Pipeline network optimization-an application to slurry pipelines

Abstract

The problem considered here is that of obtaining the least cost design of a pipeline network supplying demand points with known demand functions for dry solids from a single source over a finite time horizon. The problem is decomposed into a network problem and a subproblem which is the optimum design of a single arc (a pipeline). The subproblem is solved by a technique developed which exploits the monotonicity relationships of the decision variables in the objective function and in the constraints. For the network problem, it is shown that the objective function is quasi-concave and that it takes its minimum at at least one of the extreme points. The extreme points are shown to correspond to arborescences. An adjacent extreme point method searching over adjacent arborescences is developed. The method makes extensive use of the subproblem. A local optimum is defined and the solution procedure is shown to converge to this local optimum in a finite number of iterations.