Assignment problem

About: Assignment problem is a research topic. Over the lifetime, 7588 publications have been published within this topic receiving 172820 citations. The topic is also known as: marriage problem.

Network Equilibrium of Coupled Transportation and Power Distribution Systems

Abstract: This paper presents a holistic modeling framework for the interdependent transportation network and power distribution network. From a system-level perspective, on-road fast charging stations would simultaneously impact vehicle routing in the transportation system and load flows in the distribution system, therefore tightly couple the two systems. In this paper, a dedicated traffic user equilibrium model is proposed to describe the steady-state distribution of traffic flows comprised of gasoline vehicles and electric vehicles. It encapsulates route selections, charging opportunities, electricity prices, and individual rationalities of minimum travel expense in a convex traffic assignment problem over an extended transportation network. An adaptive path generation oracle is suggested to solve the problem in a tractable manner. Economic operation of the power distribution system is formulated as an alternating current optimal power flow problem. Convex relaxation is performed. The optimal generation dispatch and nodal electricity prices can be computed from a second-order cone program. It is revealed that an equilibrium state will emerge due to the rational behaviors in the coupled systems, which is characterized via a fixed-point problem. A best-response decomposition algorithm is suggested to identify the network equilibrium through iteratively solving the traffic assignment problem and the optimal power flow problem, both of which entail convex optimization. Illustrative examples are presented to validate related concepts and methods.

The Dynamic Hungarian Algorithm for the Assignment Problem with Changing Costs

Abstract: In this paper, we present the dynamic Hungarian algorithm, applicable to optimally solving the assignment problem in situations with changing edge costs or weights This problem is relevant, for example, in a transportation domain where the unexpected closing of a road translates to changed transportation costs When such cost changes occur after an initial assignment has been made, the new problem, like the original problem, may be solved from scratch using the well-known Hungarian algorithm However, the dynamic version of the algorithm which we present solves the new problem more efficiently by repairing the initial solution obtained before the cost changes We present proofs of the correctness and efficiency of our algorithm and present simulation results illustrating its efficiency

Traffic grooming, routing, and wavelength assignment in optical WDM mesh networks

Abstract: In this paper, we consider the traffic grooming, routing, and wavelength assignment (GRWA) problem for optical mesh networks. In most previous studies on optical mesh networks, traffic demands are usually assumed to be wavelength demands, in which case no traffic grooming is needed. In practice, optical networks are typically required to carry a large number of lower rate (sub-wavelength) traffic demands. Hence, the issue of traffic grooming becomes very important since it can significantly impact the overall network cost. In our study, we consider traffic grooming in combination with traffic routing and wavelength assignment. Our objective is to minimize the total number of transponders required in the network. We first formulate the GRWA problem as an integer linear programming (ILP) problem. Unfortunately, for large networks it is computationally infeasible to solve the ILP problem. Therefore, we propose a decomposition method that divides the GRWA problem into two smaller problems: the traffic grooming and routing problem and the wavelength assignment problem, which can then be solved much more efficiently. In general, the decomposition method only produces an approximate solution for the GRWA problem. However, we also provide some sufficient condition under which the decomposition method gives an optimal solution. Finally, some numerical results are provided to demonstrate the efficiency of our method.

Technical Note-Minimizing Average Flow Time with Parallel Machines

Abstract: This note shows that the assignment and sequencing of single-operation jobs in a parallel-machine environment can be formulated as an assignment problem. Means for reducing the size and computational difficulty of this problem are identified.