AN ALGORITHM FOR THE 3-INDEX ASSIGNMENT PROBLEM

• 成果类型: Article
• 署名作者: BALAS, E; SALTZMAN, MJ
• 署名单位: Clemson University
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.39.1.150
• 发表日期: 1991
• 页码: 150-161
• 关键词: NETWORKS GRAPHS; matchings; 3-DIMENSIONAL; programming; INTEGER ALGORITHMS; PRIMAL HEURISTICS; queues; optimization; SUBGRADIENT OPTIMIZATION WITH FACET DEFINING CUTTING PLANES

摘要

We describe a branch-and-bound algorithm for solving the axial three-index assignment problem. The main features of the algorithm include a Lagrangian relaxation that incorporates a class of facet inequalities and is solved by a modified subgradient procedure to find good lower bounds, a primal heuristic based on the principle of minimizing maximum regret plus a variable depth interchange phase for finding good upper bounds, and a novel branching strategy that exploits problem structure to fix several variables at each node and reduce the size of the total enumeration tree. Computational experience is reported on problems with up to 78 equations and 17,576 variables. The primal heuristics were tested on problems with up to 210 equations and 343,000 variables.