Browsing by Subject "Flow shop"
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Item Open Access Constrained optimal hybrid control of a flow shop system(Institute of Electrical and Electronics Engineers, 2007) Gokbayrak, K.; Selvi, O.We consider an optimal control problem for the hybrid model of a deterministic flow shop system, in which the jobs are processed in the order they arrive at the system. The problem is decomposed into a higher-level discrete-event system control problem of determining the optimal service times, and a set of lower-level classical control problems of determining the optimal control inputs for given service times. We focus on the higher-level problem which is nonconvex and nondifferentiable. The arrival times are known and the decision variables are the service times that are controllable within constraints. We present an equivalent convex optimization problem with linear constraints. Under some cost assumptions, we show that no waiting is observed on the optimal sample path. This property allows us to simplify the convex optimization problem by eliminating variables and constraints. We also prove, under an additional strict convexity assumption, the uniqueness of the optimal solution and propose two algorithms to decompose the simplified convex optimization problem into a set of smaller convex optimization problems. The effects of the simplification and the decomposition on the solution times are shown on an example problem.Item Open Access A search method for optimal control of a flow shop system of traditional machines(Elsevier, 2010) Selvi, O.; Gokbayrak, K.We consider a convex and nondifferentiable optimization problem for deterministic flow shop systems in which the arrival times of the jobs are known and jobs are processed in the order they arrive. The decision variables are the service times that are to be set only once before processing the first job, and cannot be altered between processes. The cost objective is the sum of regular costs on job completion times and service costs inversely proportional to the controllable service times. A finite set of subproblems, which can be solved by trust-region methods, are defined and their solutions are related to the optimal solution of the optimization problem under consideration. Exploiting these relationships, we introduce a two-phase search method which converges in a finite number of iterations. A numerical study is held to demonstrate the solution performance of the search method compared to a subgradient method proposed in earlier work.Item Open Access A subgradient descent algorithm for optimization of initially controllable flow shop systems(2009) Gokbayrak, K.; Selvi, O.We consider an optimization problem for deterministic flow shop systems processing identical jobs. The service times are initially controllable; they can only be set before processing the first job, and cannot be altered between processes. We derive some waiting and completion time characteristics for fixed service time flow shop systems, independent of the cost formulation. Exploiting these characteristics, an equivalent convex optimization problem, which is non-differentiable, is derived along with its subgradient descent solution algorithm. This algorithm not only eliminates the need for convex programming solvers but also allows for the solution of larger systems due to its smaller memory requirements. Significant improvements in solution times are also observed in the numerical examples.