Effective algorithms for pickup and delivery problem with loading restrictions and handling costs

The Pickup-and-Delivery problem is an important category of Vehicle Routing Problem with a lot of practical applications. In practice, the problems in this category often have to be solved with cargo loading/unloading restrictions. For example, shippers may incur cargo handling costs if a driver has to unload and reload pallets into the vehicle at shipment delivery sites. However, this cost can be eliminated by following the Last-In-First-Out (LIFO) order for cargo loading/unloading. Motivated by this application, we explore the Pickup-and-Delivery Problem (PDP) with LIFO loading restrictions in single and multi-vehicle settings. We also study the PDP with handling costs in single and multi-vehicle settings because strictly imposing the LIFO order might force the vehicles to travel long distances. For single-vehicle problems, we present multiple mathematical models and branch-and-cut algorithms. We also introduce new inequalities, warm start, and bound tightening procedures to enhance the scalability of our implementations. The multi-vehicle problems are formulated and solved with many practical considerations including vehicle capacity, customer time windows, and maximum on-road time for drivers. We also propose new heuristic algorithms which were very effective in solving the multi-vehicle problems. This dissertation also introduces new conditional integral separation procedures which could be applicable in large scale mathematical models outside the vehicle routing discipline

Decomposition Algorithms for the Elementary Shortest Path Problem in Networks Containing Negative Cycles

The Elementary Shortest Path Problem in Networks containing Negative Cycles (ESPPNC) is an NP-hard problem. Although there are exact formulation approaches to solve the ESPPNC, a decomposition setting for this problem has not been explored. In this thesis, two Decomposition and Branch-and-Cut (DBC) algorithms to solve the ESPPNC in directed networks are proposed. A master relaxation of the ESPPNC is presented and later strengthened by adding negative cycle elimination constraints in a branch-and-bound framework. The scalability of these approaches is analyzed by extracting their running times on two different test-beds. Also, the performance of these approaches is compared against the performance of an exact formulation on the same test-beds. From the results, the DBC approaches are able to solve all the instances much faster than the exact formulation approach, so the DBC algorithms scale much better than direct formulation in these test-beds. However, a pathological instance is also identified for which the direct formulation is the favorable approach.Industrial Engineering & Managemen