A primary/secondary memory implementation of a forward network simplex algorithm for multiperiod network flow problems

Abstract

The minimum cost, multiperiod network flow problem is an optimization model that is frequently used to assist decision makers in the areas of resource planning, scheduling and distribution. This model describes network structured decision making problems over time. Important problems in the areas of production/distribution systems, economic planning, communication systems, material handling systems, traffic systems, railway systems, building evacuation systems, energy systems, economic systems, etc. can be described by this model. Usually, standard network codes are used to solve such problems because of their availability and perceived efficiency. To date, few researchers have considered the multiperiod structure in devising efficient solution methods. The forward network simplex algorithm of Aronson and Chen is one such method. It is a forward algorithm that exploits the natural decomposition of the problem by limiting its pivoting activity to later time periods. A forward algorithm is an approach to solving dynamic problems by solving successively longer finite subproblems, terminating when a stopping rule can be invoked or a decision horizon found. Such procedures are available for the multiperiod linear programming problem, some of its specializations and generalizations and a large number of specially structured models. The forward network simplex algorithm solves multiperiod network flow problems efficiently. Encouraging computational results indicate that the forward network simplex implementation is significantly more efficient than standard network optimization codes that do not exploit the multiperiod structure. Even though the forward network simplex method is efficient, there are still limitations to the size of problems that can be solved in-core. In this paper, we discuss a primary/secondary storage implementation of the forward network simplex method and report computational results. This implementation is capable of solving much larger problems than the in-core code and is more efficient than standard codes. Problems having 700 time periods for a total of 3500 nodes and 9095 arcs were solved in less than one third the time of the standard code on which the forward network implementation is based. Furthermore, problems up to about double this size, which the standard code could not solve, were solved by the primary/secondary implementation.