A mathematical model and extension algorithm for assembly flexible flow shop scheduling problem

In this paper, a scheduling problem for a two-stage production system including machining operations and assembly operations is studied. In this system, a number of products of different kinds are produced. Each product is assembled with a set of several parts. The first stage is a hybrid flow shop to produce parts. All machines can process all kinds of parts in this stage, but each machine can process only one part at a time. The second stage is a single assembly machine or a single assembly team of workers. The considered objective is to minimize the completion time of all products (makespan). A mathematical modeling is presented, and since this problem has been proved strongly nondeterministic polynomial-time hard, a series of heuristic algorithms based on the basic idea of Johnson algorithm is proposed. Also, two lower bounds is introduced and improved to evaluate the final solution obtained from heuristic algorithms. The numerical experiments are used to evaluate the performance of the proposed algorithms.