Two-machine flowshop scheduling with flexible operations and controllable processing times

Abstract

In this study, we consider a two-machine flowshop scheduling problem with identical jobs. Each of these jobs has three operations, where the first operation must be performed on the first machine, the second operation must be performed on the second machine, and the third operation (named as flexible operation) can be performed on either machine but cannot be preempted. Highly flexible CNC machines are capable of performing different operations as long as the required cutting tools are loaded on these machines. The processing times on these machines can be changed easily in albeit of higher manufacturing cost by adjusting the machining parameters like the speed of the machine, feed rate, and/or the depth of cut. The overall problem is to determine the assignment of the flexible operations to the machines and processing times for each job simultaneously, with the bicriteria objective of minimizing the manufacturing cost and minimizing makespan. For such a bicriteria problem, there is no unique optimum but a set of nondominated solutions. Using ǫ constraint approach, the problem could be transformed to be minimizing total manufacturing cost objective for a given upper limit on the makespan objective. The resulting single criteria problem is a nonlinear mixed integer formulation. For the cases where the exact algorithm may not be efficient in terms of computation time, we propose an efficient approximation algorithm.