Scheduling and discrete event control of flexible manufacturing systems based on Petri nets

A flexible manufacturing system (FMS) is a computerized production system that can simultaneously manufacture multiple types of products using various resources such as robots and multi-purpose machines. The central problems associated with design of flexible manufacturing systems are related to process planning, scheduling, coordination control, and monitoring. Many methods exist for scheduling and control of flexible manufacturing systems, although very few methods have addressed the complexity of whole FMS operations. This thesis presents a Petri net based method for deadlock-free scheduling and discrete event control of flexible manufacturing systems. A significant advantage of Petri net based methods is their powerful modeling capability. Petri nets can explicitly and concisely model the concurrent and asynchronous activities, multi-layer resource sharing, routing flexibility, limited buffers and precedence constraints in FMSs. Petri nets can also provide an explicit way for considering deadlock situations in FMSs, and thus facilitate significantly the design of a deadlock-free scheduling and control system. The contributions of this work are multifold. First, it develops a methodology for discrete event controller synthesis for flexible manufacturing systems in a timed Petri net framework. The resulting Petri nets have the desired qualitative properties of liveness, boundedness (safeness), and reversibility, which imply freedom from deadlock, no capacity overflow, and cyclic behavior, respectively. This precludes the costly mathematical analysis for these properties and reduces on-line computation overhead to avoid deadlocks. The performance and sensitivity of resulting Petri nets, thus corresponding control systems, are evaluated. Second, it introduces a hybrid heuristic search algorithm based on Petri nets for deadlock-free scheduling of flexible manufacturing systems. The issues such as deadlock, routing flexibility, multiple lot size, limited buffer size and material handling (loading/unloading) are explored. Third, it proposes a way to employ fuzzy dispatching rules in a Petri net framework for multi-criterion scheduling. Finally, it shows the effectiveness of the developed methods through several manufacturing system examples compared with benchmark dispatching rules, integer programming and Lagrangian relaxation approaches

Dynamic Job Shop Scheduling Using Ant Colony Optimization Algorithm Based On A Multi-Agent System

Ph.DDOCTOR OF PHILOSOPH

Some topics on deterministic scheduling problems

Sequencing and scheduling problems are motivated by allocation of limited resources over time. The goal is to find an optimal allocation where optimality is defined by some problem specific objectives. This dissertation considers the scheduling of a set of ri tasks, with precedence constraints, on m \u3e= 1 identical and parallel processors so as to minimize the makespan. Specifically, it considers the situation where tasks, along with their precedence constraints, are released at different times, and the scheduler has to make scheduling decisions without knowledge of future releases. Both preemptive and nonpreemptive schedules are considered. This dissertation shows that optimal online algorithms exist for some cases, while for others it is impossible to have one. The results give a sharp boundary delineating the possible and the impossible cases. Then an O(n log n)-time implementation is given for the algorithm which solves P|pj = 1, rj, outtree| ΣCj and P|pmtn, pj=1,rj,outtree|ΣCj. A fundamental problem in scheduling theory is that of scheduling a set of n unit-execution-time (UET) tasks, with precedence constraints, on m \u3e 1 parallel and identical processors so as to minimize the mean flow time. For arbitrary precedence constraints, this dissertation gives a 2-approximation algorithm. For intrees, a 1.5-approximation algorithm is given. Six dual criteria problems are also considered in this dissertation. Two open problems are first solved. Both problems are single machine scheduling problems with the number of tardy jobs as the primary criterion and with the total completion time and the total tardiness as the secondary criterion, respectively. Both problems are shown to be NP-hard. Then it focuses on bi-criteria scheduling problems involving the number of tardy jobs, the maximum weighted tardiness and the maximum tardiness. NP-hardness proofs are given for the scheduling problems when the number of tardy jobs is the primary criterion and the maximum weighted tardiness is the secondary criterion, or vice versa. It then considers complexity relationships between the various problems, gives polynomial-time algorithms for some special cases, and proposes fast heuristics for the general case

A Comparison of Optimal Tax Policies when Compensation or Responsibility Matter

This paper examines optimal redistribution in a model with high- and low-skilled individuals with heterogeneous tastes for labor. We compare the extent to which optimal policies based on different normative criteria obey the principles of compensation (for differential skills) and responsibility (for preferences for labor) when labor supply is along the extensive margin. With heterogeneity in skills and preferences, traditional Welfarist criteria including Utilitarianism present unappealing policy recommendations in some scenarios as they fail to take compensation and responsibility issues into account. Criteria from the social choice literature perform better in this regard in first-and second-best. More importantly, these equality of opportunity criteria push the second-best policy away from an Earned Income Tax Credit and in the direction of a Negative Income Tax.optimal income taxation, equality of opportunity, heterogeneous preferences for labor

A comparison of optimal tax policies when compensation or responsibility matter

This paper examines optimal redistribution in a model with high and low-skilled individuals with heterogeneous tastes for labor, that either work or not. With such double heterogeneity, traditional Welfarist criteria including Utilitarianism fail to take the compensation-responsibility trade-off into account. As a response, several other criteria have been proposed in the literature. This paper is the first to compare the extent to which optimal policies based on different normative criteria obey the principles of compensation (for differential skills) and responsibility (for preferences for labor), when labor supply is along the extensive margin. The criteria from the social choice literature perform better in this regard than the traditional criteria, both in first and second best. More importantly, these equality of opportunity criteria push the second best policy away from an Earned Income Tax Credit and in the direction of a Negative Income tax.optimal income taxation, equality of opportunity, heterogeneous preferences for labor

Guidelines for Scheduling in Primary Care: An Empirically Driven Mathematical Programming Approach

Primary care practices play a vital role in healthcare delivery since they are the first point of contact for most patients, and provide health prevention, counseling, education, diagnosis and treatment. Practices, however, face a complex appointment scheduling problem because of the variety of patient conditions, the mix of appointment types, the uncertain service times with providers and non-provider staff (nurses/medical assistants), and no-show rates which all compound into a highly variable and unpredictable flow of patients. The end result is an imbalance between provider idle time and patient waiting time. To understand the realities of the scheduling problem we analyze empirical data collected from a family medicine practice in Massachusetts. We study the complete chronology of patient flow on nine different workdays and identify the main patient types and sources of inefficiency. Our findings include an easy-to-identify patient classification, and the need to focus on the effective coordination between nurse and provider steps. We incorporate these findings in an empirically driven stochastic integer programming model that optimizes appointment times and patient sequences given three well-differentiated appointment types. The model considers a session of consecutive appointments for a single-provider primary care practice where one nurse and one provider see the patients. We then extend the integer programming model to account for multiple resources, two nurses and two providers, since we have observed that such team primary care practices are common in the course of our data collection study. In these practices, nurses prepare patients for the providers’ appointments as a team, while providers are dedicated to their own patients to ensure continuity of care. Our analysis focuses on finding the value of nurse flexibility and understanding the interaction between the schedules of the two providers. The team practice leads us to a challenging and novel multi step multi-resource mixed integer stochastic scheduling formulation, as well as methods to tackle the ensuing computational challenge. We also develop an Excel scheduling tool for both single provider and team practices to explore the performance of different schedules in real time. Overall, the main objective of the dissertation is to provide easy-to-implement scheduling guidelines for primary care practices using both an empirically driven stochastic optimization model and a simulation tool

A Random Keys Genetic Algorithm for Job Shop Scheduling

https://deepblue.lib.umich.edu/bitstream/2027.42/154143/1/39015099114574.pd