This paper presents an algorithm for solving Bi-criteria Minimum Cost Dynamic Flow (BiCMCDF) problem with continuous flow variables. The approach is to transform a bi-criteria problem into a parametric one by building...This paper presents an algorithm for solving Bi-criteria Minimum Cost Dynamic Flow (BiCMCDF) problem with continuous flow variables. The approach is to transform a bi-criteria problem into a parametric one by building a single parametric linear cost out of the two initial cost functions. The algorithm consecutively finds efficient extreme points in the decision space by solving a series of minimum parametric cost flow problems with different objective functions. On each of the iterations, the flow is augmented along a cheapest path from the source node to the sink node in the time-space network avoiding the explicit time expansion of the network.展开更多
The minimum cost of capacity expansion for time-limited transportation problem on-demand (MCCETLTPD) is to find such a practicable capacity expansion transportation scheme satisfying the time-limited T along with all ...The minimum cost of capacity expansion for time-limited transportation problem on-demand (MCCETLTPD) is to find such a practicable capacity expansion transportation scheme satisfying the time-limited T along with all origins’ supply and all destinations’ demands as well as the expanding cost is minimum. Actually, MCCETLTPD is a balance transportation problem and a variant problem of minimum cost maximum flow problem. In this paper, by creating a mathematical model and constructing a network with lower and upper arc capacities, MCCETLTPD is transformed into searching feasible flow in the constructed network, and consequently, an algorithm MCCETLTPD-A is developed as MCCETLTPD’s solution method basing minimum cost maximum flow algorithm. Computational study validates that the MCCETLTPD-A algorithm is an efficient approach to solving the MCCETLTPD.展开更多
Let C be a set of colors, and let ?be an integer cost assigned to a color c in C. An edge-coloring of a graph ?is assigning a color in C to each edge ?so that any two edges having end-vertex in common have different c...Let C be a set of colors, and let ?be an integer cost assigned to a color c in C. An edge-coloring of a graph ?is assigning a color in C to each edge ?so that any two edges having end-vertex in common have different colors. The cost ?of an edge-coloring f of G is the sum of costs ?of colors ?assigned to all edges e in G. An edge-coloring f of G is optimal if ?is minimum among all edge-colorings of G. A cactus is a connected graph in which every block is either an edge or a cycle. In this paper, we give an algorithm to find an optimal edge- ??coloring of a cactus in polynomial time. In our best knowledge, this is the first polynomial-time algorithm to find an optimal edge-coloring of a cactus.展开更多
The algorithm under this name, together with the variants, is a method that solves the problems of optimal flow and costs. Examples of such problems are planning and procurement, scheduling by contractors, distributio...The algorithm under this name, together with the variants, is a method that solves the problems of optimal flow and costs. Examples of such problems are planning and procurement, scheduling by contractors, distribution and supply systems, transport on the road or rail network, electricity transmission, computer and telecommunications networks, pipe transmission systems (water, oil, …), and the like. The main goal of any business organization is to increase profits and satisfy its customers. Because business is an integral part of our environment, their goals will be limited by certain environmental factors and economic conditions. The out-of-kilter algorithm is used to solve a complex allocation problem involving interactive and conflicting personal choices subject to interactive resource constraints. The paper presents an example of successful use of this algorithm and proposes an extension to the areas of corporate and social planning. Customer demand, warehousing, and factory capacity were used as input for the model. First, we propose a linear programming approach to determine the optimal distribution pattern to reduce overall distribution costs. The proposed model of linear programming is solved by the standard simplex algorithm and the Excel-solver program. It is noticed that the proposed model of linear programming is suitable for finding the optimal distribution pattern and total minimum costs.展开更多
Given a generalized minimum cost flow problem,the corresponding inverse problem is to find a minimal adjustment of the cost function so that the given generalized flow becomes optimal to the problem.In this paper,we c...Given a generalized minimum cost flow problem,the corresponding inverse problem is to find a minimal adjustment of the cost function so that the given generalized flow becomes optimal to the problem.In this paper,we consider both types of the weighted Hamming distances for measuring the adjustment.In the sum-type case,it is shown that the inverse problem is APX-hard.In the bottleneck-type case,we present a polynomial time algorithm.展开更多
文摘This paper presents an algorithm for solving Bi-criteria Minimum Cost Dynamic Flow (BiCMCDF) problem with continuous flow variables. The approach is to transform a bi-criteria problem into a parametric one by building a single parametric linear cost out of the two initial cost functions. The algorithm consecutively finds efficient extreme points in the decision space by solving a series of minimum parametric cost flow problems with different objective functions. On each of the iterations, the flow is augmented along a cheapest path from the source node to the sink node in the time-space network avoiding the explicit time expansion of the network.
文摘The minimum cost of capacity expansion for time-limited transportation problem on-demand (MCCETLTPD) is to find such a practicable capacity expansion transportation scheme satisfying the time-limited T along with all origins’ supply and all destinations’ demands as well as the expanding cost is minimum. Actually, MCCETLTPD is a balance transportation problem and a variant problem of minimum cost maximum flow problem. In this paper, by creating a mathematical model and constructing a network with lower and upper arc capacities, MCCETLTPD is transformed into searching feasible flow in the constructed network, and consequently, an algorithm MCCETLTPD-A is developed as MCCETLTPD’s solution method basing minimum cost maximum flow algorithm. Computational study validates that the MCCETLTPD-A algorithm is an efficient approach to solving the MCCETLTPD.
文摘Let C be a set of colors, and let ?be an integer cost assigned to a color c in C. An edge-coloring of a graph ?is assigning a color in C to each edge ?so that any two edges having end-vertex in common have different colors. The cost ?of an edge-coloring f of G is the sum of costs ?of colors ?assigned to all edges e in G. An edge-coloring f of G is optimal if ?is minimum among all edge-colorings of G. A cactus is a connected graph in which every block is either an edge or a cycle. In this paper, we give an algorithm to find an optimal edge- ??coloring of a cactus in polynomial time. In our best knowledge, this is the first polynomial-time algorithm to find an optimal edge-coloring of a cactus.
文摘The algorithm under this name, together with the variants, is a method that solves the problems of optimal flow and costs. Examples of such problems are planning and procurement, scheduling by contractors, distribution and supply systems, transport on the road or rail network, electricity transmission, computer and telecommunications networks, pipe transmission systems (water, oil, …), and the like. The main goal of any business organization is to increase profits and satisfy its customers. Because business is an integral part of our environment, their goals will be limited by certain environmental factors and economic conditions. The out-of-kilter algorithm is used to solve a complex allocation problem involving interactive and conflicting personal choices subject to interactive resource constraints. The paper presents an example of successful use of this algorithm and proposes an extension to the areas of corporate and social planning. Customer demand, warehousing, and factory capacity were used as input for the model. First, we propose a linear programming approach to determine the optimal distribution pattern to reduce overall distribution costs. The proposed model of linear programming is solved by the standard simplex algorithm and the Excel-solver program. It is noticed that the proposed model of linear programming is suitable for finding the optimal distribution pattern and total minimum costs.
文摘Given a generalized minimum cost flow problem,the corresponding inverse problem is to find a minimal adjustment of the cost function so that the given generalized flow becomes optimal to the problem.In this paper,we consider both types of the weighted Hamming distances for measuring the adjustment.In the sum-type case,it is shown that the inverse problem is APX-hard.In the bottleneck-type case,we present a polynomial time algorithm.
