Browsing by Subject "Scheduling (Management)--Mathematical models."

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Open Access
An analysis of pure robotic cycles
(2008) Yıldız, Serdar
This thesis is focused on scheduling problems in robotic cells consisting of a number of CNC machines producing identical parts. We consider two different cell layouts which are in-line robotic cells and robot centered cells. The problem is to find the robot move sequence and processing times on machines minimizing the total manufacturing cost and cycle time simultaneously. The automation in manufacturing industry increased the flexibility, however it is not widely studied in the literature. The flexibility of machines enables us to process all the required operations for a part on the same machine. Furthermore, the processing times on CNC machines can be increased or decreased by changing the feed rate and cutting speed. Hence, we assume that a part is processed on one of the machines and the processing times are assumed to be controllable. The flexibility of machines results in a new class of cycles named pure cycles. We determined efficient pure cycles and corresponding processing times dominating the rest of pure cycles in the specified cycle time regions. In addition, for in-line robotic cells, the optimum number of machines is determined for given parameters.
Open Access
Analysis of reactive scheduling problems in manufacturing systems
(1997) Bayız, Murat
In this study we develop a new scheduling algorithm for the job shop problem. The proposed algorithm is a heuristic method based on the filtered beam search. After extensive analyses on the evaluation functions and search parameters of the beam search, we measure the performance of the algorithm in terms of quality of solutions and CPU times for both the makespan and mean tardiness criteria. In the second half of the research, we study the reactive scheduling problem. Specifically, we analyze several reactive methods such as no response, periodic response and continuous response under various experimental conditions. The beam search based partial scheduling is also studied in this thesis. The method is analyzed for both deterministic and stochastic environments under several job shop configurations.
Open Access
An exact approach to minimize single machine total weighted tardiness problem with unequal release dates
(1998) Özdemir, Deniz
In this research, the problem of scheduling a set of jobs on a single machine to minimize total weighted tardiness with unequal release dates is considered. We present a new dominance rule by considering the time depending orderings between each pair of jobs. The proposed 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. Based on the dominance rule, an algorithm is developed which is compared to a number of heuristics in the literature. Our computational results indicate that the proposed algorithm dominates the competing algorithms in all runs, therefore it can improve the upper bounding scheme and can be used in reducing the number of alternatives in any enumerative algorithm. Furthermore, the proposed dominance rule is incorporated in a branch and bound algorithm in conjunction with lower bounding scheme, branching condition and search strcitegy. To the best of our knowledge, author know of no other published exact approach for l|rj| problem. This enhances contribution of our study in the literature.
Open Access
Flowtime estimation in dynamic job shops
(1996) Çömlekçi, Abdullah
In the scheduling literature, estimation of job flowtimes has always been an important issue since the late sixties. The previous studies focus on the problem in the context of due date assignment and develop methods using aggregate information in the estimation process. In this study, we propose a new method which utilizes the job, shop and route information on an operational basis. The performance of the proposed method is measured using a simulation model. It is also compared with the existing methods for a wide variety of performance measures under various experimental conditions.
Open Access
Generating robust and stable machine schedules from a proactive standpoint
(2009) Gören, Selçuk
In practice, scheduling systems are subject to considerable uncertainty in highly dynamic operating environments. The ability to cope with uncertainty in the scheduling process is becoming an increasingly important issue. In this thesis we take a proactive approach to generate robust and stable schedules for the environments with two sources of uncertainty: processing time variability and machine breakdowns. The information about the uncertainty is modeled using cumulative distribution functions and probability theory is utilized to derive inferences. We first focus on the single machine environment. We define two robustness (expected total flow time and expected total tardiness) and three stability (the sum of the squared and absolute differences of the job completion times and the sum of the variances of the realized completion times) measures. We identify special cases for which the measures can be optimized without much difficulty. We develop a dominance rule and two lower bounds for one of the robustness measures, which are employed in a branch-and-bound algorithm to solve the problem exactly. We also propose a beam-search heuristic to solve large problems for all five measures. We provide extensive discussion of our numerical results. Next, we study the problem of optimizing both robustness and stability simultaneously. We generate the set of all Pareto optimal points via -constraint method. We formulate the sub-problems required by the method and establish their computational complexity status. Two variants of the method that works with only a single type of sub-problem are also considered. A dominance rule and alternative ways to enforce the rule to strengthen one of these versions are discussed. The performance of the proposed technique is evaluated with an experimental study. An approach to limit the total number of generated points while keeping their spread uniform is also proposed. Finally, we consider the problem of generating stable schedules in a job shop environment with processing time variability and random machine breakdowns. The stability measure under consideration is the sum of the variances of the realized completion times. We show that the problem is not in the class NP. Hence, a surrogate stability measure is developed to manage the problem. This version of the problem is proven to be NP-hard even without machine breakdowns. Two branchand-bound algorithms are developed for this case. A beam-search and a tabu-search based two heuristic algorithms are developed to handle realistic size problems with machine breakdowns. The results of extensive computational experiments are also provided.
Open Access
A heuristic algorithm for an integrated routing and scheduling problem with stops en-route
(2009) Uzun, Emre
In this study, we examine an integrated routing and scheduling problem that arises in the context of transportation of hazardous materials. The purpose of the problem is to find a minimum risk route between an origin and a destination point on a given network and to build a schedule on this route that determines where and how long to stop for a truck carrying hazardous materials. The objective is to minimize the risk imposed to the society while completing the path within a given time limit. The risk is defined as the expected population exposure in the presence of an accident which varies different times in a day. There are exact algorithms available in the literature that solve the problem. However, these algorithms are not capable of solving large sized networks due to memory constraints. Our aim is to develop a heuristic procedure that can handle larger networks. We separate the problem into two independent components, routing and scheduling, and propose solution algorithms which would communicate each other when running the algorithm. For the routing component we define a neighborhood structure that can be used to generate several paths around a given path on a network. The search procedure takes an initial path and improves it by generating different paths in the defined neighborhood. For the scheduling component, we discuss mixed integer programming, dynamic programming and heuristic approaches. We run the proposed heuristic algorithm on several test networks and compare its performance with the optimal solutions. We also present the application of the heuristic procedure on a large sized Turkey Road Network.
Open Access
Job shop scheduling under dynamic and stochastic manufacturing environment
(1995) Kutanoğlu, Erhan
In practice, manufacturing systems operate under dynamic and stochastic environment where unexpected events (or interruptions) occur continuously in the shop. Most of the scheduling literature deals with the schedule generation problem which is only one aspect of the scheduling decisions. The reactive scheduling and control aspect has scarcely been addressed. This study investigates the effects of the stochastic events on the s\'stem performance and develops alternative reactive scheduling methods. In this thesis, we also study the single-pass and multi-pass scheduling heuristics in dynamic and stochastic job shop scheduling environment. We propose a simulation-based scheduling system for the multi-pass heuristics. Finally, we analyze the interactions among the operational strategies (i.e, lookahead window, scheduling period, method used for scheduling), the system conditions, and the unexpected events such as machine breakdowns and processing time variations.
Open Access
Lot streaming in flow shops
(1994) Topaloğlu, Engin
Lot streaming is permitting partial transfer of processed portions of a job to downstream machines, thus allowing ovelapping operations. The primary motivation is to improve the measures of performance by the quick movement of work in the shop. In this thesis, we study various forms of the lot streaming problem in flow shops to derive the characteristics of optimal solutions. We first analyze single job lot streaming problems, then extend the results to multi-job problems. When there is a single job, the lot streaming problem is to find the best transfer batch sizes that optimizes the given criterion. We consider three different measures of performance, job, sublot and item completion time criteria. We derive a closed form solution for a special case of job completion time criterion. Under sublot completion time criterion, when the first machine has the largest processing time, we show that partial transfers of equal size are optimal. We propose two polynomial time algorithms for the problem in which only two transfer batches are permitted between each consecutive machines for sublot and item completion time criteria. In multi-job lot streaming problems, the sequencing and lot streaming decisions must be considered simultaneously. For multi-job problems we investigate the hierarchical application of lot streaming and sequencing decisions.
Open Access
Lot streaming in multi stage shops
(1994) Şen, Alper
In this thesis, a number of lot streaming problems in flow, open and job shops are investigated. Lot streaming is the process of splitting a job to allow for overlapping of its operations on various machines resulting in shorter completion times. When there is a single job, the problem is to find the size of the transfer batches (“sublots”) which minimizes a given performance measure (e.g., makespan, mean flow time). Multi-job problems are harder, since sequencing and sizing decisions must be made simultaneously. Most of the current research in lot streaming is concerned with minimum makespan problems in flow shops. In this study, other performance measures and shop structures are also analyzed. Optimal sublot sizes are derived for the single job two machine flow shop mean flow time problem. Solution methods are proposed for the minimum makespan problem in open shops both for multiple job and single job cases.
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
Minimazing the total completion time in a two stage flow shop with a single setup server
(2012) Kolay, Muhammet
In this thesis, we study a two stage flow shop problem with a single server. All jobs are available for processing at time zero. Processing of a job is preceded by a sequence independent setup operation on both machines. The setup and processing times of all jobs on the two machines are given. All setups are performed by the same server who can perform one setup at a time. Setups cannot be performed simultaneously with job processing on the same machine. Once the setup is completed for a job, processing can automatically progress without any further need for the server. Setup for a job may start on the second machine before that job finishes its processing on the first machine. Preemption of setup or processing operations is not allowed. A job is completed when it finishes processing on the second machine. The objective is to schedule the setup and processing operations on the two machines in such a way that the total completion time is minimized. This problem is known to be strongly NP-hard [3]. We propose a new mixed integer programming formulation for small-sized instances and a Variable Neighborhood Search (VNS) mechanism for larger problems. We also develop several lower bounds to help assess the quality of heuristic solutions on large instances for which optimum solutions are not available. Experimental results indicate that the proposed heuristic provides reasonably effective solutions in a variety of instances and it is very efficient in terms of computational requirements.
Open Access
Mobile health services for rubal areas in Turkey : a case study for Burdur
(2013) Kurugöl, Damla
Currently, healthcare services in urban areas are provided by family health centers coordinated by community health centers. By the application of family physician based system, it is planned to provide mobile healthcare services (MHS) for the people living in the rural areas which have difficulties to reach those health centers in urban areas. In the scope of these ongoing studies, family physicians procure primary health services to the determined villages in between defined time periods. The aim of this project is to schedule a working plan by using family physicians’ mobile healthcare service times effectively. In this context, when the problem was examined, we realized that it has similarities with the periodic vehicle routing problem (PVRP). We proposed several different solution approaches to the PVRP in the context of the mobile healthcare services application that we are interested in. We tested the implementation of our proposed solution approaches using both simulated data and extended data obtained from the villages of Burdur city
Open Access
Models and algorithms for deterministic and robust discrete time/cost trade-off problems
(2008) Hazır, Öncü
Projects are subject to various sources of uncertainties that often negatively impact activity durations and costs. Therefore, it is of crucial importance to develop effective approaches to generate robust project schedules that are less vulnerable to disruptions caused by uncontrollable factors. This dissertation concentrates on robust scheduling in project environments; specifically, we address the discrete time/cost trade-off problem (DTCTP). Firstly, Benders Decomposition based exact algorithms to solve the deadline and the budget versions of the deterministic DTCTP of realistic sizes are proposed. We have included several features to accelerate the convergence and solve large instances to optimality. Secondly, we incorporate uncertainty in activity costs. We formulate robust DTCTP using three alternative models. We develop exact and heuristic algorithms to solve the robust models in which uncertainty is modeled via interval costs. The main contribution is the incorporation of uncertainty into a practically relevant project scheduling problem and developing problem specific solution approaches. To the best of our knowledge, this research is the first application of robust optimization to DTCTP. Finally, we introduce some surrogate measures that aim at providing an accurate estimate of the schedule robustness. The pertinence of proposed measures is assessed through computational experiments. Using the insight revealed by the computational study, we propose a two-stage robust scheduling algorithm. Furthermore, we provide evidence that the proposed approach can be extended to solve a scheduling problem with tardiness penalties and earliness rewards.
Open Access
Multiple part-type scheduling in flexible robotic cells
(2009) Batur, Gül Didem
This thesis considers the scheduling problem arising in two-machine manufacturing cells which repeatedly produce a set of multiple part-types, and where transportation of the parts between the machines is performed by a robot. The cycle time of the cell depends on 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 adjusted. As a result, this study tries to find the robot move sequence as well as the processing times of the parts on each machine that minimize the cycle time. The problem of determining the best cycle in a 2- machine cell is first modeled as a travelling salesman problem. Then, an efficient 2-stage heuristic algorithm is constructed and compared with the most common heuristic approach of Longest Processing Time.
Open Access
A re-examination of the effectiveness of priority rules in a dynamic job shop environment
(1997) Lejmi, Tahar
III dyiiaiuic job .shop .sdiccliiliiig li(cra(urc, an cxicnsivc research clioil lias been spent to study the performance of priority rules, wliich play an important role to manage scheduling tasks in real life manufacturing systems. This study extends the previous research on priority rules by investigating the effect of due date, processing time, and load variation on the pei (drmance of some well used priority rules in a Job shop environment. Furthermore, tliis study will analyze the performance of the rules under the due window approach. The performance of the rules will be measured in terms of two regular criteria: mean flow time and mean tardiness. In addition, with the incieasing emphasis on using non regular measures, we further study the performance of the rules with respect to the mean absolute deviation (MAD) criterion. Finally, we propose two new rules that perform quiet effectively for the MAD criterion.
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
Robotic assembly line design with tool changes
(2009) Tula, Adnan
This thesis is focused on assembly line design problems in robotic cells. The mixed-model assembly line design problem that we study has several subproblems such as allocating operations to the stations in the robotic cell and satisfying the demand and cycle time within a desired interval for each model to be produced. We also ensure that assignability, precedence and tool life constraints are met. The existing studies in the literature overlook the limited lives of tools that are used for production in the assembly lines. Furthermore, the studies in the literature do not consider the unavailability periods of the assembly lines and assume that assembly lines work 24 hours a day continuously. In this study, we consider limited lives for the tools and hence we handle tool change decisions. In order to reflect a more realistic production environment, we deal with designing a mixed-model assembly line that works 24 hours a day in three 8-hour shifts and we consider lunch and tea breaks that are present in each shift. This study is the first one to propose using such breaks as tool change periods and hence eliminate tool change related line stoppages. In this setting, we determine the number of stations, operation allocations and tool change decisions jointly. We provide a heuristic algorithm for our problem and test the performances of our heuristic algorithm and DICOPT and CPLEX solvers included in GAMS software on different instances with varying problem parameters.
Open Access
Scheduling with tool changes to minimize total completion time under controllable machining conditions
(2001) Köylü, Rabia
In the literature, scheduling models ignore the unavailability of the cutting tools. Tool management literature considers tool loading problem when tools change due to part mix. In practice, tools are changed more often due to tool wear. The studies on tool management issues consider machining conditions as constant values. In fact, it is possible to change the processing time and tool usage rate of a job by changing the machining conditions. However, the machining conditions, such as cutting speed and feed rate e ect the processing time and usage rate of the tool in opposite directions. Increasing the usage rates of jobs will lead to an increase in number of tool switches. Processing times and number of tool switches are two components of our ob jective function. This two-side e ect creates a tradeo between processing time and tool usage rate. Therefore machining conditions should be selected appropriately in order to minimize the total completion time. We proposed a set of single-pass dispatching rules and a local search algorithm to determine the machine conditions for each job and to schedule them on a single CNC machine simultaneously to minimize the total completion time.
Open Access
Single machine scheduling problems: early-tardy penalties
(1993) Oguz, Ceyda
The primary concern of this dissertation is to analyze single machine total earliness and tardiness scheduling problems with different due dates and to develop both a dynamic programming formulation for its exact solution and heuristic algorithms for its approximate solution within acceptable limits. The analyses of previous works on the single machine earliness and tardiness scheduling problems reveal that the research mainly focused on a restricted problem type in which no idle time insertion is allowed in the schedule. This study deals with the general case where idle time insertion is allowed whenever necessary. Even though this problem is known to be A'P-hard in the ordinary sense, there is still a need to develop an optimizing algorithm through dynamic programming formulation. Development of such an algorithm is necessary for further identifying an approximation scheme for the problem which is an untouched issue in the earliness and tardiness scheduling theory. Furthermore, the developed dynamic programming formulation is extended to an incomplete dynamic programming which forms the core of one of the heuristic procedure proposed.A second aspect of this study is to investigate two special structures for the different due dates, namely Equal-Slack and Total-Work-Content rules, and to discuss computational complexity of the problem with these special structures. Consequently, solution procedures which bear on the characteristics of the special due date structures are proposed. This research shows that the total earliness and tardiness scheduling problem with Equal-Slack rule is A/’P-hard but can be solvable in polynomial time in certain cases. Moreover, a very efficient heuristic algorithm is proposed for the problem with the other due date structure and the results of this part leads to another heuristic algorithm for the general due date structure. Finally, a lower bound procedure is presented which is motivated from the structure of the optimal solution of the problem. This lower bound is compared with another lower bound from the literature and it is shown that it performs well on randomly generated problems.
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.