Solving Non-Quadratic Matrices In Assignment Problems With An Improved Version Of Vogel's Approximation Method

—The efficient allocation of tasks to vehicles in a fleet of self-driving vehicles (SDV) becomes challenging for largescale systems (e. g. more than hundred vehicles). Operations research provides different methods that can be applied to solve such assignment problems. Integer Linear Programming (ILP), the Hungarian Method (HM) or Vogel’s Approximation Method (VAM) are frequently used in related literature (Paul 2018; Dinagar and Keerthivasan 2018; Nahar et al. 2018; Ahmed et al. 2016; Korukoglu and Ballı 2011; Balakrishnan 1990). The under- ˘lying paper proposes an adapted version of VAM which reaches better solutions for non-quadratic matrices, namely Vogel’s Approximation Method for non-quadratic Matrices (VAM-nq). Subsequently, VAM-nq is compared with ILP, HM and VAM by solving matrices of different sizes in computational experiments in order to determine the proximity to the optimal solution and the computation time. The experimental results demonstrated that both VAM and VAM-nq are five to ten times faster in computing results than HM and ILP across all tested matrix sizes. However, we proved that VAM is not able to generate optimal solutions in large quadratic matrices constantly (starting at approx. 15 × 15) or small non-quadratic matrices (starting at approx. 5 × 6). In fact, we show that VAM produces insufficient results especially for non-quadratic matrices. The result deviate further from the optimum if the matrix size increases. Our proposed VAM-nq is able to provide similar results as the original VAM for quadratic matrices, but delivers much better results in non-quadratic instances often reaching an optimum solution. This is especially important for practical use cases since quadratic matrices are rather rare

Transportation problems and assignment problems

Special computation techniques have been developed for certain types of linear programming problems that are widely used in mathematical modeling of real life situations. One of the most useful of these special purpose algorithms is transportation method. In a classical transportation problem the cost is minimized by selecting the optimal path for transporting goods from a set of origins to a set of destinations. Assignment method is a special case of more general transportation problem. A discussion of linear programming in general, theory supporting transportation method, methods of finding optimal solution, applications of transportation and assignment problems are presented. Transportation and assignment methods are found to offer significant computational efficiency over the simplex method for certain types of linear problems

The Sixth Copper Mountain Conference on Multigrid Methods, part 1

The Sixth Copper Mountain Conference on Multigrid Methods was held on 4-9 Apr. 1993, at Copper Mountain, CO. This book is a collection of many of the papers presented at the conference and as such represents the conference proceedings. NASA LaRC graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The multigrid discipline continues to expand and mature, as is evident from these proceedings. The vibrancy in this field is amply expressed in these important papers, and the collection clearly shows its rapid trend to further diversity and depth

Research on the topics of neutrosophic operations research. Volume 1

In this volume, we present a set of research that was published in cooperation with a number of researchers and those interested in keeping pace with the great scientific development that our contemporary world is witnessing, and one of its products was neutrosophic science, which was founded by the American scientist and mathematical philosopher Florentin Smarandache in 1995. Through it, we present a new vision for some research methods. Operations research to the concepts of this science

Heuristic Solution Methods for Multi-resource Generalized Assignment Problems

Industrial Engineerin

Proceedings of the Mobile Satellite Conference

A satellite-based mobile communications system provides voice and data communications to mobile users over a vast geographic area. The technical and service characteristics of mobile satellite systems (MSSs) are presented and form an in-depth view of the current MSS status at the system and subsystem levels. Major emphasis is placed on developments, current and future, in the following critical MSS technology areas: vehicle antennas, networking, modulation and coding, speech compression, channel characterization, space segment technology and MSS experiments. Also, the mobile satellite communications needs of government agencies are addressed, as is the MSS potential to fulfill them