to achieve overseas interests. The Navy maintains the forward presence of aircraft carriers in three major Areas of Responsibility (AORs): the Mediterranean Sea, the Persian Gulf, and the Western Pacific. Considering the cost of carrier operations and the desire to maximize coverage of the AORs, planning deployments for the carriers not only significantly affects the achievement of U.S. defense strategy, but also impacts the Navy financially.

Previous studies have maximized the deployment of aircraft carriers to the AORs while strictly adhering to the fixed, long-range maintenance schedules.

• Optimized aircraft carrier deployment and maintenance planning using a two-commodity network flow model with side constraints.
• This synchronous planning of deployments and major maintenance yields at least 15% more planned coverage in the AORs with the existing carrier fleet.

Such an increase had been thought to require three additional aircraft carriers.

“A Multi-stage Decomposition Heuristic for the Container Stowage Problem,” by Gumus, M. (Professor McGill University), Kaminski, P. (Professor, UC Berkeley), Tiemroth, E. (VP Research, Navis), and Ayik, M., March 2008

A significant and growing volume of global trade travels on container ships, and each year larger ships are introduced. For this reason, the Container Stowage Proble, a fundamental problem in marine cargo transportation involving the optimal assignment of shipping containers of various types to specific storage locations in container ship at each port in order to maximize loading and unloading efficiency and minimize shipping costs, is growing in importance. In spite of this, the problem is currently solved in an ad-hoc manner based on experience and rules-of thumb. In this paper, we develop a multi-stage decomposition heuristic for this problem that accounts for the many complexities of real-world versions of the problem. This approach is performing well in testing on real-life problems, and is currently being developed for inclusion in commercial software.