Transportation Science current issue

Per-Seat, On-Demand Air Transportation Part I: Problem Description and an Integer Multicommodity Flow Model

Espinoza, D., Garcia, R., Goycoolea, M., Nemhauser, G. L., Savelsbergh, M. W. P. — 2008-08-01

The availability of relatively cheap small jet planes has led to the creation of on-demand air transportation services in which travelers call a few days in advance to schedule a flight. A successful on-demand air transportation service requires an effective scheduling system to construct minimum-cost pilot and jet itineraries for a set of accepted transportation requests. We present an integer multicommodity network flow model with side constraints for such dial-a-flight problems. We develop a variety of techniques to control the size of the network and to strengthen the quality of the linear programming relaxation, which allows the solution of small instances. In Part II, we describe how this core optimization technology is embedded in a parallel, large-neighborhood, local search scheme to produce high-quality solutions efficiently for large-scale real-life instances.

Per-Seat, On-Demand Air Transportation Part II: Parallel Local Search

Espinoza, D., Garcia, R., Goycoolea, M., Nemhauser, G. L., Savelsbergh, M. W. P. — 2008-08-01

The availability of relatively cheap small jet aircrafts suggests a new air transportation business: dial-a-flight, an on-demand service in which travelers call a few days in advance to schedule transportation. A successful on-demand air transportation service requires an effective scheduling system to construct minimum-cost pilot and jet itineraries for a set of accepted transportation requests. In Part I, we introduced an integer multicommodity network flow model with side constraints for the dial-a-flight problem and showed that small instances can be solved effectively. Here, we demonstrate that high-quality solutions for large-scale real-life instances can be produced efficiently by embedding the core optimization technology in a local search scheme. To achieve the desired level of performance, metrics were devised to select neighborhoods intelligently, a variety of search diversification techniques were included, and an asynchronous parallel implementation was developed.

Modelling Robust Flight-Gate Scheduling as a Clique Partitioning Problem

Dorndorf, U., Jaehn, F., Pesch, E. — 2008-08-01

This paper considers the problem of assigning flights to airport gates. We examine the general case in which an aircraft serving a flight may be assigned to different gates for arrival and departure processing and for optional intermediate parking. Restrictions to this assignment include gate closures and shadow restrictions, i.e., the situation in which certain gate assignments may cause the blocking of neighboring gates. The objectives include maximization of the total assignment preference score, minimization of the number of unassigned flights during overload periods, minimization of the number of tows, as well as maximization of the robustness of the resulting schedule with respect to flight delays. We are presenting a simple transformation of the flight-gate scheduling (FGS) problem to a graph problem, i.e., the clique partitioning problem (CPP). The algorithm used to solve the CPP is a heuristic based on the ejection chain algorithm by Dorndorf and Pesch [Dorndorf, U., E. Pesch. 1994. Fast clustering algorithms. ORSA J. Comput. 6 141–153]. This leads to a very effective approach for solving the original problem.

Queuing Models for Sizing and Structuring Rental Fleets

Papier, F., Thonemann, U. W. — 2008-08-01

This paper has been motivated by a fleet optimization problem faced by one of the leading European cargo rail companies. The company operates a fleet of more than 100,000 rail cars and annually invests significant sums of money into new cars. Because the price tag of a new car is over 50,000 euros, planning such a fleet is an important activity at the company. In this paper, we develop and solve analytical models for fleet planning. We first describe the rental process and show how it can be modeled as a queuing loss system. We then develop a profit function and derive several structural results, such as the concavity of the profit function in the fleet size. Building on these structural results, we show how the fleet size can be optimized, how the fleet structure (i.e., the types of cars being used) can be optimized, and how a joint fleet of owned and leased cars can be optimized. Because some of the optimal methods are difficult to implement, we also develop and test an approximation that is easy to implement. To illustrate our findings and to validate our approach, we provide numerical results that are based on data of the company that motivated our research.

An Integrated Framework for Intercity Bus Scheduling Under Stochastic Bus Travel Times

Yan, S., Tang, C.-H. — 2008-08-01

In this research, we develop an integrated framework to help the intercity bus carriers plan bus routes and schedules under stochastic bus travel times. Unlike past research, where stochastic disturbances in the planning and real-time stages are handled separately, the integrated framework embedded in an iterative solution process combines these two stages by repeatedly solving a series of planned bus scheduling and real-time schedule adjustment problems to find suitable bus routes and schedules. The test results, related to a major Taiwan intercity bus operation, show the good performance of the proposed framework.

A Branch-and-Price-and-Cut Method for Ship Scheduling with Limited Risk

Hwang, H.-S., Visoldilokpun, S., Rosenberger, J. M. — 2008-08-01

Maritime logistics operations are full of uncertainty such as severe weather, mechanical problems, strikes, and fluctuating freight rates. Traditional ship-scheduling models ignore uncertainty, even in highly volatile markets. Although ship operators can increase revenue by delivering many spot cargoes, they have to embrace the risk of the fluctuation of spot rates. We present a set-packing model that limits risk using a quadratic variance constraint. We use a traditional Kelley's cutting plane algorithm and a delayed column-and-cut generation (branch-and-price-and-cut) algorithm on medium-sized ship-scheduling problems with restricted variance. We develop a second set of cuts that are more restrictive under certain conditions. Computational results show that the variance of profit can be significantly reduced with a reasonable increase in cost.

Route Design for Lean Production Systems

Ohlmann, J. W., Fry, M. J., Thomas, B. W. — 2008-08-01

We consider the problem of routing a fleet of vehicles to pick up components from a network of suppliers and to deliver them to a fixed depot in a lean production system. The pursuit of low work-in-process inventory and production smoothing throughout the system introduces complicating side constraints, creating an enriched case of the vehicle routing problem with time windows and split deliveries. We present a two-phase routing and scheduling approach to address this problem. The routing phase consists of a nested tabu search heuristic that iterates between determining the suppliers' visit frequencies and developing vehicle routes. Given a routing plan, the scheduling phase determines the timing of supplier visits using a binary integer program designed to promote production leveling. Through computational testing on real-world data sets, we compare our solutions to those in the literature and those used by practitioners in the industry.

An Effective Multirestart Deterministic Annealing Metaheuristic for the Fleet Size and Mix Vehicle-Routing Problem with Time Windows

Braysy, O., Dullaert, W., Hasle, G., Mester, D., Gendreau, M. — 2008-08-01

This paper presents a new deterministic annealing metaheuristic for the fleet size and mix vehicle-routing problem with time windows. The objective is to service, at minimal total cost, a set of customers within their time windows by a heterogeneous capacitated vehicle fleet. First, we motivate and define the problem. We then give a mathematical formulation of the most studied variant in the literature in the form of a mixed-integer linear program. We also suggest an industrially relevant, alternative definition that leads to a linear mixed-integer formulation. The suggested metaheuristic solution method solves both problem variants and comprises three phases. In Phase 1, high-quality initial solutions are generated by means of a savings-based heuristic that combines diversification strategies with learning mechanisms. In Phase 2, an attempt is made to reduce the number of routes in the initial solution with a new local search procedure. In Phase 3, the solution from Phase 2 is further improved by a set of four local search operators that are embedded in a deterministic annealing framework to guide the improvement process. Some new implementation strategies are also suggested for efficient time window feasibility checks. Extensive computational experiments on the 168 benchmark instances have shown that the suggested method outperforms the previously published results and found 167 best-known solutions. Experimental results are also given for the new problem variant.

Tabu Search, Partial Elementarity, and Generalized k-Path Inequalities for the Vehicle Routing Problem with Time Windows

Desaulniers, G., Lessard, F., Hadjar, A. — 2008-08-01

The vehicle routing problem with time windows consists of delivering goods at minimum cost to a set of customers using an unlimited number of capacitated vehicles assigned to a single depot. Each customer must be visited within a prescribed time window. The most recent successful solution methods for this problem are branch-and-price-and-cut algorithms where the column generation subproblem is an elementary shortest-path problem with resource constraints (ESPPRC). In this paper, we propose new ideas having the potential to improve such a methodology. First, we develop a tabu search heuristic for the ESPPRC that allows, in most iterations, the generation of negative reduced cost columns in a short computation time. Second, to further accelerate the subproblem solution process, we propose to relax the elementarity requirements for a subset of the nodes. This relaxation, however, yields weaker lower bounds. Third, we introduce a generalization of the k-path inequalities and highlight that these generalized inequalities can, in theory, be stronger than the traditional ones. Finally, combining these ideas with the most recent advances published in the literature, we present a wide variety of computational results on the Solomon's 100-customer benchmark instances. In particular, we report solving five previously unsolved instances.