In this paper the concept of the Minimum Universal Cost Flow (MUCF) for an infeasible flow network is introduced. A new mathematical model in which the objective function includes the total costs of changing arc capacities and sending flow is built and analyzed. A polynomial time algorithm is presented to find the MUCF.

An Ant Colony Optimization (ACO) algorithm is proposed for optimal tree-structured natural gas distribution network. Design of pipelines, facilities, and equipment systems are necessary tasks to configure an optimal natural gas network. A mixed integer programming model is formulated to minimize the total cost in the network. The aim is to optimize pipe diameter sizes so that the location-alloc...

This paper proposed a parallel automated assembly line system to produce multiple products having multiple autonomous guided vehicles (AGVs). Several assembly lines are configured to produce multiple products in which the technologies of machines are shared among the assembly lines when required. The transportation between the stations in an assembly line (intra assembly line) and among station...

In this paper, we consider the inverse spanning tree problem. Given an undi0 Ž 0 0 . rected graph G s N , A with n nodes, m arcs, an arc cost vector c, and a spanning tree T 0, the inverse spanning tree problem is to perturb the arc cost vector c to a vector d so that T 0 is a minimum spanning tree with respect to the < < < < cost vector d and the cost of perturbation given by d y c s Ý d y c i...

This paper investigates the minimum cost multicommodity flow problem with uncertain costs and uncertain capacities. Uncertainty theory is used to deal with indeterminacy factors in uncertain network. An (α, β)-minimum cost multicommodity flow model is formulated. Some properties of the model are analyzed. An equivalence relationship between the (α, β)-minimum cost multicommodity flow and the mi...

This paper shows that partial differential equations may be a possible area of application of mathematical programming. The solution of Laplace's equation with Neumann's condition is shown to be a minimum cost network flow problem with cost proportional to the arc flow. An algorithm of solving minimum quadratic cost network flow is given.

Given an instance of the minimum cost flow problem, the corresponding inverse problem is to modify the arc costs as little as possible so that a given feasible flow becomes optimal to the modified minimum cost flow problem. In this article, we study this inverse problem in that the modifications are measured by the weighted bottleneck-type Hamming distance. We present a new efficient algorithm ...

We consider the quickest flow problem in dynamic networks with a single source s and a single sink t: given a flow F , find the minimum time needed to send F from s to t, and the corresponding optimal flow over time. We introduce new mathematical formulations and derive optimality conditions for the quickest flow problem. Based on the optimality conditions, we develop a new cost-scaling algorit...

Ravindra K. Ahuja and Dorit S. Hochbaum Abstract In this paper, we study capacitated dynamic lot sizing problems with or without backorders, under the assumption that production costs are linear, that is, there are no set up costs. These two dynamic lot sizing problems (with or without backorders) are minimum cost flow problems on an underlying network that possess a special structure. We show ...