Selim Akturk | Bilkent University (original) (raw)

Papers by Selim Akturk

European Journal of Operational Research, 2006

In this study, we deal with the robotic cell scheduling problem with two machines and identical p... more In this study, we deal with the robotic cell scheduling problem with two machines and identical parts. In an ideal FMS, CNC machines are capable of performing all the required operations as long as the required tools are stored in their tool magazines. However, this assumption may be unrealistic at times since the tool magazines have limited capacity and in many practical instances the required number of tools exceeds this capacity. In this respect, our study assumes that some operations can only be processed on the first machine while some others can only be processed on the second machine due to tooling constraints. Remaining operations can be processed on either machine. The problem is to find the allocation of the remaining operations to the machines and the optimal robot move cycle that jointly minimize the cycle time. We prove that the optimal solution is either a 1-unit or a 2-unit robot move cycle and we present the regions of optimality. Finally, a sensitivity analysis on the results is conducted.

Discrete Applied Mathematics, 2005

In this paper, we study the problem of two-machine, identical parts robotic cell scheduling with ... more In this paper, we study the problem of two-machine, identical parts robotic cell scheduling with operational exibility. We assume that every part to be processed has a number of operations to be completed in these two machines and both machines are capable of performing all of the operations. The decision to be made includes ÿnding the optimal robot move cycle and the corresponding optimal allocation of operations to these two machines that jointly minimize the cycle time. We prove that with this deÿnition of the problem 1-unit robot move cycles are no longer necessarily optimal and that according to the given parameters either one of the 1-unit robot move cycles or a 2-unit robot move cycle is optimal. The regions of optimality are presented.

Computers & Operations Research, 2010

Consider a manufacturing cell of two identical CNC machines and a material handling robot. Identi... more Consider a manufacturing cell of two identical CNC machines and a material handling robot. Identical parts requesting the completion of a number of operations are to be produced in a cyclic scheduling environment through a flow shop type setting. The existing studies in the literature overlook the flexibility of the CNC machines by assuming that both the allocation of the operations to the machines as well as their respective processing times are fixed. Consequently, the provided results may be either suboptimal or valid under unnecessarily limiting assumptions for a flexible manufacturing cell. The allocations of the operations to the two machines and the processing time of an operation on a machine can be changed by altering the machining conditions of that machine such as the speed and the feed rate in a CNC turning machine. Such flexibilities constitute the point of origin of the current study. The allocation of the operations to the machines and the machining conditions of the machines affect the processing times which, in turn, affect the cycle time. On the other hand, the machining conditions also affect the manufacturing cost. This study is the first to consider a bicriteria model which determines the allocation of the operations to the machines, the processing times of the operations on the machines, and the robot move sequence that jointly minimize the cycle time and the total manufacturing cost. We provide algorithms for the two 1-unit cycles and test their efficiency in terms of the solution quality and the computation time by a wide range of experiments on varying design parameters.

International Journal of Production Research, 2008

The focus of this study is the identical parts robotic cell scheduling problem with m machines un... more The focus of this study is the identical parts robotic cell scheduling problem with m machines under the assumption of process and operational flexibility. A direct consequence of this assumption is a new robot move cycle that has been overlooked in the existing literature. We prove that this new cycle dominates all classical robot move cycles considered in the literature for m ¼ 2. We also prove that changing the layout from an in-line robotic cell to a robot-centered cell reduces the cycle time of the proposed cycle even further, whereas the cycle times of all other cycles remain the same. For the m-machine case, we find the regions where the proposed cycle dominates the classical robot move cycles, and for the remaining regions present its worst case performance with respect to classical robot move cycles. Considering the number of machines as a decision variable, we also find the optimal number of machines that minimizes the cycle time of the proposed cycle.

Computers & Operations Research, 2013

We consider a two-machine flowshop scheduling problem with identical jobs. Each of these jobs has... more 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. Furthermore, the processing times on these machines can be changed easily in albeit of higher manufacturing cost by adjusting the machining parameters like the speed and/or feed rate of the machine. The overall problem is to determine the assignment of the flexible operations to the machines and processing times for each operation to minimize the total manufacturing cost and makespan simultaneously. For such a bicriteria problem, there is no unique optimum but a set of nondominated solutions. Using E-constraint approach, the problem could be transformed to be minimizing total manufacturing cost for a given upper limit on the makespan. The resulting single criterion problem can be reformulated as a mixed integer nonlinear problem with a set of linear constraints. We use this formulation to optimally solve small instances of the problem while a heuristic procedure is constructed to solve larger instances in a reasonable time.

Journal of Scheduling, 2008

This paper considers the scheduling problems arising in two-and three-machine manufacturing cells... more This paper considers the scheduling problems arising in two-and three-machine manufacturing cells configured in a flowshop which repeatedly produces one type of product and where transportation of the parts between the machines is performed by a robot. The cycle time of the cell is affected by the robot move sequence as well as the processing times of the parts on the machines. For highly flexible CNC machines, the processing times can be changed by altering the machining conditions at the expense of increasing the manufacturing cost. As a result, we try to find the robot move sequence as well as the processing times of the parts on each machine that not only minimize the cycle time but, for the first time in robotic cell scheduling literature, also minimize the manufacturing cost. For each 1-unit cycle in two-and three-machine cells, we determine the efficient set of processing time vectors such that no other processing time vector gives both a smaller cycle time and a smaller cost value. We also compare these cycles with each other to determine the sufficient conditions under which each of the cycles dominates the rest. Finally, we show how different assumptions on cost structures affect the results.

Computers & Operations Research, 2007

In this study, we consider a flexible manufacturing cell (FMC) processing identical parts on whic... more In this study, we consider a flexible manufacturing cell (FMC) processing identical parts on which the loading and unloading of machines are made by a robot. The machines used in FMCs are predominantly CNC machines and these machines are flexible enough for performing several operations provided that the required tools are stored in their tool magazines. Traditional research in this area considers a flowshop type system. The current study relaxes this flowshop assumption which unnecessarily limits the number of alternatives. In traditional robotic cell scheduling literature, the processing time of each part on each machine is a known parameter. However, in this study the processing times of the parts on the machines are decision variables. Therefore, we investigated the productivity gain attained by the additional flexibility introduced by the FMCs. We propose new lower bounds for the 1-unit and 2-unit robot move cycles (for which we present a completely new procedure to derive the activity sequences of 2-unit cycles in a three-machine robotic cell) under the new problem domain for the flowshop type robot move cycles. We also propose a new robot move cycle which is a direct consequence of process and operational flexibility of CNC machines. We prove that this proposed cycle dominates all 2-unit robot move cycles and present the regions where the proposed cycle dominates all 1-unit cycles. We also present a worst case performance bound of using this proposed cycle. ᭧

Computers & Operations Research, 2009

In this study, an m-machine flexible robotic manufacturing cell consisting of CNC machines is con... more In this study, an m-machine flexible robotic manufacturing cell consisting of CNC machines is considered. The flexibility of the machines leads to a new class of robot move cycles called the pure cycles. We first model the problem of determining the best pure cycle in an m-machine cell as a special travelling salesman problem in which the distance matrix consists of decision variables as well as parameters. We focus on two specific cycles among the huge class of pure cycles. We prove that, in most of the regions, either one of these two cycles is optimal. For the remaining regions we derive worst case performances of these cycles. We also prove that the set of pure cycles dominates the flowshop-type robot move cycles considered in the literature. As a design problem, we consider the number of machines in a cell as a decision variable. We determine the optimal number of machines that minimizes the cycle time for given cell parameters such as the processing times, robot travel times and the loading/unloading times of the machines.

International Journal of Production Research, 2003

In this study, we solve the non-identical parallel CNC machine scheduling problem. We have two ob... more In this study, we solve the non-identical parallel CNC machine scheduling problem. We have two objectives: minimizing the manufacturing cost (comprising machining, non-machining and tooling costs) and minimizing the total weighted tardiness. The tooling constraints affect the non-machining times as well as the machining conditions, such as cutting speed and feed rate, which in turn specify the machining times and tool lives. We propose a two-stage algorithm to find optimal machining conditions and to determine machine allocation, tool allocation and part scheduling decisions. The proposed algorithm generates different schedules according to the relative importance of the objectives.

International Journal of Production Research, 2007

In this study, we consider flexible manufacturing system loading, scheduling and tool management ... more In this study, we consider flexible manufacturing system loading, scheduling and tool management problems simultaneously. Our aim is to determine relevant tool management decisions, which are machining conditions selection and tool allocation, and to load and schedule parts on non-identical parallel CNC machines. The dual objectives are minimization of the manufacturing cost and total weighted tardiness. The manufacturing cost is comprised of machining and tooling costs (which are affected by machining conditions) and non-machining cost (which is affected by tool replacement decisions). We used both sequential and simultaneous approaches to solve our problem to show the superiority of the simultaneous approach. The proposed heuristics are used in a problem space genetic algorithm in order to generate a series of approximately efficient solutions.

IIE Transactions, 2009

ABSTRACT In this study, a machine scheduling problem with controllable processing times in a para... more ABSTRACT In this study, a machine scheduling problem with controllable processing times in a parallel-machine environment is considered. The objectives are the minimization of manufacturing cost, which is a convex function of processing time, and total weighted earliness and tardiness. It is assumed that parts have job-dependent earliness and tardiness penalties and distinct due dates, and idle time is allowed. The problem is formulated as a time-indexed integer programming model with discrete processing time alternatives for each part. A linear-relaxation-based algorithm is used to assign the parts to the machines and to find a sequence on each machine. A non-linear programming model is proposed to find the optimal starting and processing times of the parts for a given sequence. The proposed non-linear programming model is converted to a minimum-cost network flow model by piecewise linearization of the convex manufacturing cost in the objective function. The proposed method is used to find initial schedules in predictive scheduling. The proposed models are revised to incorporate a stability measure for reacting to unexpected disruptions such as machine breakdown, arrival of a new job, delay in the arrival or the shortage of materials in reactive scheduling.

IIE Transactions, 2000

The study deals with scheduling a set of independent jobs with unequal release dates to minimize ... more The study deals with scheduling a set of independent jobs with unequal release dates to minimize total weighted tardiness on a single machine. We propose new dominance properties that are incorporated in a branch and bound algorithm. The proposed algorithm is tested on a set of randomly generated problems with 10, 15 and 20 jobs. To the best of our knowledge, this is the first exact approach that attempts to solve the 1jr j j P w j T j problem.

IIE Transactions, 2003

We propose a problem space genetic algorithm to solve single machine total weighted tardiness sch... more We propose a problem space genetic algorithm to solve single machine total weighted tardiness scheduling problems. The proposed algorithm utilizes global and time-dependent local dominance rules to improve the neighborhood structure of the search space. They are also a powerful exploitation (intensifying) tool since the global optimum is one of the local optimum solutions. Furthermore, the problem space search method significantly enhances the exploration (diversification) capability of the genetic algorithm. In summary, we can improve both solution quality and robustness over the other local search algorithms reported in the literature.

European Journal of Operational Research, 2001

We present a new dominance rule by considering the time-dependent orderings between each pair of ... more We present a new dominance rule by considering the time-dependent orderings between each pair of jobs for the single machine total weighted tardiness problem with release dates. The proposed dominance rule provides a sufficient condition for local optimality. Therefore, if any sequence violates the dominance rule then switching the violating jobs either lowers the total weighted tardiness or leaves it unchanged. We introduce an algorithm based on the dominance rule, which is compared to a number of competing heuristics for a set of randomly generated problems. Our computational results indicate that the proposed algorithm dominates the competing algorithms in all runs, therefore it can improve the upper bounding scheme in any enumerative algorithm. The proposed time-dependent local dominance rule is also implemented in two local search algorithms to guide these algorithms to the areas that will most likely contain the good solutions.