The objective of this paper is to review the current status of ship routing and scheduling. We focus on literature published during the last decade. Because routing and scheduling problems are closely related to many other fleet planning problems, we have divided this review into several parts. We start at the strategic fleet planning level and discuss the design of fleets and sea transport systems. We continue with the tactical and operational fleet planning level and consider problems that comprise various ship routing and scheduling aspects. Here, we separately discuss the different modes of operations: industrial, tramp, and liner shipping. Finally, we take a glimpse at naval applications and other related problems that do not naturally fall into these categories. The paper also presents some perspectives regarding future developments and use of optimization-based decision-support systems for ship routing and scheduling. Several of the trends indicate both accelerating needs for and benefits from such systems and, hopefully, this paper will stimulate further research in this area.

https://www.jstor.org/stable/pdfplus/25769174.pdf

Ship Routing and Scheduling: Status and Perspectives

Massachusetts Institute of Technology, Cambridge, Massachusetts (Received August 1994; revision received October 1995; accepted May 1996) Throughout the United States and Europe, demand for airport use has been increasing rapidly, while airport capacity has been stagnating. Over the last ten years the number of passengers has increased by more than 50 percent and is expected to continue increasing at this rate. Acute congestion in many major airports has been the unfortunate result. For U.S. airlines, the expected yearly cost of the resulting delays is currently estimated at $3 billion. In order to put this number in perspective, the total reported losses of all U.S. airlines amounted to approximately $2 billion in 1991 and $2.5 billion in 1990. Furthermore, every day 700 to 1100 flights are delayed by 15 minutes or more. European airlines are in a similar plight. Optimally controlling the flow of aircraft either by adjusting their release times into the network (ground-holding) or their speed once they are airborne is a cost effective method to reduce the impact of congestion on the air traffic system. This paper makes the following contributions: (a) we build a model that takes into account the capacities of the National Airspace System (NAS) as well as the capacities at the airports, and we show that the resulting formulation is rather strong as some of the proposed inequalities are facet defining for the convex hull of solutions; (b) we address the complexity of the problem; (c) we extend that model to account for several variations of the basic problem, most notably, how to reroute flights and how to handle banks in the hub and spoke system; (d) we show that by relaxing some of our constraints we obtain a previously addressed problem and that the LP relaxation bound of our formulation is at least as strong when compared to all others proposed in the literature for this problem; and (e) we solve large scale, realistic size problems with several thousand flights.

/pdf/the-air-traffic-flow-management-problem-with-enroute-2siiz8v115.pdf

The Air Traffic Flow Management Problem with Enroute Capacities

https://www.sintef.no/globalassets/project/vip08/vip08-hoff.pdf

Review: Industrial aspects and literature survey: Fleet composition and routing

This paper presents an overview of several important areas of operations research applications in the air transport industry. Specific areas covered are: the various stages of aircraft and crew schedule planning; revenue management, including overbooking and leg-based and network-based seat inventory management; and the planning and operations of aviation infrastructure (airports and air traffic management). For each of these areas, the paper provides a historical perspective on OR contributions, as well as a brief summary of the state of the art. It also identifies some of the main challenges for future research.

https://pubsonline.informs.org/doi/pdf/10.1287/trsc.37.4.368.23276

Applications of Operations Research in the Air Transport Industry

A major goal of air traffic management is to strategically control the flow of traffic so that the demand at an airport meets but does not exceed the operational capacity. This work considers the major aspects of airport operational capacities relevant to the strategic management of air traffic. A representation of airport capacity that properly reflects an airport's operational limits is discussed. A method is presented for estimating practical airport capacities under various operational conditions. A technique is proposed for optimizing the available airport capacity to best satisfy the expected traffic demand. The optimization is achieved by considering arrival and departure operations as interdependent processes and by strategically allocating the airport capacity between arrivals and departures. The underlying mathematical model is presented, as well as numerical examples illustrating the benefits when solving airport congestion problems. >

Airport capacity: representation, estimation, optimization

As air traffic congestion grows, ground-holding (or “gate-holding”) of aircraft is becoming increasingly common. The “ground-holding policy problem” (GHPP) consists of developing strategies for deciding which aircraft to hold on the ground and for how long. In this paper we present a stochastic linear programming solution to the static GHPP for a single airport. The computational complexity of existing solutions requires heuristic approaches in order to solve practical instances of the problem. The advantage of our solution is that, even for the largest airports, problem instances result in linear programs that can be solved optimally using just a personal computer. We present a set of algorithms and compare their performance to a deterministic solution and to the passive strategy of no ground-holds (i.e., to the strategy of taking all delays in the air) under different weather scenarios.

Solving Optimally the Static Ground-Holding Policy Problem in Air Traffic Control

Existing probabilistic solutions to the ground-holding problem in air traffic control are of a static nature, with ground-holds assigned to aircraft at the beginning of daily operations. In this paper we present an optimal dynamic solution that simplifies the structure of the control mechanism by exercising ground-holding on groups of aircraft instead of individual flights. Using stochastic linear programming with recourse, we have been able to solve problem instances for one of the largest airports in the U.S. with just a powerful PC. We illustrate the advantage of the probabilistic dynamic solution over: (a) the static solution; (b) a deterministic solution; and (c) the passive strategy of no ground-holding.

Dynamic solution to the ground-holding problem in air traffic control

The adoption of collaborative decision making within the ground-delay program rendered obsolete much of the published research on the ground-holding problem as the emphasis was on control of individual flights. We focus on two pertinent static-stochastic models that exercise control on groups of flights instead of individual flights. We show that the first model, developed previous to the collaborative decision-making initiative, is capable of providing the information needed for the assignment of ground holds under the current system; however, the integrality and equity of solutions is not guaranteed. We then prove that by focusing on marginally nondecreasing ground-hold cost functions, solutions to the linear programming relaxation of the first model are guaranteed to be integer and equitable. We also show that the second model, a model with linear costs developed after collaborative decision-making procedures were in place, is a simplified version of the first that offers the advantage of a smaller number of variables at the expense of modeling flexibility. Our computational results show that the size advantage does not translate into significantly faster running times and demonstrate the relevance of the modeling flexibility associated with the first model. These results suggest that implementation of the earlier model is still an attractive option.

Equitable Models for the Stochastic Ground-Holding Problem Under Collaborative Decision Making

Since it is safer and less expensive to absorb delays on the ground, air traffic control management tries to limit the duration of airborne delays by holding aircraft previous to departure when congestion at the airport of destination is anticipated The problem of assigning appropriate ground-holds to aircraft is known as the ground-holding problem Ground-holding decisions must be implemented in real time and for multiple airports; therefore, the speed of solution for algorithms is critical This paper tests static and dynamic optimal solutions, and a very fast heuristic for the assignment of ground-holds in air traffic control The optimal solutions are based on stochastic linear programming The heurtstic incorporates elements of stochastic modeling by utilizing information conveyed by a probabilistic forecast of airport landing capacity, while taking into consideration the dynamic nature of the problem In extensive computational experiments based on data for Logan airport, the heuristic performed significantly better than the optimal static solution, a deterministic solution, and the passive strategy of no-ground-holds; and within 5% of the optimal dynamic solution at a fraction of the computational time Due to its remarkable efficiency, the stochastic-dynamic heuristic appears to be a promising building block in the development of fast ground-holding algorithms for the complete network of airports

Optimal Algorithms and a Remarkably Efficient Heuristic for the Ground-Holding Problem in Air Traffic Control

Traffic congestion has become pervasive in the most developed air transportation systems in the world, i.e., those. of North America, Western Europe and East Asia. While the available statistics on the magnitude of air traffic delays are not very precise, there is no doubt that the total direct and indirect costs of these delays are very large. If one combines the various numbers reported, worldwide direct airline costs may add up to $5 billion or more per year. By comparison the world’s scheduled airlines suffered in 1990, one of the worst years in aviation history in economic terms, a total net loss of $4.3 billion. An equally telling statistic is that ground-holding delays (please see below for a definition) to airline aircraft in the United States averaged 2000 hours per day in 1986, approximately equivalent to grounding the entire fleet (250 aircraft at that time) of Delta Airlines, the third largest carrier in the United States. With significant increases in demand expected to continue, congestion is now cited by many experts and organizations as one of the principal impediments to the future growth of the airline industry.

Octavio Richetta

Papers

Solving Optimally the Static Ground-Holding Policy Problem in Air Traffic Control

Dynamic solution to the ground-holding problem in air traffic control

Equitable Models for the Stochastic Ground-Holding Problem Under Collaborative Decision Making

Optimal Algorithms and a Remarkably Efficient Heuristic for the Ground-Holding Problem in Air Traffic Control

Models for the Ground Holding Problem