The focus area of this paper is on the assignment problem with budget constraints which is one of the application area of combinatorial optimization that operates on the domain of those optimization problems,in which the set of feasible solutions is discrete or can be reduced to discrete,and in which the goal is to find the best solution. It is particularly concerned with solving the unconstrained assignment problems with Hungarian algorithm and the constrained assignment problem by cutting plane or outer linearization algorithm for solving the Lagrangian dual problem in which, at each iteration,the function that approximates the dual function is optimized. The paper is divided in to two chapters. In the first chapter,the classical assignment problem,the problem of finding optimum (minimum or maximum) cost or profit assignment a set of workers or resources to jobs or activities to gather with its mathematical formulation,solution methods and special cases in assignment problems were considered. Under the second chapter, we have considered generalization of the classical assignment problem concerning resource(or budget) constraints, due to the variety of real life problems.
A wireless mesh networks (WMNs) has emerged recently, WMN consist of two types of nodes mesh routers and mesh clients.WMN is dynamically self-organized and self-configured, with the nodes in the network automatically establishing and maintaining mesh connectivity among themselves. Channel assignment is a critical issue in WMN which is the mapping between the available channels and the radios at each node such that the network performance is optimized, and hence the focus of this work along with static channel assignment, multi-radio, multi-channel. Multi-radio MAC can potentially achieve higher network capacity than single-radio MAC. We design and implement a new agent (DSBCA) distributed channel assignment spanner base, the routing protocol Optimize the network performance considering the throughput, end-to-end delay, connectivity and the interference of our channel assignment algorithm. Base on the network simulations NS2.34 on Linux Fedora and our proposed channel assignment algorithm improved the throughput, minimal-connectivity preserving channel assignment algorithm.