A branch and bound algorithm for flexible job shop scheduling problem followed by an assembly stage

Concurrently scheduling for two-stage production systems consist of a processing stage and an assembly stage causes to achieve the ideal result for these systems. This paper aims to propose a branch and bound (B&B) algorithm for the scheduling problem in a flexible job shop followed by an assembly stage. The objective function is the total completion time of products (makespan). Due to time consuming the classic B&B algorithms in solving optimization problems, two efficient lower bounds are developed to reduce the run time. Moreover, two search strategies the so-called the Best First Search (BFS) and the Depth-First Search (DFS) are introduced to enhance performance of the proposed algorithm. The variable neighborhood search (VNS) is applied to determine proper upper bound for solution of the problem. To more clarification, the problem is modeled as a mixed-integer linear programming (MIP) model with definition need parameters and decision variables. Since the problem is well known as NP-hard strongly, performance of the proposed algorithm is investigated in comparison to the exact solutions provided by the mathematical model for the small-sized instances. The evaluation results showed that the depth search strategy has performed better than the other one. This search strategy has could to enhance efficiency of the proposed algorithm, and has significantly reduced the solution time.