Two-machine flowshop dynamic scheduling problem

In this paper, we aim to solve a two-machine flowshop dynamic scheduling problem, in which the objective is to minimize the sum of makespan and total flow time. A frozen-event procedure is first proposed to transform a dynamic scheduling problem into a static one. To solve the transformed static scheduling problem, an integer programming model with N2+4N variables and 6N constraints is formulated. In the consideration of computing time and complexity, a heuristic algorithm with the complexity of O(N2) is then presented. Experimental results show that the proposed heuristic algorithm can quickly solve this problem with very good solution quality. The average solution quality of the heuristic algorithm is above 96%. In a 15-job environment, it takes only 0.1483 seconds on average to obtain a ultimate solution. Compared with the integer programming model, the heuristic algorithm is much more practical to real world applications.