Esnek operasyonlar ve kontrol edilebilir işlem zamanları ile iki-makinalı akış tipi çizelgeleme

In this study, we consider a two-machine flowshop scheduling problem with identicaljobs. Each of these jobs has three operations, where the first operation mustbe performed on the first machine, the second operation must be performed onthe second machine, and the third operation (named as flexible operation) canbe performed on either machine but cannot be preempted. Highly flexible CNCmachines are capable of performing different operations as long as the requiredcutting tools are loaded on these machines. The processing times on these machinescan be changed easily in albeit of higher manufacturing cost by adjustingthe machining parameters like the speed of the machine, feed rate, and/or thedepth of cut. The overall problem is to determine the assignment of the flexibleoperations to the machines and processing times for each job simultaneously,with the bicriteria objective of minimizing the manufacturing cost and minimizingmakespan. For such a bicriteria problem, there is no unique optimum but aset of nondominated solutions. Using epsilon-constraint approach, the problem couldbe transformed to be minimizing total manufacturing cost objective for a givenupper limit on the makespan objective. The resulting single criteria problemis a nonlinear mixed integer formulation. For the cases where the exact algorithmmay not be efficient in terms of computation time, we propose an efficientapproximation algorithm.