Amy Cohn

Airline Crew Scheduling

An airline must cover each flight leg with a full complement of cabin crew in a manner consistent with safety regulations and award requirements. Methods are investigated for solving the set partitioning and covering problem. A test example illustrates the problem and the use of heuristics. The Study Group achieved an understanding of the problem and a plan for further work.

Airline Schedule Planning: Accomplishments and Opportunities

Plagued by high labor costs, low profitability margins, airspace and airport congestion, high capital and operating costs, security and safety concerns, and complex and large-scale management and operations decisions, the airline industry has armed its planners with sophisticated optimization tools to improve decision making and increase airline profits. In this paper, we describe optimization approaches for airline schedule planning, demonstrating how optimization can facilitate the management of a diverse and finite set of expensive, highly constrained resources. We focus on the art and science of modeling and solving these problems, providing illustrative examples of the associated impacts and challenges, and highlighting effective techniques that might be applicable to problems arising in other industries.

Decreasing airline delay propagation by re-allocating scheduled slack

Passenger airline delays have received increasing attention over the past several years as air space congestion, severe weather, mechanical problems, and other sources cause substantial disruptions to a planned flight schedule. Adding to this challenge is the fact that each flight delay can propagate to disrupt subsequent downstream flights that await the delayed flights aircraft and crew. This potential for delays to propagate is exacerbated by a fundamental conflict: slack in the planned schedule is often viewed as undesirable, as it implies missed opportunities to utilize costly perishable resources, whereas slack is critical in operations as a means for absorbing disruption. This article shows how delay propagation can be reduced by redistributing existing slack in the planning process, making minor modifications to the flight schedule while leaving the original fleeting and crew scheduling decisions unchanged. Computational results based on data from a major U.S. carrier are presented that show that significant improvements in operational performance can be achieved without increasing planned costs.

Scheduling Medical Residents at Boston University School of Medicine

The chief residents in the psychiatry program at Boston University School of Medicine (BUSM) must construct a schedule that simultaneously assigns residents to five types of call shifts, spanning three different hospitals, over a 365-day planning horizon. We show how user expertise and heuristic approaches alone fail to find acceptable solutions to this complex combinatorial problem; likewise, mathematical programming techniques alone are inadequate, largely because they lack a clearly definable objective function. However, by combining both approaches, we were able to find high-quality solutions in a very short time. The resulting schedule, which BUSM uses currently, has yielded substantial benefits; the solution quality has improved, and the effort required to develop the solution has been reduced.

Solving Truckload Procurement Auctions Over an Exponential Number of Bundles

Truckload carriers provide hundreds of billions of dollars worth of services to shippers in the United States alone each year. Internet auctions provide these shippers with a fast and easy way to negotiate potential contracts with a large number of carriers. Combinatorial auctions have the added benefit of allowing multiple lanes to be considered simultaneously in a single auction. This is important because it enables carriers to connect multiple lanes in continuous moves or tours, decreasing the empty mileage that must be driven, and therefore increasing overall efficiency. On the other hand, combinatorial auctions require bidding on an exponential number of bundles to achieve full economies of scope and scale, which is not tractable except for very small auctions. In most real-world auctions, bidding is instead typically limited to a very small subset of the potential bids. We present an implicit bidding approach to combinatorial auctions for truckload procurement that enables the complete set of all possible bids to be considered implicitly, without placing the corresponding burden of an exponential number of bids on the bidders or the auctioneer. We present the models needed to solve this problem. We then provide extensive computational results to demonstrate the tractability of our approach. Finally, we conclude with numerical analysis to assess the quality of the solutions that are generated and to demonstrate the benefits of our approach over existing bidding methods in practice.

An integer programming approach to generating airline crew pairings

The ability to generate crew pairings quickly is essential to solving the airline crew scheduling problem. Although techniques for doing so are well-established, they are also highly customized and require significant implementation efforts. This greatly impedes researchers studying important problems such as robust planning, integrated planning, and automated recovery, all of which also require the generating of crew pairings. As an alternative, we present an integer programming (IP) approach to generating crew pairings, which can be solved via traditional methods such as branch-and-bound using off-the-shelf commercial solvers. This greatly facilitates the prototyping and testing of new research ideas. In addition, we suggest that our modeling approach, which uses both connection variables and marker variables to capture the non-linear cost function and constraints of the crew scheduling problem, can be applicable in other scheduling contexts as well. Computational results using data from a major US hub-and-spoke carrier demonstrate the performance of our approach.

Contingency-Risk Informed Power System Design

We consider the problem of designing (or augmenting) an electric power system at a minimum cost such that it satisfies the N-k-ε survivability criterion. This survivability criterion is a generalization of the well-known N-k criterion, and it requires that at least (1-εj) fraction of the steady-state demand be met after failures of j components, for j=0,1,...,k. The network design problem adds another level of complexity to the notoriously hard contingency analysis problem, since the contingency analysis is only one of the requirements for the design optimization problem. We present a mixed-integer programming formulation of this problem that takes into account both transmission and generation expansion. We propose an algorithm that can avoid combinatorial explosion in the number of contingencies, by seeking vulnerabilities in intermediary solutions and constraining the design space accordingly. Our approach is built on our ability to identify such system vulnerabilities quickly. Our empirical studies on modified instances of the IEEE 30-bus and IEEE 57-bus systems show the effectiveness of our methods. We were able to solve the transmission and generation expansion problems for k=4 in approximately 30 min, while other approaches failed to provide a solution at the end of 2 h.

Composite-variable modeling for service parts logistics

Service parts logistics focuses on providing repair parts for computer, medical, and other high-cost equipment, typically in a very short period of time. Problems within this domain are often challenging to solve, due to the complexity of the network, tight constraints on time and warehouse capacity, and the high costs of inventory and transportation resources. Mathematical modeling can be critical in solving such difficult problems, but basic modeling approaches often suffer from complicating factors such as large numbers of constraints and integer variables, non-linearities, and weak linear programming relaxations. To address some of these difficulties, we present a modeling framework based on composite variables---variables that encompass multiple decisions. We begin by considering the problem of how to stock those repair parts which are both high cost and very low demand. We then discuss how this relatively simple problem can become much more computationally challenging when we expand the scope to consider a more global view of the system. As an example, we consider what happens when warehouse capacity constraints are added. We show that a basic modeling approach to this new problem is intractable for many instances of realistic size. We then present a composite-variable model and show how it enables us to improve tractability significantly. Our experience suggests potential opportunities to be found in modeling other SPL problems within a composite-variable framework as well. We conclude by presenting modeling approaches to address a broad class of problems within this challenging and important arena.

Optimization-based scheduling for the single-satellite, multi-ground station communication problem

In this paper, we develop models and algorithms for solving the single-satellite, multi-ground station communication scheduling problem, with the objective of maximizing the total amount of data downloaded from space. With the growing number of small satellites gathering large quantities of data in space and seeking to download this data to a capacity-constrained ground station network, effective scheduling is critical to mission success. Our goal in this research is to develop tools that yield high-quality schedules in a timely fashion while accurately modeling on-board satellite energy and data dynamics as well as realistic constraints of the space environment and ground network. We formulate an under-constrained mixed integer program (MIP) to model the problem. We then introduce an iterative algorithm that progressively tightens the constraints of this model to obtain a feasible and thus optimal solution. Computational experiments are conducted on diverse real-world data sets to demonstrate tractability and solution quality. Additional experiments on a broad test bed of contrived problem instances are used to test the boundaries of tractability for applying this approach to other problem domains. Our computational results suggest that our approach is viable for real-world instances, as well as providing a strong foundation for more complex problems with multiple satellites and stochastic conditions.

Integration of the Load-Matching and Routing Problem with Equipment Balancing for Small Package Carriers

Small package delivery is a multibillion dollar industry with complex planning decisions required to efficiently utilize costly resources and meet tight time requirements. The planning process is typically decomposed into sequential subproblems to establish tractability. This decomposition can greatly degrade solution quality. This paper therefore considers the integration of two closely related key subproblems: load matching and routing and equipment balancing. First, we identify critical challenges faced in trying to solve these problems. Then we present a novel modeling approach to address these challenges. Finally, we conclude with computational results from United Parcel Service, the worlds largest package delivery company, demonstrating an improvement of approximately 5% over the companys existing methods for solving this pair of problems.