Implementation and Computational Study on an In-Core, Out-of-Core Primal Network Code

Abstract

This paper presents extensive computational experience with a special-purpose primal simplex code using the augmented threaded index method for solving capacitated and uncapacitated transshipment and transportation problems. This code is distinguished from other codes for solving such problems in that not all of the data resides in central memory simultaneously; thus, it is referred to as an in-core, out-of-core code. The major advantages of such a code over an in-core code are (1) it can solve problems that the latter can not solve because of central memory requirements; (2) even for problems that the latter can solve, it requires less central memory, which is critical for fast job processing on multiprogrammed computer systems; and (3) the code can also be used as an in-core code. The design of such codes presents numerous computational difficulties in selecting the best starting and pivot procedures in order to minimize central as well as peripheral processing time. We present computational experience with various pivot, start and capacity buffer procedures, as well as different buffer sizes. Computational results are also provided for different types of network problems, including assignment, transportation, and minimum cost flow problems. These computational results are compared with in-core, out-of-kilter, negative cycle, and primal simplex network codes for problem sizes that these codes could solve.

An evaluation of mathematical programming and minicomputers

“…This belief is partly based on the work reported in (11] wh ich illustrates that general network codes can be designed which only requi re two more node length array s than the PAP E code . Further , Karney and Klingman [16] indicate that these simplex based codes do not suffer undue increases in solution times by keeping a portion of the problem data on external computer memory network is large ly due to the time spent in changing node potentials (dual variable values) (7 , 111 . Experience has shown that the node potentials change 1½ times, on the average , for the label-correcting algorithms [7] and 6-10 times for the mini mum cost flow network.…”

Generalized Networks: A Fundamental Computer-Based Planning Tool

“…Earlier research with pure network problems [19], [20], [33] has established that certain factors play a critical role in determining solution speed. These are: start procedures, pivot selection techniques, degeneracy, tolerance levels, Big-M value, and pivot tie-breaking rules.…”

Real World Applications of Network Related Problems and Breakthroughs in Solving Them Efficiently

“…A transshipment problem with 1100 nodes and 3700 arcs is a very large problem to solve in a reasonable time on such a computer since this is an LP with 1100 constraints and 3700 variables. Using our codes [13,26] we were able to solve this problem in 37 seconds compared with 45 minutes using the GM transshipment code on the same computer. aiding in the planning of loans, purchases, and sales of securities, etc.…”