In this paper we consider a job scheduling problem where each job can be executed only by a subset of available processors. This problem arises when we are scheduling a set of cannons to be fired on a set of targets. Each cannon can destroy only a subset of targets and we want the targets to be destroyed in the shortest possible time. We define what is meant by a balanced solution. We then consider three problems: How can we detect that there is a balanced solution? If this solution exists, find such a solution. If no such solution exists, find an optimal assignment which minimizes the makespan. We show that there are polynomial time algorithms to solve these problems. © 1988.
Chang, R. S., & Lee, R. C. T. (1988). On a scheduling problem where a job can be executed only by a limited number of processors. Computers and Operations Research, 15(5), 471–478. https://doi.org/10.1016/0305-0548(88)90063-9