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Introduction

## Publications

Publications (175)

Runway scheduling deals with the sequencing of arriving and departing aircraft at airports such that a predefined objective is optimized subject to several operational constraints. Different from the existing deterministic approaches in the literature, we consider a new approach to the stochastic version of this problem within the general context o...

Air traffic efficiency is heavily influenced by unanticipated factors that result in capacity reduction. Of these factors, weather is the most significant cause of delays in airport and airspace operations. Considering weather-related uncertainty, air traffic flow management involves controlling air traffic through allocation of available airspace...

We identify binary group facets with complete support and non-binary coefficients. These inequalities can be used to obtain new facets for larger problems using Gomory’s homomorphic lifting.

We identify binary group facets with complete support and non-binary coefficients. These inequalities can be used to obtain new facets for larger problems using Gomory's homomorphic lifting.

Industries such as aviation, hospitality, and package tours often face both individual and batch bookings, requiring one unit and multiple units of capacity, respectively. Using bid prices is a common practice in accepting or rejecting an incoming booking (or equivalently, deciding which price bucket to offer to the incoming bookings at a given tim...

Although the airline industry has benefited from advancements made in computational and operational research methods, most implementations arise from the frictionless environment of the planning stage. Because 22% of all flights have been delayed and 3% have been cancelled in the United States since 2001, schedule perturbations are inevitable. The...

Gomory (Linear Algebra Appl 2:451–558, 1969) gave a subadditive characterization of the facets of the group polyhedron. Although there are exponentially many facets (see Gomory and Johnson in Math Program 3:359–389, 1972, Example 4.6) and exponentially many vertices for the group polyhedron for the master cyclic group problem, Gomory’s characteriza...

Node-arc incidence matrices in network flow problems exhibit several special least-squares properties. We show how these properties
can be leveraged in a least-squares primal-dual algorithm for solving minimum-cost network flow problems quickly. Computational
results show that the performance of an upper-bounded version of the least-squares minimum...

Efficient runway operations are a necessary input for the optimal use of the air transportation system. Most efforts at improving runway efficiency have failed to capture the impact of environmental costs. Here we develop an integrated approach that models this complex relationship, and provides insights regarding the value of environmental optimiz...

Observers of operations research(OR) in the 1950s were faced with a curious phenomenon: While OR was established in some departments
of industrial engineering and a few schools of business, it continued to be ignored by mainstream, scientifically oriented
departments, especially mathematics departments. This seemed strange as OR rests heavily on as...

The airline industry currently has a $40-billion plus market and is expected to grow rapidly with the population growth and growth in the overall economy. Everyday, thousands of aircrafts undergo maintenance, repair, and overhaul. The aircraft maintenance problem is one of the important logistic problems in the airline industry. It is aimed at sche...

In this paper, we consider the air-traffic conflict-resolution problem and develop an optimization model to identify the required heading and speed changes of aircraft to avoid conflict such that fuel costs are minimized. Nonconvex fuel functions in the optimization problem are modeled through tight linear approximations, which enable the formulati...

Project portfolio management deals with the dynamic selection of research and development (R&D) projects and determination of resource allocations to these projects over a planning period. Given the uncertainties and resource limitations over the planning period, the objective is to maximize the expected total discounted return or the expectation o...

A stochastic runway planning model has been developed for scheduling of airport runway operations in the presence of uncertainty, where stochastic attributes include pushback delay, time spent on taxiway, and deviation from estimated arrival time. The runway planning problem is modeled as a process in two stages, where the first stage uses a two-st...

Gomory [R.E. Gomory, Some polyhedra related to combinatorial problems, Linear Algebra and its Applications 2 (1969), 451–558] solved the cyclic group problem by a dynamic programming algorithm. We discuss its complexity and introduce a (fractional) cutting plane algorithm as an alternative algorithm. Each cutting plane is generated by solving a sho...

General purpose cutting planes have played a central role in modern IP solvers. In practice, the Gomory mixed integer cut
has proven to be among the most useful general purpose cuts. One may obtain this inequality from the group relaxation of an
IP, which arises by relaxing non-negativity on the basic variables. We study the mixed integer cut as a...

In this paper a procedure is described to orient arcs of a graph so as to mimimize the sum of the distances between certain
given source-sink pairs. This work is a substantial part of the more general problem of orienting a road network in such a
way as to optimize a specified objective subject to the requirement that one can go from any point of t...

Solving the linear program associated with an all-integer program gives the group problem N x≡b(mod 1), x≥0 and integer, z=c x (minimize), upon relaxation of non-negativity of the basic variables, where c≥0 and N is the fractional part of the updated, non-basic columns. A method is given for solving this problem which does not require
an explicit g...

A theory is developed for a group problem arising from mixed integer programming. This theory gives descriptions of functions
on the unit hypercube from which cutting planes can be constructed for any mixed integer program. Methods for generating such
functions are given.

The airport terminal capacity planning problem deals with determining the optimal design and expansion capacities for different areas of the terminal in the presence of uncertainty with regards to future demand levels and expansion costs. Analytical modeling of passenger flow in airport terminals under transient demand patterns is especially diffic...

We present a novel formulation for the service network design problem in the context of large-scale, less-than-truckload (LTL) freight operations. The formulation captures the basic network design constraints; the load-planning requirement that all freight at a location, irrespective of the freight's origin, loads to the same next terminal; and oth...

Conditions are given for two sets to be the level sets of a support function. Then, Fulkerson’s concepts of blocking pairs
and anti-blocking pairs are generalized, and similar conditions are given for two polyhedra to be an anti-blocker and blocker
of some polyhedron.

A dual or polar set is studied to characterize facets of polyhedra arising from problems in which the variables y are allowed
to be continuous but the vector Wy is required to be equal to one of a finite set S. These facets are supported functions of a polar set C
*, and some properties are given for those C
* corresponding to a facet.

The airline fleet assignment problem involves assigning aircrafts to flights to maximize profit. Different fleet assignment solutions cause dramatically different performance in subsequent crew planning and operational processes. We have developed an integrated fleet and crew robust planning method to provide fleet assignment solutions that are bot...

In this paper we consider the Capacitated Arc Routing Problem with Time windows. We suggest two algorithms for solving the problem to optimality and a heuristic for obtaining high quality solutions. To our knowledge this is the first paper to consider optimal solution of that problem.

We consider a production planning problem of an assembly item, where each component of the item has several different versions. In flexible customization, rather than specifying only one version for each component, customers are willing to accept any variation of the product complying with their customization rules. The problem of constructing the...

This paper presents a new methodology for incorporating origin and destination (O&D) network effects into the fleet assignment process. The methodology uses a decomposition strategy to combine a modified version of a leg-based fleet assignment model (Leg-FAM) with the network flow aspects of probabilistic O&D yield management. By decomposing the pr...

In the fractional ownership model, the partial owner of an aircraft is entitled to certain flight hours per year, and the management company is responsible for all the operational considerations of the aircraft and for making an aircraft available to the owner at the requested time and place. In the recent years although the industry as a whole has...

We exhibit a polar relationship between two measures that have been proposed to evaluate the importance of TSP facets, the Kuhn–Gomory shooting experiment size and the probability of integrality in an augmented LP relaxation. The polarity establishes the complexity of performing the shooting experiment. We illustrate the resulting relationship on t...

The linear and integer programming modeling system was developed to design an integrated modeling environment. The application of the basic concepts of modeling system to study the fleet assignment problem had also been discussed. The modeling system used relational operators and structured query language (SQL) to implement ordering concepts. It wa...

On-demand air transportation is progressively obtaining the popularity with its flexibility, convenience, and guaranteed availability.
However, its unique dynamic characteristics, such as short-noticed new demands and disruptive unscheduled maintenance, challenge
the efficient operations, since they will significantly affect the priori algorithmic...

Technology development involves research and development (R&D) projects aimed to design, test and improve a technology, or the process of building a technology. Technology development is often an essential part of the operational strategy of an organization, during which deployment or implementation decisions are made. In most cases, organizations...

This work is supported in part by National Aeronautics and Space Administration (NASA) under the project “Approaches to TFM in the Presence Of Uncertainty,” 06-AS-06-0037. The authors are thankful to Mr. Terran Melconian of the School of Aerospace Engineering at Georgia Institute of Technology for his help in system setup for accessing the weather...

Although Gomory's work on the group problem ~ 9 ~ was contemporary with the work of Fulkerson on blocking polyhedra E 7 I, no connection was made until much later. We show that corresponding to blocking pairs of binary clutters there is a pair of binary groups problems that we call a blocking pair of binary group problems. The focus of this paper i...

Fleet assignment models (FAM) are used by many airlines to assign
aircraft to flights in a schedule to maximize profit. Major airlines
report that the use of FAM increases annual profits by more than
100 million. The results of FAM affect subsequent planning, marketing,
and operational processes within the airline. Anticipating these
processes and...

Most airlines overbook their actual capacity (for both passengers and cargo) because part of the booked demand often does not show up at the flight departure. A key element of overbooking is a model that accurately predicts the show-up rate of the current bookings. Given the increasing importance of cargo within their business, most major airlines...

Abstract Airlines are continually faced with the challenge of efficient utilization of their cockpit crew resources. In addition to regular flying crews, some airlines have to maintain significant reserve staffing levels to meet,contractual,obligations and provide,smooth,daily operations. Reserve crews are required to cover trips remaining,unassign...

This paper proposes a stochastic dynamic programming model for a short-term capacity planning model for air cargo space. Long-term cargo space is usually acquired by freight forwarders or shippers many months ahead on a contract basis, and usually the forecasted demand is unreliable. A re-planning of cargo space is needed when the date draws nearer...

An important part of the airport terminal design process is the determination of the optimal design capacity levels for different areas of the terminal under the uncertainty of future demand levels and expansion costs. Due to the difficulty of this task, most studies in this area either do not account for expandability or focus only on one particul...

On-demand air transportation is widely used because of its flexibility, privacy, and guaranteed availability. The customers can fly directly to any station in the network anytime as they wish, and request their flights only days or even hours in advance. Management companies have to serve customer demand by efficiently arranging the available aircr...

The airline industry is faced with some of the largest scheduling
problems of any industry. The crew scheduling problem involves the
optimal allocation of crews to flights. Over the last two decades
the magnitude and complexity of crew scheduling problems have grown
enormously and airlines are relying more on automated mathematical
procedures as a...

The multiple pairs shortest path problem (MPSP) arises in many applications where the shortest paths and distances between only some specific pairs of origin-destination (OD) nodes in a network are desired. The traditional repeated single-source shortest path (SSSP) and all pairs shortest paths (APSP) algorithms often do unnecessary computation to...

This paper reviews tools which have great potential for reducing the difficulty of solving IP (and also MIP) problems, if well implemented in solvers. Recent experiments with Branch and Bound solvers, in connection with "Short Start Features", have shown that implementations need and can still be improved. Concepts which are likely to be specially...

On-demand air transportation provides passengers a convenient option flying point-to-point directly anytime at their requests. Although it's convenient to customers, this type of non-scheduled service posts great challenge to the management companies, who must serve customer demand by efficiently arranging their aircraft. A set-partitioning model i...

In this paper, we propose an integrated approach to combine aircraft routing and crew scheduling problem with the consideration of multiple types of fleets where a crew can only fly the specific type of fleet. This method effectively manages the aircraft and crew because it takes aircraft maintenance into account. A rolling horizon technique is use...

Fleet assignment models are used by many airlines to assign aircraft to flights in a schedule to maximize profit [1]. A major
airline reported that the use of the fleet assignment model increased annual profits by more than $100 million [3] a year
over three years. The results of fleet assignment models affect subsequent planning, marketing and ope...

Airline decision makers cancel flights in operations because of disruptions.
When canceling a flight, they usually cancel a cycle, a sequence
of flights that begins and ends at the same airport. Consequently,
a fleet assignment and aircraft rotation with many short cycles is
frequently less sensitive to a flight cancellation than one with
only a fe...

Airlines are continually faced with the challenge of efficient utilization of their cockpit crew resources. In addition to regular flying crews, airlines maintain significant reserve staffing levels to meet contractual obligations and provide smooth daily operations. Most airlines also depend on voluntary and involuntary flying by regular crews to...

This paper describes a three-phase approach to solving the bidline generation problem within airline flightcrew scheduling. Phase 1 builds “patterns” from existing pairings. Phase 2 builds bidlines from the “patterns” found in Phase 1 and solves a set partitioning problem to generate a final schedule. If Phase 2 fails to cover enough of the schedul...

SIMAIR is a C++ based research tool meant for the simulation of airline operations. It provides a means for devising and evaluating various airline recovery mechanisms to handle disruptions, and can also be used as a tool to evaluate the performance of a given schedule of operations. The performance of a given recovery mechanism is quantified for r...

Disruptions in airline transportation systems can prevent airlines
from executing their schedules as planned. Adverse weather conditions,
congestion at airports, and mechanical failures often hinder a flight
schedule. During such events, decision makers must reschedule flight
legs, andr eroute aircraft, pilots, andpassengers. We present an
optimiza...

Delta Air Lines periodically trains its cockpit crew members to maintain their flight qualifications. The negotiation of the new pilot working agreement (PWA) in June 2001 introduced a short and stringent planning cycle and a new training-pay structure that affects operating costs. The downturn in airline business after September 11, 2001 forced De...

. Any integer program may be relaxed to a group problem. We define the master cyclic group problem and several master knapsack
problems, show the relationship between the problems, and give several classes of facet-defining inequalities for each problem,
as well as a set of mappings that take facets from one type of master polyhedra to another.

. We review the necessary background on Corner Polyhedra and use this to show how knowledge about Corner Polyhedra and subadditive
functions translates into a great variety of cutting planes for general integer programming problems. Experiments are described
that indicate the dominance of a relatively small number of the facets of Corner Polyhedra....

In this paper we show how knowledge about T-space translates directly into cutting planes for general integer programming
problems. After providing background on Corner Polyhedra and on T-space, this paper examines T-space in some detail. It gives
a variety of constructions for T-space facets, all of which translate into cutting planes, and introd...

SIMAIR is a C++ based research tool meant for the simulation of airline operations. It provides a means for devising and evaluating various airline recovery mechanisms to handle disruptions, and can also be used as a tool to evaluate the performance of a given schedule of operations. The performance of a given recovery mechanism can be quantified f...

crews possess dierent character- istics that aect which subsets of tasks they can complete. Crew scheduling problems appear in a number of transportation con- texts. Examples include bus and rail transit, truck and rail freight trans- port, and freight and passenger air transportation. There are many com- mon elements to all of these problems, incl...

The yield management (YM) problem considers the task of maximizing a company's revenue. For the competitive airline industry, profit margins depend on a good YM policy. Research on airline YM is abundant but still limited to heuristics and small cases. We address the YM problem for a major domestic airline carrier's hub-and-spoke network, involving...

The airline yield management problem considers how to allocate capacity to the different fare classes so that the airline’s revenue is maximized. In the traditional airline yield management problem it is assumed that customers specify their itineraries, i.e., flight sequences. In the context of cargo airline yield management and in the context of a...

The relation of time indexed formulations of nonpreemptive single machine schedulingproblems to the node packing problem is formally established and then used toprovide simple and intuitive alternate proofs of validity and maximality for previouslyknown results on the facial structure of the scheduling problem. Previous work on thefacial structure...

We present a stochastic model of the daily operations of an airline.
Its primary purpose is to evaluate plans, such as crew schedules,
as well as recovery policies in a random environment. We describe
the structure of the stochastic model, sources of disruptions, recovery
policies, and performance measures. Then, we describe SimAirour
simulation i...

We have developed a least-squares primal-dual algorithm for solving linear programming problems that is impervious to degeneracy, with strict improvement attained at each iteration. We tested our algorithm on a range of linear programming problems including ones that require many pivots, usually because of degeneracy, using the primal simplex metho...

Airline planning consists of several problems that are currently solved separately We address a partial integration of schedule planning, aircraft routing, and crew scheduling. In particular, we provide more flexibility for crew scheduling while maintaining the feasibility of aircraft routing by adding plane-count constraints to the crew-scheduling...

We present a polyhedral study of the complementarity knapsack problem. Tra- ditionally, complementarity constraints are modeled by introducing auxiliary binary variables and additional constraints, and the model is tightened by introducing strong inequalities valid for the resulting MIP. We use an alternative approach, in which we keep in the model...

The airline crew scheduling problem is the problem of assigning crew itineraries to flights. The problem is hard due to a large number of itineraries and the complicated cost function of an itinerary. The classic approach, which uses a set partitioning formulation, only captures the objective function of minimizing cost. We add a second goal of max...

The airline crew scheduling problem is the problem of assigning crew itineraries to flights. We develop a new approach for solving the problem that is based on enumerating hundreds of millions random pairings. The linear programming relaxation is solved first and then millions of columns with best reduced cost are selected for the integer program....

Airline crew scheduling algorithms widely used in practice assume no disruptions. Since disruptions often occur, the actual cost of the resulting crew schedules is often significantly greater. We consider algorithms for finding crew schedules that perform well in practice. The deterministic crew scheduling model is an approximation of crew scheduli...

Many optimisation problems involve combinatorial constraints on continuous variables. An example of a combinatorial constraint is that at most one variable in a group of nonnegative variables may be positive. Traditionally, in the mathematical programming community, such problems have been modeled as mixed-integer programs by introducing auxiliary...

Many optimisation problems involve combinatorial constraints on continuous variables. An example of a combinatorial constraint is that at most one variable in a group of nonnegative variables may be positive. Traditionally, in the mathematical programming community, such problems have been modeled as mixed-integer programs by introducing auxiliary...

Airline transportation systems are inherently random. However, airline planning models do not explicitly consider stochasticity in operations. Because of this, there is often a notable discrepancy between a schedule's planned and actual performance. SimAir is a modular airline simulation that simulates the daily operations of a domestic airline. It...

A main purpose of this work is to give a good algorithm for a certain welldescribed class of integer linear programming problems, called matching problems (or the matching problem). Methods developed for simple matching [2,3], a special case to which these problems can be reduced [4], are applied directly to the larger class. In the process, we der...

An airline schedule rarely operates as planned. It is often disrupted by maintenance problems or severe weather conditions. In a typical day, several flights may be delayed or canceled, and aircraft and crews may miss the rest of their assigned flights. Airline coordinators have to find a minimal cost reassignment of aircraft and crews that satisfi...

We study a generalized assignment problem that arises in production scheduling in which special ordered sets of type II appear
naturally in the formulation. We derive three families of facet-defining valid inequalities, and we show that they cut off
all infeasible vertices of the LP relaxation. We also give the complete facetial description for a p...

Recently, the primal–dual simplex method has been used to solve linear programs with a large number of columns. We present a parallel primal–dual simplex algorithm that is capable of solving linear programs with at least an order of magnitude more columns than the previous work. The algorithm repeatedly solves several linear programs in parallel an...

Given a finite graph G(V,E) of order n, the optimal linear arrangement problem (OLA) seeks a vertex labeling f: V -> {1,2,...,n} such that sum |f(u)-f(v)| is minimum over all such labelings. The problem is hard in general but is known to be solved in certain special cases among which are paths, cycles, trees, and outerplanar graphs. After a survey...

This paper is about modeling and solving mixed integer pro- gramming (MIP) problems. In the last decade, the use of mixed integer programming models has increased dramatically. Fif- teen years ago, mainframe computers were required to solve problems with a hundred integer variables. Now it is possible to solve problems with thousands of integer var...

Airline transportation systems are inherently random. However, airline planning models do not explicitly consider stochasticity in operations. Because of this, there is often a notable discrepancy between a schedule's planned and actual performance. SimAir is a modular airline simulation that simulates the daily operations of a domestic airline. It...

Airline transportation systems are inherently random. However, airline planning models do not explicitly consider stochasticity in operations. Because of this, there is often a notable discrepancy between a schedule's planned and actual performance. SimAir is a modular airline simulation that simulates the daily operations of a domestic airline. It...

Euler tours occupy an interesting position in the history of graph theory. Current interest in this area is due to problems involving tours where service is required along arcs of the tour rather than at nodes. Examples of problems of this type involve mail delivery, snow removal, street cleaning, trash pickup, etc. In considering such problems inv...

The two main ideas implemented are a primal–dual subproblem simplex method and a compact matrix storage scheme to speed up linear programming solution times. Two classes of problems are solved: crew-pairing optimization and cutting stock. The matrix storage schemes are different for these two problem classes, and the one for cutting stock is a hybr...

In recent years, the most successful approaches to solving the airline yield management (YM) problem have been based on bid pricing. Bid price control assigns a threshold price to each flight leg. Given the bid prices, the resulting policy accepts a booking request if its associated fare is greater than the sum if the bid prices along the associate...

Given a set of jobs and a set of workers, the generic problem we consider is to find a partition of the jobs into subsets so that each job is contained in exactly one subset, and each subset in the partition is assigned to a worker. The workers are interchangeable, so the essence of the problem is to create the best set of subsets that partitions t...

The PC and PC network environments continue to experience rapid technological advances pushing the bounds of both computing speed and memory size. Both of these factors have constrained us, in the past, from being able to solve practical optimization problems of any large size in this environment. This was especially true for problems such as airli...

The task of allocating capacity to the different fare classes so that an airline's revenue is maximized is known as the Yield Management (YM) problem. In this research we develop a new approach to the YM problem that incorporates existing linear programming models and regression splines to bound and estimate the value function of a Markov decision...