Optimum Flows in Directed Bipartite Dynamic Network. The Static Approach

The theory of flows is one of the most important parts of Combinatorial Optimization and it has various applications. In this paper we study optimum (maximum or minimum) flows in directed bipartite dynamic network and is an extension of article [9]. In practical situations, it is easy to see many time-varying optimum problems. In these instances, to account properly for the evolution of the underlying system overtime, we need to use dynamic network flow models. When the time is considered as a variable discrete values, these problems can be solved by constructing an equivalent, static time expanded network. This is a static approach.

Network Flow Models for Evacuation Planning

Because of increasing number of natural and human created disasters worldwide, a research on challenging issues of emergency management are being quite emerging for the betterment of today's complex real-life. The diversified operational research models and their solutions techniques together with their simulation schemes are yet not evident in realizing a generally acceptable solution of these challenging issues. We consider the planning problems in emergencies which is even unsolved yet in general. In this paper, we briefly give the models and algorithms on the existing solution approaches within the framework of evacuation planning network flow models, where the objectives are either to maximize the flow over time or minimize the time for transshipment of the estimated flow. The flow models and solution techniques with their insights presented here highlight the state of existing approaches and hint further direction of research in the field of evacuation optimization. Journal of the Institute of Engineering, 2017, 13(1): 90-101