Finding the best root node strategy for the approximation of the time-indexed bound in min-sum scheduling

— We identify the best root node strategy for the approximation of the time-indexed bound in min-sum scheduling by sorting through various options that involve the primal simplex, dual simplex, and barrier methods for linear programming, the network simplex method for network ow problems, and DantzigWolfe decomposition and column generation. Note to Practitioners— Min-sum scheduling problems are frequently encountered in manufacturing or service environments where job/entity-based accounting metrics are of prime interest. Examples of such metrics are the average earliness-tardiness of jobs through a plant and the average ow/residence time of patients through a health care facility. Recently, a new and fast method for computing lower bounds for such problems has been introduced. When used in branch-and-bound, the lower bound method has the characteristic of requiring large initial computational expense at the root node and quite marginal subsequent expenses at the other nodes. This experimental work aims to address the question of how to reduce the large initial computational expense. Index Terms— min-sum scheduling; MMT; time-indexing; simplex; barrier; column generation