Higher Education Management

The optimal arrangement of the curriculum is an important part of every educational program. During the decision making about this arrangement, one should consider many factors which have impact on the curriculum. In this chapter, a struggle to the design of the curriculum through graph theory is made.

Facility Layout Planning

The weighted maximal planar graph (WMPG) appears in many applications. It is currently used to design facilities layout in manufacturing plants. Given an edge-weighted complete simple graph G, the WMPG involves finding a sub-graph of G that is planar in the sense that it could be embedded on the plane such that none of its edges intersect, and is maximal in the sense that no more edges can be added to it unless its planarity is violated. Finally, it is optimal in the sense that the resulting maximal planar graph holds the maximum sum of edge weights. In this chapter, the aim is to explain the application of planarity in facility layout design. The mathematical models and the algorithms developed for the problem so far are explained. In the meanwhile, the corollaries and theorems needed to explain the algorithms and models are briefly given. In the last part, an explanation on how to draw block layout from the adjacency graph is given.

Networks

This chapter sheds light on various aspects of network theory and relevant concepts including basic definitions, the most common types of network flow problems that have been studied by literature, and the main algorithms and solution approaches proposed for solving network problems.

Train Timetable Construction

Railway transportation has a fundamental role in development of countries. Efficient usage of capacities in this industry is essential. Solving Train Timetabling Problem (TTP) is one of the valuable ways to exploit the capacities efficiently. In this book chapter, the author introduces TTP in general, and demonstrates the solution procedure for a special case of it via graph theory techniques.

Understanding Reinforcement Learning Theory for Operations Research and Management

The objective of this chapter is the introduction of reinforcement learning in the context of graphs. In particular, a linkage between reinforcement learning theory and graph theory is established. Within the context of semi-supervised pattern recognition, reinforcement learning theory is introduced and discussed in basic steps. Motivation, leading to learning agent development with reinforcement capabilities for massive data pattern learning is also given. The main contribution of this book chapter is the provision of a basic introductory text authored in less mathematical rigor for the benefit of students, tutors, lecturers, researchers, and/or professionals who wish to delve into the foundation, representations, concepts, and theory of graph based semi-supervised intelligent systems.

Inbound Logistics and Vehicle Routing

One of the most important factors in the design of automated guided vehicle system (AGVS) is the flow path design. The unidirectional/ conventional flow path design in automated guided vehicle (AGV) routing problem considers aisles to be undirected so that each pair of cells could be reached mutually. Regarding the flow between cells, this chapter presents a novel algorithm to minimize the total distance traveled by the loaded vehicles on the block layout graph. The algorithm is an efficient branch-and-band method with branches on the feasible solutions to solve the strongly connected graph layout. To find the feasible and efficient flow path, the authors use the Revised-DFS based on testing connectivity of the graph.

Matching Theory

Matching theory has a fundamental role in graph theory and combinatorial optimization. The authors introduce the concepts of covering and matching, which have a close relationship. The chapter aims to introduce the matching theory from an industrial engineer’s point of view. To clarify the application of matching theory, two major maximum matching algorithms are described and implemented in two well-known industrial engineering problems.

Planarity

In this chapter the authors consider a property of a whole graph, which is of theoretical and practical importance. The concept addresses the possibility of drawing a given graph in a plane such that none of its edges intersect. The authors find this property, named planarity, very useful in application. They address the problem of planarity recognition including its theorems and its algorithm. Also, they discuss the concept of duality of graphs in the context of planarity.

Connectivity

In this chapter, the concept of graph connectivity is introduced. In the first section, some concepts such as walk, path, component and connected graph are defined, and connectedness of a graph from the viewpoint of vertex connectivity, and also, edge connectivity are discussed. Then, blocks and block tree of graphs are illustrated. In addition, connectivity in directed graphs is introduced. Furthermore, in the last section, two graph traversal algorithms, depth first search and breadth first search, are described to investigate the connectedness of directed and undirected graphs.

Matrices

Matrices are one of the most important tools of representing graphs. Various types of matrices are used for this purpose. This chapter teaches about the definitions and the standard notations of the matrices. Then, some kinds of the matrices such as Adjacency, Incidence, Cycle and Cut-set are introduced. Some discussions will be made on the applications of these matrices. Advanced topics on matrices will be the final part.