Minimal cycle time determination and golf neighborhood generation for the cyclic flexible job shop problem

In the paper, a problem of scheduling operations in the cyclic flexible job shop system is considered. A new, very fast method of determining the cycle time for any order of tasks on machines is also presented. It is based on the analysis of the paths in the graph representing the examined problem. The theorems concerning specific properties of the graph are proven and used in the construction of the heuristic algorithm searching the solutions space by using the so-called golf neighborhood, which is generated in a way similar to the game of golf, which helps to intensify and diversify calculations. The conducted computational experiments fully confirmed the effectiveness of the proposed method. The proposed methods and properties can be adapted and used in the construction of local search algorithms for solving many other optimization problems.