THE 2-STAGE ASSEMBLY SCHEDULING PROBLEM - COMPLEXITY AND APPROXIMATION

This paper introduces a new two-stage assembly scheduling problem. There are m machines at the first stage, each of which produces a component of a job. When all m components are available, a single assembly machine at the second stage completes the job. The objective is to schedule jobs on the machines so that the makespan is minimized. We show that the search for an optimal solution may be restricted to permutation schedules. The problem is proved to be NP-hard in the strong sense even when m = 2. A schedule associated with an arbitrary permutation of jobs is shown to provide a worst-case ratio bound of two, and a heuristic with a worst-case ratio bound of 2 - 1/m is presented. The compact vector summation technique is applied for finding approximation solutions with worst-case absolute performance guarantees.