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We examine the first phase of a known NP-hard 2-stage assembly problem. It   consists of sequencing a set of jobs having multiple components to be   processed. Each job has to be worked on independently on a specific machine.   We consider these jobs to form a vector of tasks. Our objective is to   schedule jobs on the particular machines in order to minimize the completion   time before the second stage starts. We first develop a new mathematical   programming formulation of the problem and test it on a small problem   instance using an integer programming solver. Then, we develop a heuristic   algorithm based on Ant Colony Optimization and Variable Neighborhood Search   metaheuristics in order to minimize the total completion time. The   performance of our implementation appears to be efficient and effective

A heuristic hybrid framework for vector job scheduling