Scheduling in flowshops with flexible operations: Throughput optimization and benefits of flexibility

This study considers the throughput optimization in a two-machine flowshop producing identical jobs. Unlike the general trend in the scheduling literature, the machines are assumed to be capable of performing different operations. As a consequence, one of the three operations that a job requires can only be processed by the first and another operation can only be processed by the second machine. These are called fixed operations. The remaining one is called the flexible operation and can be processed by any one of the machines. The machines are assumed to have different technological properties, i.e. non-identical, so that the processing time of the flexible operation has different values on the two machines. We first consider the problem of assigning the flexible operations to the machines for each job in order to maximize the throughput rate. We develop constant time solution algorithms for infinite and zero capacity buffer spaces in between the machines. We then analyze the benefits of flexibility. Managerial insights are provided regarding the changes in the makespan as well as the associated cost with respect to the increase in the level of flexibility.