Leyuan Shi This paper addresses the general single-machine earliness-tardiness problem with distinct release dates, due dates, and unit costs. The aim of this research is to obtain an exact nonpreemptive solution in which machine idle time is allowed. In a hybrid approach, we formulate and then solve the problem using dynamic programming (DP) while incorporating techniques from … Read more
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 flow problems, and Dantzig-Wolfe decomposition and column generation. CitationSubmitted for publication.ArticleDownload View PDF
We study a single-machine sequencing problem with both release dates and deadlines to minimize the total weighted completion time. We propose a branch-and-bound algorithm for this problem. The algorithm exploits an effective lower bound and a dynamic programming dominance technique. As a byproduct of the lower bound, we have developed a new algorithm for the … Read more
Dynamic programming, branch-and-bound, and constraint programming are the standard solution principles for finding optimal solutions to machine scheduling problems. We propose a new hybrid optimization framework that integrates all three methodologies. The hybrid framework leads to powerful solution procedures. We demonstrate our approach through the optimal solution of the single-machine total weighted completion time scheduling … Read more
New observations are made about two lower bound schemes for single-machine min-sum scheduling problems. We find that the strongest bound of those provided by transportation problem relaxations can be computed by solving a linear program. We show the equivalence of this strongest bound and the bound provided by the LP relaxation of the time-indexed integer … Read more