Using a Variable Neighborhood Search to Solve the Single Processor Scheduling Problem with Time Restrictions

We study the single-processor scheduling problem with time restrictions in order to minimize the makespan. In this problem, n independent jobs have to be processed on a single processor, subject only to the following constraint: During any time period of length \(\alpha >0\) the number of jobs being executed is less than or equal to a given integer value B. It has been shown that the problem is NP-hard even for B = 2. We propose the two metaheuristics variable neighborhood search and a fixed neighborhood search to solve the problem. We conduct computational experiments on randomly generated instances. The results indicate that our algorithms are effective and efficient regarding the quality of the solutions and the computational times required for finding them.