The order selection and lot sizing problem in the make-to-order environment

This research is motivated by the need for considering lot sizing while accepting customer orders in a make-to-order (MTO) environment, in which each customer order must be delivered by its due date. Job shop is the typical operation model used in an MTO operation, where the production planner must make three concurrent decisions; they are order selection, lot size, and job schedule. These decisions are usually treated separately in the literature and are mostly led to heuristic solutions. The first phase of the study is focused on a formal definition of the problem. Mathematical programming techniques are applied to modeling this problem in terms of its objective, decision variables, and constraints. A commercial solver, CPLEX is applied to solve the resulting mixed-integer linear programming model with small instances to validate the mathematical formulation. The computational result shows it is not practical for solving problems of industrial size, using a commercial solver. The second phase of this study is focused on development of an effective solution approach to this problem of large scale. The proposed solution approach is an iterative process involving three sequential decision steps of order selection, lot sizing, and lot scheduling. A range of simple sequencing rules are identified for each of the three subproblems. Using computer simulation as the tool, an experiment is designed to evaluate their performance against a set of system parameters. For order selection, the proposed weighted most profit rule performs the best. The shifting bottleneck and the earliest operation finish time both are the best scheduling rules. For lot sizing, the proposed minimum cost increase heuristic, based on the Dixon-Silver method performs the best, when the demand-to-capacity ratio at the bottleneck machine is high. The proposed minimum cost heuristic, based on the Wagner-Whitin algorithm is the best lot-sizing heuristic for shops of a low demand-to-capacity ratio. The proposed heuristic is applied to an industrial case to further evaluate its performance. The result shows it can improve an average of total profit by 16.62%. This research contributes to the production planning research community with a complete mathematical definition of the problem and an effective solution approach to solving the problem of industry scale.

A comparative study of block scheduling and traditional scheduling on academic achievement

The purpose of this study was to evaluate the effectiveness of an alternate day block schedule design (n = 419) versus a traditional six-period schedule design (n = 623) on the academic achievement of the graduating classes in two schools in which the design was used respectively. Academic achievement was measured by (a) two standardized tests: the Florida Comprehensive Assessment Test Sunshine State Standards (FCAT-SSS) in mathematics and reading for 9th and 10th grade and the Scholastic Reading Inventory Test (SRI) for 9 th, 10th, and 11th grade; (b) three school grades: the mathematics final course grades for 9th, 10th, and 11th grade, the English final course grades for 9th, 10th, 11th, and 12th grade and the graduating GPA. A total of five repeated measure analyses of variance (ANOVAs) were conducted to analyze the difference between the two schools (representing the two designs) with respect to five achievement indicators (FCAT-SSS mathematics scores, FCAT-SSS reading scores, SRI scores, mathematics final course grades, and English final course grades). The between-subject factor for the five ANOVAs was the schedule design and the within-subject factor was the time the tests were taken or the time the course grades were issued. T-tests were performed on all eighth grade achievement indicators to ensure there were no significant differences in achievement between the two cohorts prior to entering high school. An independent samples t-test was conducted to analyze the difference between the two schedule designs with respect to graduating GPA. Achievement in the alternate day block schedule design was significantly higher than in the traditional six-period schedule design for some of the locally assigned school grades. The difference between the two types of schedule designs was not significant for the standardized measures (the FCAT-SSS in reading and mathematics and the SRI). This study concludes that the use of an alternate day block schedule design can be considered an educational tool that can help improve the academic achievement of students as measured by local indicators of achievement; but, apparently the design is not an important factor in achievement as measured by state examinations such as the FCAT-SSS or the SRI.

A non-linear discrete stochastic optimization model for Advanced Access patient appointment scheduling

Access to healthcare is a major problem in which patients are deprived of receiving timely admission to healthcare. Poor access has resulted in significant but avoidable healthcare cost, poor quality of healthcare, and deterioration in the general public health. Advanced Access is a simple and direct approach to appointment scheduling in which the majority of a clinic's appointments slots are kept open in order to provide access for immediate or same day healthcare needs and therefore, alleviate the problem of poor access the healthcare. This research formulates a non-linear discrete stochastic mathematical model of the Advanced Access appointment scheduling policy. The model objective is to maximize the expected profit of the clinic subject to constraints on minimum access to healthcare provided. Patient behavior is characterized with probabilities for no-show, balking, and related patient choices. Structural properties of the model are analyzed to determine whether Advanced Access patient scheduling is feasible. To solve the complex combinatorial optimization problem, a heuristic that combines greedy construction algorithm and neighborhood improvement search was developed. The model and the heuristic were used to evaluate the Advanced Access patient appointment policy compared to existing policies. Trade-off between profit and access to healthcare are established, and parameter analysis of input parameters was performed. The trade-off curve is a characteristic curve and was observed to be concave. This implies that there exists an access level at which at which the clinic can be operated at optimal profit that can be realized. The results also show that, in many scenarios by switching from existing scheduling policy to Advanced Access policy clinics can improve access without any decrease in profit. Further, the success of Advanced Access policy in providing improved access and/or profit depends on the expected value of demand, variation in demand, and the ratio of demand for same day and advanced appointments. The contributions of the dissertation are a model of Advanced Access patient scheduling, a heuristic to solve the model, and the use of the model to understand the scheduling policy trade-offs which healthcare clinic managers must make. ^

Algorithms for scheduling parallel batch processing machines with non-identical job ready times

This research is motivated by a practical application observed at a printed circuit board (PCB) manufacturing facility. After assembly, the PCBs (or jobs) are tested in environmental stress screening (ESS) chambers (or batch processing machines) to detect early failures. Several PCBs can be simultaneously tested as long as the total size of all the PCBs in the batch does not violate the chamber capacity. PCBs from different production lines arrive dynamically to a queue in front of a set of identical ESS chambers, where they are grouped into batches for testing. Each line delivers PCBs that vary in size and require different testing (or processing) times. Once a batch is formed, its processing time is the longest processing time among the PCBs in the batch, and its ready time is given by the PCB arriving last to the batch. ESS chambers are expensive and a bottleneck. Consequently, its makespan has to be minimized. ^ A mixed-integer formulation is proposed for the problem under study and compared to a formulation recently published. The proposed formulation is better in terms of the number of decision variables, linear constraints and run time. A procedure to compute the lower bound is proposed. For sparse problems (i.e. when job ready times are dispersed widely), the lower bounds are close to optimum. ^ The problem under study is NP-hard. Consequently, five heuristics, two metaheuristics (i.e. simulated annealing (SA) and greedy randomized adaptive search procedure (GRASP)), and a decomposition approach (i.e. column generation) are proposed—especially to solve problem instances which require prohibitively long run times when a commercial solver is used. Extensive experimental study was conducted to evaluate the different solution approaches based on the solution quality and run time. ^ The decomposition approach improved the lower bounds (or linear relaxation solution) of the mixed-integer formulation. At least one of the proposed heuristic outperforms the Modified Delay heuristic from the literature. For sparse problems, almost all the heuristics report a solution close to optimum. GRASP outperforms SA at a higher computational cost. The proposed approaches are viable to implement as the run time is very short. ^

Efficient asynchronous scheduling algorithms for cost-effective buffered crossbar switches

Buffered crossbar switches have recently attracted considerable attention as the next generation of high speed interconnects. They are a special type of crossbar switches with an exclusive buffer at each crosspoint of the crossbar. They demonstrate unique advantages over traditional unbuffered crossbar switches, such as high throughput, low latency, and asynchronous packet scheduling. However, since crosspoint buffers are expensive on-chip memories, it is desired that each crosspoint has only a small buffer. This dissertation proposes a series of practical algorithms and techniques for efficient packet scheduling for buffered crossbar switches. To reduce the hardware cost of such switches and make them scalable, we considered partially buffered crossbars, whose crosspoint buffers can be of an arbitrarily small size. Firstly, we introduced a hybrid scheme called Packet-mode Asynchronous Scheduling Algorithm (PASA) to schedule best effort traffic. PASA combines the features of both distributed and centralized scheduling algorithms and can directly handle variable length packets without Segmentation And Reassembly (SAR). We showed by theoretical analysis that it achieves 100% throughput for any admissible traffic in a crossbar with a speedup of two. Moreover, outputs in PASA have a large probability to avoid the more time-consuming centralized scheduling process, and thus make fast scheduling decisions. Secondly, we proposed the Fair Asynchronous Segment Scheduling (FASS) algorithm to handle guaranteed performance traffic with explicit flow rates. FASS reduces the crosspoint buffer size by dividing packets into shorter segments before transmission. It also provides tight constant performance guarantees by emulating the ideal Generalized Processor Sharing (GPS) model. Furthermore, FASS requires no speedup for the crossbar, lowering the hardware cost and improving the switch capacity. Thirdly, we presented a bandwidth allocation scheme called Queue Length Proportional (QLP) to apply FASS to best effort traffic. QLP dynamically obtains a feasible bandwidth allocation matrix based on the queue length information, and thus assists the crossbar switch to be more work-conserving. The feasibility and stability of QLP were proved, no matter whether the traffic distribution is uniform or non-uniform. Hence, based on bandwidth allocation of QLP, FASS can also achieve 100% throughput for best effort traffic in a crossbar without speedup.

Scheduling medical application workloads on virtualized computing systems

This dissertation presents and evaluates a methodology for scheduling medical application workloads in virtualized computing environments. Such environments are being widely adopted by providers of "cloud computing" services. In the context of provisioning resources for medical applications, such environments allow users to deploy applications on distributed computing resources while keeping their data secure. Furthermore, higher level services that further abstract the infrastructure-related issues can be built on top of such infrastructures. For example, a medical imaging service can allow medical professionals to process their data in the cloud, easing them from the burden of having to deploy and manage these resources themselves. In this work, we focus on issues related to scheduling scientific workloads on virtualized environments. We build upon the knowledge base of traditional parallel job scheduling to address the specific case of medical applications while harnessing the benefits afforded by virtualization technology. To this end, we provide the following contributions: (1) An in-depth analysis of the execution characteristics of the target applications when run in virtualized environments. (2) A performance prediction methodology applicable to the target environment. (3) A scheduling algorithm that harnesses application knowledge and virtualization-related benefits to provide strong scheduling performance and quality of service guarantees. In the process of addressing these pertinent issues for our target user base (i.e. medical professionals and researchers), we provide insight that benefits a large community of scientific application users in industry and academia. Our execution time prediction and scheduling methodologies are implemented and evaluated on a real system running popular scientific applications. We find that we are able to predict the execution time of a number of these applications with an average error of 15%. Our scheduling methodology, which is tested with medical image processing workloads, is compared to that of two baseline scheduling solutions and we find that it outperforms them in terms of both the number of jobs processed and resource utilization by 20–30%, without violating any deadlines. We conclude that our solution is a viable approach to supporting the computational needs of medical users, even if the cloud computing paradigm is not widely adopted in its current form.

Power and thermal aware scheduling for real-time computing systems

Over the past few decades, we have been enjoying tremendous benefits thanks to the revolutionary advancement of computing systems, driven mainly by the remarkable semiconductor technology scaling and the increasingly complicated processor architecture. However, the exponentially increased transistor density has directly led to exponentially increased power consumption and dramatically elevated system temperature, which not only adversely impacts the system's cost, performance and reliability, but also increases the leakage and thus the overall power consumption. Today, the power and thermal issues have posed enormous challenges and threaten to slow down the continuous evolvement of computer technology. Effective power/thermal-aware design techniques are urgently demanded, at all design abstraction levels, from the circuit-level, the logic-level, to the architectural-level and the system-level. ^ In this dissertation, we present our research efforts to employ real-time scheduling techniques to solve the resource-constrained power/thermal-aware, design-optimization problems. In our research, we developed a set of simple yet accurate system-level models to capture the processor's thermal dynamic as well as the interdependency of leakage power consumption, temperature, and supply voltage. Based on these models, we investigated the fundamental principles in power/thermal-aware scheduling, and developed real-time scheduling techniques targeting at a variety of design objectives, including peak temperature minimization, overall energy reduction, and performance maximization. ^ The novelty of this work is that we integrate the cutting-edge research on power and thermal at the circuit and architectural-level into a set of accurate yet simplified system-level models, and are able to conduct system-level analysis and design based on these models. The theoretical study in this work serves as a solid foundation for the guidance of the power/thermal-aware scheduling algorithms development in practical computing systems.^

Leakage temperature dependency aware real-time scheduling for power and thermal optimization

Catering to society's demand for high performance computing, billions of transistors are now integrated on IC chips to deliver unprecedented performances. With increasing transistor density, the power consumption/density is growing exponentially. The increasing power consumption directly translates to the high chip temperature, which not only raises the packaging/cooling costs, but also degrades the performance/reliability and life span of the computing systems. Moreover, high chip temperature also greatly increases the leakage power consumption, which is becoming more and more significant with the continuous scaling of the transistor size. As the semiconductor industry continues to evolve, power and thermal challenges have become the most critical challenges in the design of new generations of computing systems. ^ In this dissertation, we addressed the power/thermal issues from the system-level perspective. Specifically, we sought to employ real-time scheduling methods to optimize the power/thermal efficiency of the real-time computing systems, with leakage/ temperature dependency taken into consideration. In our research, we first explored the fundamental principles on how to employ dynamic voltage scaling (DVS) techniques to reduce the peak operating temperature when running a real-time application on a single core platform. We further proposed a novel real-time scheduling method, “M-Oscillations” to reduce the peak temperature when scheduling a hard real-time periodic task set. We also developed three checking methods to guarantee the feasibility of a periodic real-time schedule under peak temperature constraint. We further extended our research from single core platform to multi-core platform. We investigated the energy estimation problem on the multi-core platforms and developed a light weight and accurate method to calculate the energy consumption for a given voltage schedule on a multi-core platform. Finally, we concluded the dissertation with elaborated discussions of future extensions of our research. ^

On-Line Real-Time Service-Oriented Task Scheduling Using TUF

We present our approach to real-time service-oriented scheduling problems with the objective of maximizing the total system utility. Different from the traditional utility accrual scheduling problems that each task is associated with only a single time utility function (TUF), we associate two different TUFs—a profit TUF and a penalty TUF—with each task, to model the real-time services that not only need to reward the early completions but also need to penalize the abortions or deadline misses. The scheduling heuristics we proposed in this paper judiciously accept, schedule, and abort real-time services when necessary to maximize the accrued utility. Our extensive experimental results show that our proposed algorithms can significantly outperform the traditional scheduling algorithms such as the Earliest Deadline First (EDF), the traditional utility accrual (UA) scheduling algorithms, and an earlier scheduling approach based on a similar model.

Real-time scheduling of embedded applications on multi-core platforms

For the past several decades, we have experienced the tremendous growth, in both scale and scope, of real-time embedded systems, thanks largely to the advances in IC technology. However, the traditional approach to get performance boost by increasing CPU frequency has been a way of past. Researchers from both industry and academia are turning their focus to multi-core architectures for continuous improvement of computing performance. In our research, we seek to develop efficient scheduling algorithms and analysis methods in the design of real-time embedded systems on multi-core platforms. Real-time systems are the ones with the response time as critical as the logical correctness of computational results. In addition, a variety of stringent constraints such as power/energy consumption, peak temperature and reliability are also imposed to these systems. Therefore, real-time scheduling plays a critical role in design of such computing systems at the system level. We started our research by addressing timing constraints for real-time applications on multi-core platforms, and developed both partitioned and semi-partitioned scheduling algorithms to schedule fixed priority, periodic, and hard real-time tasks on multi-core platforms. Then we extended our research by taking temperature constraints into consideration. We developed a closed-form solution to capture temperature dynamics for a given periodic voltage schedule on multi-core platforms, and also developed three methods to check the feasibility of a periodic real-time schedule under peak temperature constraint. We further extended our research by incorporating the power/energy constraint with thermal awareness into our research problem. We investigated the energy estimation problem on multi-core platforms, and developed a computation efficient method to calculate the energy consumption for a given voltage schedule on a multi-core platform. In this dissertation, we present our research in details and demonstrate the effectiveness and efficiency of our approaches with extensive experimental results.

Delay-sensitive service request scheduling for cloud computing

Cloud computing realizes the long-held dream of converting computing capability into a type of utility. It has the potential to fundamentally change the landscape of the IT industry and our way of life. However, as cloud computing expanding substantially in both scale and scope, ensuring its sustainable growth is a critical problem. Service providers have long been suffering from high operational costs. Especially the costs associated with the skyrocketing power consumption of large data centers. In the meantime, while efficient power/energy utilization is indispensable for the sustainable growth of cloud computing, service providers must also satisfy a user's quality of service (QoS) requirements. This problem becomes even more challenging considering the increasingly stringent power/energy and QoS constraints, as well as other factors such as the highly dynamic, heterogeneous, and distributed nature of the computing infrastructures, etc. ^ In this dissertation, we study the problem of delay-sensitive cloud service scheduling for the sustainable development of cloud computing. We first focus our research on the development of scheduling methods for delay-sensitive cloud services on a single server with the goal of maximizing a service provider's profit. We then extend our study to scheduling cloud services in distributed environments. In particular, we develop a queue-based model and derive efficient request dispatching and processing decisions in a multi-electricity-market environment to improve the profits for service providers. We next study a problem of multi-tier service scheduling. By carefully assigning sub deadlines to the service tiers, our approach can significantly improve resource usage efficiencies with statistically guaranteed QoS. Finally, we study the power conscious resource provision problem for service requests with different QoS requirements. By properly sharing computing resources among different requests, our method statistically guarantees all QoS requirements with a minimized number of powered-on servers and thus the power consumptions. The significance of our research is that it is one part of the integrated effort from both industry and academia to ensure the sustainable growth of cloud computing as it continues to evolve and change our society profoundly.^

Delay-Sensitive Service Request Scheduling for Cloud Computing

Cloud computing realizes the long-held dream of converting computing capability into a type of utility. It has the potential to fundamentally change the landscape of the IT industry and our way of life. However, as cloud computing expanding substantially in both scale and scope, ensuring its sustainable growth is a critical problem. Service providers have long been suffering from high operational costs. Especially the costs associated with the skyrocketing power consumption of large data centers. In the meantime, while efficient power/energy utilization is indispensable for the sustainable growth of cloud computing, service providers must also satisfy a user's quality of service (QoS) requirements. This problem becomes even more challenging considering the increasingly stringent power/energy and QoS constraints, as well as other factors such as the highly dynamic, heterogeneous, and distributed nature of the computing infrastructures, etc. In this dissertation, we study the problem of delay-sensitive cloud service scheduling for the sustainable development of cloud computing. We first focus our research on the development of scheduling methods for delay-sensitive cloud services on a single server with the goal of maximizing a service provider's profit. We then extend our study to scheduling cloud services in distributed environments. In particular, we develop a queue-based model and derive efficient request dispatching and processing decisions in a multi-electricity-market environment to improve the profits for service providers. We next study a problem of multi-tier service scheduling. By carefully assigning sub deadlines to the service tiers, our approach can significantly improve resource usage efficiencies with statistically guaranteed QoS. Finally, we study the power conscious resource provision problem for service requests with different QoS requirements. By properly sharing computing resources among different requests, our method statistically guarantees all QoS requirements with a minimized number of powered-on servers and thus the power consumptions. The significance of our research is that it is one part of the integrated effort from both industry and academia to ensure the sustainable growth of cloud computing as it continues to evolve and change our society profoundly.

Leakage Temperature Dependency Aware Real-Time Scheduling for Power and Thermal Optimization

Catering to society’s demand for high performance computing, billions of transistors are now integrated on IC chips to deliver unprecedented performances. With increasing transistor density, the power consumption/density is growing exponentially. The increasing power consumption directly translates to the high chip temperature, which not only raises the packaging/cooling costs, but also degrades the performance/reliability and life span of the computing systems. Moreover, high chip temperature also greatly increases the leakage power consumption, which is becoming more and more significant with the continuous scaling of the transistor size. As the semiconductor industry continues to evolve, power and thermal challenges have become the most critical challenges in the design of new generations of computing systems. In this dissertation, we addressed the power/thermal issues from the system-level perspective. Specifically, we sought to employ real-time scheduling methods to optimize the power/thermal efficiency of the real-time computing systems, with leakage/ temperature dependency taken into consideration. In our research, we first explored the fundamental principles on how to employ dynamic voltage scaling (DVS) techniques to reduce the peak operating temperature when running a real-time application on a single core platform. We further proposed a novel real-time scheduling method, “M-Oscillations” to reduce the peak temperature when scheduling a hard real-time periodic task set. We also developed three checking methods to guarantee the feasibility of a periodic real-time schedule under peak temperature constraint. We further extended our research from single core platform to multi-core platform. We investigated the energy estimation problem on the multi-core platforms and developed a light weight and accurate method to calculate the energy consumption for a given voltage schedule on a multi-core platform. Finally, we concluded the dissertation with elaborated discussions of future extensions of our research.