Postoptimal Analysis in Nonserial Dynamic Programming

Usually, discrete optimization problems (DOPs) from applications have a special structure, and the matrices of constraints for largescale problems have a lot of zero elements (sparse matrices). One of the promising ways to exploit sparsity in the interaction graph of the DOP is nonserial dynamic programming (NSDP), which allows to compute a solution in stages such that each of them uses results from previous stages. The drawback of NSDP methods consists on exponential time and space complexity that is exponential in the induced width of the DOP’s interaction graph. This causes an expediency and an urgency of development of tools that could help to cope with this difficulty. In this paper is shown that NSDP algorithm generates a family of related DOPs that differ from each other in their right-hand sides. For solving this family of related problems postoptimal and sensitivity analysis methods are proposed.