Browsing by Subject "Controllable processing times"

Now showing 1 - 20 of 21

Open Access
An analysis of cyclic scheduling problems in robot centered cells
(Elsevier, 2012) Yıldız, Serdar; Karasan, Oya Ekin; Aktürk, M. Selim
The focus of this study is a robot centered cell consisting of m computer numerical control (CNC) machines producing identical parts. Two pure cycles are singled out and further investigated as prominent cycles in minimizing the cycle time. It has been shown that these two cycles jointly dominate the rest of the pure cycles for a wide range of processing time values. For the remaining region, the worst case performances of these pure cycles are established. The special case of 3-machines is studied extensively in order to provide further insight for the more general case. The situation where the processing times are controllable is analyzed. The proposed pure cycles also dominate the rest when the cycle time and total manufacturing cost objectives are considered simultaneously from a bicriteria optimization point of view. Moreover, they also dominate all of the pure cycles in in-line robotic cells. Finally, the efficient frontier of the 3-machine case with controllable processing times is depicted as an example.
Open Access
An anticipative scheduling approach with controllable processing times
(Elsevier, 2010) Gürel, S.; Körpeoǧlu, E.; Aktürk, M. S.
In practice, machine schedules are usually subject to disruptions which have to be repaired by reactive scheduling decisions. The most popular predictive approach in project management and machine scheduling literature is to leave idle times (time buffers) in schedules in coping with disruptions, i.e. the resources will be under-utilized. Therefore, preparing initial schedules by considering possible disruption times along with rescheduling objectives is critical for the performance of rescheduling decisions. In this paper, we show that if the processing times are controllable then an anticipative approach can be used to form an initial schedule so that the limited capacity of the production resources are utilized more effectively. To illustrate the anticipative scheduling idea, we consider a non-identical parallel machining environment, where processing times can be controlled at a certain compression cost. When there is a disruption during the execution of the initial schedule, a match-up time strategy is utilized such that a repaired schedule has to catch-up initial schedule at some point in future. This requires changing machine-job assignments and processing times for the rest of the schedule which implies increased manufacturing costs. We show that making anticipative job sequencing decisions, based on failure and repair time distributions and flexibility of jobs, one can repair schedules by incurring less manufacturing cost. Our computational results show that the match-up time strategy is very sensitive to initial schedule and the proposed anticipative scheduling algorithm can be very helpful to reduce rescheduling costs.
Open Access
Bicriteria robotic cell scheduling
(Springer, 2008) Gultekin, H.; Akturk, M. S.; Karasan, O. E.
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.
Open Access
Bicriteria robotic cell scheduling with controllable processing times
(Taylor & Francis, 2011) Yildiz, S.; Akturk, M. S.; Karasan, O. E.
The current study deals with a bicriteria scheduling problem arising in an m-machine robotic cell consisting of CNC machines producing identical parts. Such machines by nature possess the process flexibility of altering processing times by modifying the machining conditions at differing manufacturing costs. Furthermore, they possess the operational flexibility of being capable of processing all the operations of these identical parts. This latter flexibility in turn introduced a new class of robot move cycles, called pure cycles, to the literature. Within the restricted class of pure cycles, our task is to find the processing times on machines so as to minimise the cycle time and the manufacturing cost simultaneously. We characterise the set of all non-dominated solutions for two specific pure cycles that have emerged as prominent ones in the literature. We prove that either of these pure cycles is non-dominated for the majority of attainable cycle time values. For the remaining regions, we provide the worst case performance of one of these two cycles.
Open Access
Considering manufacturing cost and scheduling performance on a CNC turning machine
(Elsevier, 2007) Gurel, S.; Akturk, M. S.
A well known industry application that allows controllable processing times is the manufacturing operations on CNC machines. For each turning operation as an example, there is a nonlinear relationship between the manufacturing cost and its required processing time on a CNC turning machine. If we consider total manufacturing cost (F1) and total weighted completion time (F2) objectives simultaneously on a single CNC machine, making appropriate processing time decisions is as critical as making job sequencing decisions. We first give an effective model for the problem of minimizing F1 subject to a given F2 level. We deduce some optimality properties for this problem. Based on these properties, we propose a heuristic algorithm to generate an approximate set of efficient solutions. Our computational results indicate that the proposed algorithm performs better than the GAMS/MINOS commercial solver both in terms of solution quality and computational requirements such that the average CPU time is only 8% of the time required by the GAMS/MINOS.
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.
Open Access
Essays on scheduling with controllable processing times in flexible manufacturing systems
(2003) Türkcan, Ayten
In this study, we consider FMS loading, scheduling and tool management problems simultaneously. Our aim is to determine the machining conditions, to load and schedule parts on the nonidentical parallel CNC machines and to determine tool allocation and replacement decisions. We consider due date and cost based objectives. The due date related objectives are minimization of weighted tardiness, and weighted earliness/tardiness. The cost related objective is the minimization of the manufacturing cost, which is the sum of machining, tooling and nonmachining costs. An important issue in flexible manufacturing systems is that the processing times can be controlled by changing the machining conditions. In this study, we consider controllable processing times because of the flexibility they provide for finding alternative solutions in predictive and reactive scheduling.
Open Access
Lot sizing with nonlinear production cost functions
(2015-07) Koca, Esra
In this study, we consider di erent variations of the lot sizing problem encountered in many real life production, procurement and transportation systems. First, we consider the deterministic lot sizing problem with piecewise concave production cost functions. A piecewise concave function can represent quantity discounts, subcontracting, overloading, minimum order quantities, and capacities. Computational complexity of this problem was an open question in the literature. We develop a dynamic programming (DP) algorithm to solve the problem and show that the problem is polynomially solvable when number of breakpoints of the production cost function is xed and the breakpoints are time-invariant. We observe that the time complexity of our algorithm is as good as the complexity of existing algorithms in the literature for the special cases with capacities, minimum order quantities, and subcontracting. Our algorithm performs quite well for small and medium sized instances. For larger instances, we propose a DP based heuristic to nd a good quality solution in reasonable time. Next, we consider the stochastic lot sizing problem with controllable processing times where processing times can be reduced in return for extra compression cost. We assume that the compression cost function is a convex function in order to re ect the increasing marginal cost of larger reductions in processing times. We formulate the problem as a second-order cone mixed integer program, strengthen the formulation and solve it by a commercial solver. Moreover, we obtain some convex hull and computational complexity results. We conduct an extensive computational study to see the e ect of controllable processing times in solution quality and observe that even with small reductions in processing times, it is possible to obtain a less costly production plan. As a nal problem, we study the multistage stochastic lot sizing problem with nervousness considerations and controllable processing times. System nervousness is one of the main problems of dynamic solution strategies developed for stochastic lot sizing problems. We formulate the problem so that the nervousness of the system is restricted by some additional constraints and parameters. Mixing and continuous mixing set structures are observed as relaxations of our formulation. We develop valid inequalities for the problem based on these structures and computationally test these inequalities.
Open Access
Master production scheduling under uncertainty with controllable processing times
(2009) Körpeoğlu, Ersin
Master Production Schedules (MPS) are widely used in industry especially within Enterprise Resource Planning (ERP) Software. MPS assumes infinite capacity, fixed processing times and a single scenario for demand forecasts. In this thesis, we questioned these assumptions and considered a problem with finite capacity, controllable processing times and finally and most importantly, several demand scenarios instead of just one. We used a multi-stage stochastic programming approach in order to come up with maximum expected profit given the demand scenarios. We used controllable processing times, which are feasible in most of the scheduling practice in industry, to achieve a flexibility in capacity usage. We provided a non-linear mixed integer programming formulation for our problem. Afterwards, we analyzed two sub-problems to simplify the structure of the objective function and suggested alternative linearizations. We considered easier cases of our problem, proposed sufficient conditions for optimality and established the computational complexity status for two special cases. We conducted three experiments, to test computational performance of the formulations, to analyze the profit performance of the multi-stage solutions and finally, to analyze the effect of controllability on profit. Our computational studies show that one of the proposed formulations solves large instances in a very small amount of time. The second experiment suggests that the performance of multi-stage solutions is significantly better than the one of solutions obtained using single scenario strategies in terms of relative regret. Finally, the third experiment shows that controllability significantly increases the performance of multi-stage solutions.
Open Access
A multi-stage stochastic programming approach in master production scheduling
(Elsevier, 2011) Körpeoğlu, E.; Yaman, H.; Aktürk, M. S.
Master Production Schedules (MPS) are widely used in industry, especially within Enterprise Resource Planning (ERP) software. The classical approach for generating MPS assumes infinite capacity, fixed processing times, and a single scenario for demand forecasts. In this paper, we question these assumptions and consider a problem with finite capacity, controllable processing times, and several demand scenarios instead of just one. We use a multi-stage stochastic programming approach in order to come up with the maximum expected profit given the demand scenarios. Controllable processing times enlarge the solution space so that the limited capacity of production resources are utilized more effectively. We propose an effective formulation that enables an extensive computational study. Our computational results clearly indicate that instead of relying on relatively simple heuristic methods, multi-stage stochastic programming can be used effectively to solve MPS problems, and that controllability increases the performance of multi-stage solutions.
Open Access
A new bounding mechanism for the CNC machine scheduling problems with controllable processing times
(Elsevier, 2005) Kayan, R. K.; Akturk, M. S.
In this study, we determine the upper and lower bounds for the processing time of each job under controllable machining conditions. The proposed bounding scheme is used to find a set of discrete efficient points on the efficient frontier for a bi-criteria scheduling problem on a single CNC machine. We have two objectives; minimizing the manufacturing cost (comprised of machining and tooling costs) and minimizing makespan. The technological restrictions of the CNC machine along with the job specific parameters affect the machining conditions; such as cutting speed and feed rate, which in turn specify the processing times and tool lives. Since it is well known that scheduling problems are extremely sensitive to processing time data, system resources can be utilized much more efficiently by selecting processing times appropriately.
Open Access
Parallel machine match-up scheduling with manufacturing cost considerations
(Springer, 2010) Aktürk, M. S.; Atamtürk, A.; Gürel, S.
Many scheduling problems in practice involve rescheduling of disrupted schedules. In this study, we show that in contrast to fixed processing times, if we have the flexibility to control the processing times of the jobs, we can generate alternative reactive schedules considering the manufacturing cost implications in response to disruptions. We consider a non-identical parallel machining environment where processing times of the jobs are compressible at a certain manufacturing cost, which is a convex function of the compression on the processing time. In rescheduling it is highly desirable to catch up the original schedule as soon as possible by reassigning the jobs to the machines and compressing their processing times. On the other hand, one must also keep the manufacturing cost due to compression of the jobs low. Thus, one is faced with a tradeoff between match-up time and manufacturing cost criteria. We introduce alternative match-up scheduling problems for finding schedules on the efficient frontier of this time/cost tradeoff. We employ the recent advances in conic mixed-integer programming to model these problems effectively. We further provide a fast heuristic algorithm driven by dual prices of convex subproblems for generating approximate efficient schedules.
Unknown
Predictive/reactive scheduling with controllable processing times and earliness-tardiness penalties
(Taylor & Francis, 2009) Turkcan, A.; Akturk, M. S.; Storer, R. H.
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.
Open Access
Rescheduling parallel machines with controllable processing times
(2012) Muhafız, Müge
In many manufacturing environments, the production does not always endure as it is planned. Many times, it is interrupted by a disruption such as machine breakdown, power loss, etc. In our problem, we are given an original production schedule in a non-identical parallel machine environment and we assume that one of the machines is disrupted at time t. Our aim is to revise the schedule, although there are some restrictions that should be considered while creating the revised schedule. Disrupted machine is unavailable for a certain time. New schedule has to satisfy the maximum completion time constraint of each machine. Furthermore, when we revise the schedule we have to satisfy the constraint that the revised start time of a job cannot be earlier than its original start time. Because, we assume that jobs are not ready before their original start times in the revised schedule. Therefore, we have to find an alternative solution to decrease the negative impacts of this disruption as much as possible. One way to process a disrupted job in the revised schedule is to reallocate the job to another machine. The other way is to keep the disrupted job at its original machine, but to delay its start time after the end time of the disruption. Since the machines might be fully utilized originally, we may have to compress some of the processing times in order to add a new job to a machine or to reallocate the jobs after the disruption ends. Consequently, we assume that the processing times are controllable within the given lower and upper bounds. Our first objective is to minimize the sum of reallocation and nonlinear compression costs. Besides, it is important to deliver the orders on time, not earlier or later than they are promised. Therefore, we try to maintain the original completion times as much as possible. So, the second objective is to minimize the total absolute deviations of the completion times in the revised schedule from the original completion times. We developed a bi-criteria non-linear mathematical model to solve this nonidentical parallel machine rescheduling problem. Since we have two objectives, we handled the second objective by giving it an upper bound and adding this bound as a constraint to the problem. By utilizing the second order cone programming, we solved this mixed-integer nonlinear mathematical model using a commercial MIP solver such as CPLEX. We also propose a decision tree based heuristic algorithm. Our algorithm generates a set of solutions for a problem instance and we test the solution quality of the algorithm solving same problem instances by the mathematical model. According to our computational experiments, the proposed heuristic approach could obtain close solutions for the first objective for a given upper bound on the second objective.
Open Access
Scheduling in flexible robotic manufacturing cells
(2006) Gültekin, Hakan
The focus of this thesis is the scheduling problems arising in robotic cells which consist of a number of machines and a material handling robot. The machines used in such systems for metal cutting industries are highly flexible CNC machines. Although flexibility is the key term that affects the performance of these systems, the current literature ignores this. As a consequence, the problems considered in the current literature are either too limiting or the provided solutions are suboptimal for the flexible systems. This thesis analyzes different robotic cell configurations with different sources of flexibility. This study is the first one to consider operation allocation problems and controllable processing times as well as some design problems and bicriteria models in the context of robotic cell scheduling. Also, a new class of robot move cycles is defined, which is overlooked in the existing literature. Optimal solutions are provided for solvable cases, whereas complexity analyses and efficient heuristic algorithms are provided for the remaining problems.
Open Access
Scheduling parallel CNC machines with time/cost trade-off considerations
(Elsevier, 2007) Gurel, S.; Akturk, M. S.
When the processing times of jobs are controllable, selected processing times affect both the manufacturing cost and the scheduling performance. A well-known example for such a case that this paper specifically deals with is the turning operation on a CNC machine. Manufacturing cost of a turning operation is a nonlinear convex function of its processing time. We also know that scheduling decisions are quite sensitive to the processing times. Therefore, this paper considers minimizing total manufacturing cost (F1) and total completion time (F2) objectives simultaneously on identical parallel CNC turning machines. Since decreasing processing time of a job increases its manufacturing cost, we cannot minimize both objectives at the same time, so the problem is to generate non-dominated solutions. We consider the problem of minimizing F1 subject to a given F2 level and give an effective formulation for the problem. For this problem, we prove some optimality properties which facilitated designing an efficient heuristic algorithm to generate approximate non-dominated solutions. Computational results show that proposed algorithm performs almost equal with the GAMS/MINOS commercial solver although it spends much less computation time.
Open Access
Single CNC machine scheduling with controllable processing times and multiple due dates
(Taylor & Francis, 2008) Atan, M. O.; Akturk, M. S.
In this study, we solve the single CNC machine scheduling problem with controllable processing times. Our objective is to maximize the total profit that is composed of the revenue generated by the set of scheduled jobs minus the sum of total weighted earliness and weighted tardiness, tooling and machining costs. Customers offer multiple due dates to the manufacturer, each coming with a distinct price for the order that is decreasing as the date gets later, and the manufacturer has the flexibility to accept or reject the orders. We propose a number of ranking rules and scheduling algorithms that we employ in a four-stage heuristic algorithm that determines the processing times for each job and a final schedule for the accepted jobs simultaneously, to maximize the overall profit.
Open Access
Stochastic lot sizing problem with controllable processing times
(Elsevier, 2015) Koca, E.; Yaman, H.; Aktürk, M. S.
In this study, we consider the stochastic capacitated lot sizing problem with controllable processing times where processing times can be reduced in return for extra compression cost. We assume that the compression cost function is a convex function as it may reflect increasing marginal costs of larger reductions and may be more appropriate when the resource life, energy consumption or carbon emission are taken into consideration. We consider this problem under static uncertainty strategy and α service level constraints. We first introduce a nonlinear mixed integer programming formulation of the problem, and use the recent advances in second order cone programming to strengthen it and then solve by a commercial solver. Our computational experiments show that taking the processing times as constant may lead to more costly production plans, and the value of controllable processing times becomes more evident for a stochastic environment with a limited capacity. Moreover, we observe that controllable processing times increase the solution flexibility and provide a better solution in most of the problem instances, although the largest improvements are obtained when setup costs are high and the system has medium sized capacities.
Open Access
Stochastic lot sizing problem with nervousness considerations
(Elsevier, 2018) Koca, E.; Yaman, Hande; Aktürk, M. Selim
In this paper, we consider the multistage stochastic lot sizing problem with controllable processing times under nervousness considerations. We assume that the processing times can be reduced in return for extra cost (compression cost). We generalize the static and static-dynamic uncertainty strategies to eliminate setup oriented nervousness and control quantity oriented nervousness. We restrict the quantity oriented nervousness by introducing a new concept called promised production amounts, and considering new range constraints and a nervousness cost function. We formulate the problem as a second-order cone mixed integer program (SOCMIP), and apply the conic strengthening. We observe the continuous mixing set substructure in our formulation that arises due the controllable processing times. We reformulate the problem by using an extended formulation for the continuous mixing set and solve the problem by a branch-and-cut approach. The computational experiments indicate that the reformulation reduces the root gaps and this helps to solve the problem in less computation times. Moreover, in our computational experiments we investigate the impact of new restrictions, specifically the additional cost of eliminating the setup oriented nervousness, on the total costs and the system nervousness. Our computational results clearly indicate that we could significantly reduce the nervousness costs and generate more stable production schedules with a relatively small increase in the total cost.
Open Access
Time/cost trade-offs in machine scheduling with controllable processing times
(2008) Gürel, Sinan
Processing time controllability is a critical aspect in scheduling decisions since most of the scheduling practice in industry allows controlling processing times. A very well known example is the computer numerically controlled (CNC) machines in flexible manufacturing systems. Selected processing times for a given set of jobs determine the manufacturing cost of the jobs and strongly affect their scheduling performance. Hence, when making processing time and scheduling decisions at the same time, one must consider both the manufacturing cost and the scheduling performance objectives. In this thesis, we have studied such bicriteria scheduling problems in various scheduling environments including single, parallel and non-identical parallel machine environments. We have included some regular scheduling performance measures such as total weighted completion time and makespan. We have considered the convex manufacturing cost function of CNC turning operation. We have provided alternative methods to find efficient solutions in each problem. We have particularly focused on the single objective problems to get efficient solutions, called the -constraint approach. We have provided efficient formulations for the problems and shown useful properties which led us to develop fast heuristics to generate set of efficient solutions. In this thesis, taking another point of view, we have also studied a conic quadratic reformulation of a machine-job assignment problem with controllable processing times. We have considered a convex compression cost function for each job and solved a profit maximization problem. The convexity of cost functions is a major source of difficulty in finding optimal integer solutions in this problem, but our strengthened conic reformulation has eliminated this difficulty. Our reformulation approach is sufficiently general so that it can also be applied to other mixed 0-1 optimization problems with separable convex cost functions.Our computational results demonstrate that the proposed conic reformulation is very effective for solving the machine-job assignment problem with controllable processing times to optimality. Finally, in this thesis, we have considered rescheduling with controllable processing times. In particular, we show that in contrast to fixed processing times, if we have the flexibility to control the processing times of the jobs, we can generate alternative reactive schedules in response to a disruption such as machine breakdown. We consider a non-identical parallel machining environment where processing times of the jobs are compressible at a certain cost which is a convex function of the compression on the processing time. When rescheduling, it is critical to catch up the initial schedule as soon as possible by reassigning the jobs to the machines and changing their processing times. On the other hand, one must keep the total cost of the jobs at minimum. We present alternative match-up scheduling problems dealing with this trade-off. We use the strong conic reformulation approach in solving these problems. We further provide fast heuristic algorithms.