Integer programming based solution approaches for the train dispatching problem

Railroads face the challenge of competing with the trucking industry in a fastpaced environment. In this respect, they are working toward running freight trains on schedule and reducing travel times. The planned train schedules consist of departure and arrival times at main stations on the rail network. A detailed timetable, on the other hand, consists of the departure and arrival times of each train in each track section of its route. The train dispatching problem aims to determine detailed timetables over a rail network in order to minimize deviations from the planned schedule. We provide a new integer programming formulation for this problem based on a spacetime network; we propose heuristic algorithms to solve it and present computational results of these algorithms. Our approach includes some realistic constraints that have not been previously considered as well as all the assumptions and practical issues considered by the earlier works

Solving a robust airline crew pairing problem with column generation

In this study, we solve a robust version of the airline crew pairing problem. Our concept of robustness was partially shaped during our discussions with small local airlines in Turkey which may have to add a set of extra flights into their schedule at short notice during operation. Thus, robustness in this case is related to the ability of accommodating these extra flights at the time of operation by disrupting the original plans as minimally as possible. We focus on the crew pairing aspect of robustness and prescribe that the planned crew pairings incorporate a number of predefined recovery solutions for each potential extra flight. These solutions are implemented only if necessary for recovery purposes and involve either inserting an extra flight into an existing pairing or partially swapping the flights in two existing pairings in order to cover an extra flight. The resulting mathematical programming model follows the conventional set covering formulation of the airline crew pairing problem typically solved by column generation with an additional complication. The model includes constraints that depend on the columns due to the robustness consideration and grows not only column-wise but also row-wise as new columns are generated. To solve this dicult model, we propose a row and column generation approach. This approach requires a set of modifications to the multi-label shortest path problem for pricing out new columns (pairings) and various mechanisms to handle the simultaneous increase in the number of rows and columns in the restricted master problem during column generation. We conduct computational experiments on a set of real instances compiled from a local airline in Turkey

An efficient heuristic for the multi-vehicle one-to-one pickup and delivery problem with split loads

In this study, we consider the Multi-vehicle One-to-one Pickup and Delivery Problem with Split Loads (MPDPSL). This problem is a generalization of the one-to-one Pickup and Delivery Problem (PDP) where each load can be served by multiple vehicles as well as multiple stops by the same vehicle. In practice, split deliveries is a viable option in many settings where the load can be physically split, such as courier services of third party logistics operators. We propose an efficient heuristic that combines the strengths of Tabu Search and Simulated Annealing for the solution of MPDPSL. Results from experiments on two problems sets in the literature indicate that the heuristic is capable of producing good quality solutions in reasonable time. The experiments also demonstrate that up to 33\% savings can be obtained by allowing split loads; however, the magnitude of savings is dependent largely on the spatial distribution of the pickup and delivery points

Railway crew capacity planning problem with connectivity of schedules

We study a tactical level crew capacity planning problem in railways which determines the minimum required crew size in a region while both feasibility and connectivity of schedules are maintained. We present alternative mathematical formulations which depend on network representations of the problem. A path-based formulation in the form of a set-covering problem along with a column-and-row generation algorithm is proposed. An arc-based formulation of the problem is solved with a commercial linear programming solver. The computational study illustrates the effect of schedule connectivity on crew capacity decisions and shows that arc-based formulation is a viable approach

A note on "A LP-based heuristic for a time-constrained routing problem"

In their paper, Avella et al. (2006) investigate a time-constrained routing problem. The core of the proposed solution approach is a large-scale linear program that grows both row- and column-wise when new variables are introduced. Thus, a column-and-row generation algorithm is proposed to solve this linear program optimally, and an optimality condition is presented to terminate the column-and-row generation algorithm. We demonstrate by using Lagrangian duality that this optimality condition is incorrect and may lead to a suboptimal solution at termination

A note on "A LP-based heuristic for a time-constrained routing problem"

Avella et al. (2006) [Avella, P., D'Auria, B., Salerno, S. (2006). A LP-based heuristic for a time-constrained routing problem. European Journal of Operational Research 173:120-124] investigate a time-constrained routing (TCR) problem. The core of the proposed solution approach is a large-scale linear program (LP) that grows both row- and column-wise when new variables are introduced. Thus, a column-and-row generation algorithm is proposed to solve this LP optimally, and an optimality condition is presented to terminate the column-and-row generation algorithm. We demonstrate that this optimality condition is incorrect and may lead to a suboptimal solution at termination. We identify the source of this error and discuss how the generic column-and-row generation algorithm proposed by Muter et al. (2010) may be applied to this TCR problem in order to solve the proposed large-scale LP correctly