Approaches for solving m-best 3-dimensional dynamic scheduling problems for large m

Dynamic scheduling problems arise in areas, including traveling salesman problems, vehicle routing, nuclear fuel assembly loading patterns, and asset scheduling for resource allocation problems, to name a few. A generalized 3-dimensional scheduling problem is a decision making process that involves allocating limited resources to a set of tasks over time, where the objective is to optimize a cost function subject to realistic constraints. In addition, the realistic constraints complicate the problem further due to a possibly large number of disconnected feasible solution subspaces. These 3-dimensional assignment problems are known to be NP-hard. In this paper, we investigate a 3-dimensional assignment problem widely applicable to many fields (e.g., teacher scheduling, asset routing/scheduling, nuclear fuel management, multi-target tracking). We propose a novel approach to efficiently solve an m-best 3-dimensional scheduling problem, where m may be large (up to 104), by decomposing it into two sequential phases. In phase I, we partition the original problem space into a series of subproblems via Murty's m-best search space decomposition procedure. In phase II, we solve each subproblem using a combination of relaxed 2-dimensional assignments through reformulation into either a simplex-based transportation or transauction problem. We follow this two-step approach and generate large numbers of solutions in a relatively short amount of time. We validate and compare the performance of our proposed algorithm via experimental results.