A branch‐and‐price algorithm for parallel machine scheduling with time windows and job priorities

This paper presents a branch‐and‐price algorithm for scheduling n jobs on m nonhomogeneous parallel machines with multiple time windows. An additional feature of the problem is that each job falls into one of ρ priority classes and may require two operations. The objective is to maximize the weighted number of jobs scheduled, where a job in a higher priority class has “infinitely” more weight or value than a job in a lower priority class. The methodology makes use of a greedy randomized adaptive search procedure (GRASP) to find feasible solutions during implicit enumeration and a two‐cycle elimination heuristic when solving the pricing subproblems. Extensive computational results are presented based on data from an application involving the use of communications relay satellites. Many 100‐job instances that were believed to be beyond the capability of exact methods, were solved within minutes. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006