Krishna C. Jha

Solving Real-Life Railroad Blocking Problems

Each major US railroad ships millions of cars over its network annually. To reduce the intermediate handlings of shipments as they travel over the railroad network, a set of shipments is classified (or grouped together) at a railroad yard to create a block. The railroad blocking problem is to identify this classification plan for all shipments at all yards in the network to minimize the total shipment cost, i.e., to create a blocking plan. The railroad blocking problem is a very large-scale, multicommodity, flow-network-design and routing problem with billions of decision variables. Its size and mathematical difficulty preclude solving it using any commercial software package. We developed an algorithm using an emerging technique known as very large-scale neighborhood (VLSN) search that is able to solve the problem to near optimality using one to two hours of computer time on a standard workstation computer. This algorithm can also handle a variety of practical and business constraints that are necessary for implementing a solution. When we applied this algorithm to the data that several railroads provided us, the computational results were excellent. Three Class I railroad companies (a Class I railroad, as defined by the Association of American Railroads, has an operating revenue exceeding

Exact and Heuristic Algorithms for the Weapon-Target Assignment Problem

319.3 million) in the United States---CSX Transportation, Norfolk Southern Corporation, and Burlington Northern and Santa Fe Railway---used it in developing their operating plans. Two US Class I railroads have also licensed it for regular use in developing their operating plans, and other railroads are showing considerable interest. We expect this algorithm to become an industry standard for freight railroads worldwide. In this paper, we outline our algorithm, show the computational results we received using real data, and describe areas for future research.

Multicommodity network flow approach to the railroad crew-scheduling problem

The weapon-target assignment (WTA) problem is a fundamental problem arising in defense-related applications of operations research. This problem consists of optimally assigning n weapons to m targets so that the total expected survival value of the targets after all the engagements is minimal. The WTA problem can be formulated as a nonlinear integer programming problem and is known to be NP-complete. No exact methods exist for the WTA problem that can solve even small-size problems (for example, with 20 weapons and 20 targets). Although several heuristic methods have been proposed to solve the WTA problem, due to the absence of exact methods, no estimates are available on the quality of solutions produced by such heuristics. In this paper, we suggest integer programming and network flow-based lower-bounding methods that we obtain using a branch-and-bound algorithm for the WTA problem. We also propose a network flow-based construction heuristic and a very large-scale neighborhood (VLSN) search algorithm. We present computational results of our algorithms, which indicate that we can solve moderately large instances (up to 80 weapons and 80 targets) of the WTA problem optimally and obtain almost optimal solutions of fairly large instances (up to 200 weapons and 200 targets) within a few seconds.

Exact and Heuristic Methods for the Weapon Target Assignment Problem

We present our solution to the crew-scheduling problem Jor North American railroads. (Crew scheduling in North America is very different from scheduling in Europe, where it has been well studied.) The crew-scheduling problem is to assign operators to scheduled trains over a time horizon at minimal cost while honoring operational and contractual requirements. Currently, decisions related to crew are made manually. We present our work developing a network-flow-based crew-optimization model that can be applied at the tactical, planning, and strategic levels of crew scheduling. Our network flow model maps the assignment of crews to trains as the flow of crews on an underlying network, where different crew types are modeled as different commodities in this network. We formulate the problem as an integer programming problem on this network, which allows it to be solved to optimality. We also develop several highly efficient algorithms using problem decomposition and relaxation techniques, in which we use the special structure of the underlying network model to obtain significant increases in speed. We present very promising computational results of our algorithms on the data provided by a major North American railroad. Our network flow model is likely to form a backbone for a decision-support system for crew scheduling.