Tactical crew planning at Turkish state railways

Tactical crew planning problem at Turkish State Railways (TCDD) involves finding the minimum crew capacity in a crew region required to operate a predetermined set of train duties assigned to the region by the headquarters. The problem is to be solved for each crew region by satisfying various rules and constraints associated with the requirements of the company. One of the most important constraints is the day-off requirement which makes the problem computationally intractable. In this study, we use a space-time network flow representation to solve the tactical capacity planning problem with day-off requirement. To solve the problem, we develop two solution approaches: the sequential approach and the integrated approach. In the sequential approach we mimic the current practice at TCDD and solve the problem in two stages. In the first stage, we solve a minimum flow problem over a space-time network by relaxing the day-off requirement. After obtaining the tentative schedules of crew members, we solve an assignment problem to fill-in the days-off in the tentative schedules by using additional substitute crew members. In the integrated approach, we solve a minimum flow problem with side constraints using a layered space-time network representation of the problem. We present the computational study on a real-life data set acquired from TCDD. We, then, study a higher level crew capacity planning problem. In this tactical-to-strategic level capacity planning problem, we minimize the total crew capacity of all regions by simultaneously considering multiple regions. We do this by re-assigning duties to different regions or allowing two neighboring crew regions share the train duties in different settings. For tactical-to-strategic capacity planning problem, we present the mathematical formulation of single-region and two-region models with various crew exchange policies. Given the large scale of the search space, we choose to employ a neighborhood search heuristic in order to solve the problem. The neighborhood search heuristic uses the minimum flow problem in the sequential approach as a subprocedure. We present the computational study again for the TCDD data set

Tactical crew planning in railways

Tactical crew capacity planning problem in railways involves finding the minimum number of crews in a region required to operate a predetermined set of train duties satisfying the strict day-off requirement for crew. For the single-region problem, we develop two solution approaches based on a space-time network representation: the sequential approach and the integrated approach. We also study the multi-regional capacity planning problem where we minimize total system-wide capacity by simultaneously considering multiple regions within a neighborhood search algorithm based on our solution methods for the single-region problem. We present the computational study on problem instances from Turkish State Railways

A branch-and-price algorithm for the rainbow cycle cover problems

A rainbow cycle in an undirected edge-colored graph is a cycle in which all edges have different colors. A rainbow cycle cover of a graph is a set of disjoint rainbow cycles, where each vertex belongs to exactly one cycle. The objective of the rainbow cycle cover problem is to minimize the number of rainbow cycles used to cover the vertices of the graph while the trivial cycle version also keeps the number of isolated vertices (called trivial rainbow cycles) at minimum. We present a branch-and-price procedure with column generation to solve both versions of the rainbow cycle cover problem. We compare our results with the literature in terms of computational performance. We also discuss two approaches to possibly improve the performance of the branch-and-price procedure

Dispersion with connectivity in wireless mesh networks

We study a multi-objective access point dispersion problem, where the conflicting objectives of maximizing the distance and maximizing the connectivity between the agents are considered with explicit coverage (or Quality of Service) constraints. We model the problem first as a multi-objective model, and then, we consider the constrained single objective alternatives, which we propose to solve using three approaches: The first approach is an optimal tree search algorithm, where bounds are used to prune the search tree. The second approach is a beam search heuristic, which is also used to provide lower bound for the first approach. The third approach is a straightforward integer programming approach. We present an illustrative application of our solution approaches in a real wireless mesh network deployment problem