Service time optimization of flow shop systems

Abstract

One of the key questions that engineers face in áow shop systems is the service time control, i.e., how long jobs should be processed at each machine. This is an important question because processing times can have great impacts on the cost e¢ ciency of the áow shop systems. In order to meet job completion deadlines and to decrease inventory costs, one may set the service times as small as possible; however, this usually comes at the expense of reduced tool life increasing service costs. In this thesis, we study the áow shop systems under such trade-o§s. We consider the service time optimization of deterministic áow shop systems processing identical jobs that arrive at the system at known times and are processed in the order they arrive within deadlines. The cost function to be minimized consists of service costs at machines and regular completion-time costs of jobs. The decision variables are the service times that are controllable within constraints. We Örst consider the Öxed service time áow shop systems formed of initially controllable machines, where the service times are set only once at the start up time and cannot be altered between processes, and uncontrollable machines, where the service times are Öxed and known in advance. For such systems, we formulate a non-convex and non-di§erentiable optimization problem with a standard solution procedure based on the linearization of the constraints allowing for a convex optimization problem with high memory requirements. Regardless of the cost function, we present a set of waiting and completion time characteristics in such áow shop systems and employ them to derive a simpler equivalent convex optimization problem which improves solution times and alleviates the memory requirements enabling solutions for larger systems. However, the resulting simpliÖed convex optimization problem still needs the use of a convex optimization solver which may not be available at some of the manufacturing companies. To overcome such need, we introduce another equivalent convex optimization problem along with its subgradient algorithm yielding substantial improvements in solution times and solvable system sizes. We also consider a speciÖc nonlinear decreasing service cost structure allowing us to introduce a new search algorithm much faster than the subgradient solution algorithm. Building on the results for Öxed service time áow shop systems, we also consider the mixed line áow shop systems formed of fully controllable machines, where the service times are adjustable for each process, initially controllable machines, and uncontrollable machines. Similarly, we formulate a non-convex and non-di§erentiable optimization problem for such systems and, as a standard way of solving the formulated problem, we apply the method of linearization on the constraints to present a convex optimization problem with high memory requirements. Then, we present a set of optimal waiting characteristics in such áow shop systems and employ them to derive simpler equivalent convex optimization problems. A "forward in time" algorithm is also proposed to decompose the resulting simpliÖed equivalent convex optimization problem into smaller convex optimization problems for the áow shop systems formed of only fully controllable and uncontrollable machines. The computational results demonstrate that the simpliÖcations and the decomposition not only improve the solution times considerably but also allow us to solve larger problems by alleviating memory constraints.