Algebraic, Mathematical Programming, And Network Models Of The Deterministic Job-Shop Scheduling Problem

In the contemporary literature on deterministic machine scheduling, problems are formulated from three different, but equivalent, perspectives. Algebraic models provide a rigorous problem statement in the language of set theory and are typical of the more abstract development of scheduling theory in mathematics and computer science. Mathematical programming models rely on familiar concepts of nonlinear optimization and are generally the most accessible. Network models (disjunctive graphs) are best suited to the development of solution approaches and figure prominently in discussions of algorithm design and analysis. In this tutorial, it is shown how the minimum-makespan job-shop problem (n/m/G/Cmax) is realized in each of these three model forms. A common notation is developed and how the underlying structure and fundamental difficulty of the problem are expressed in each model is demonstrated. © 1991 IEE

Algebraic, Mathematical-Programming, And Network Models Of The Deterministic Job-Shop Scheduling Problem

In the contemporary literature on deterministic machine scheduling, problems are formulated from three different, but equivalent, perspectives. Algebraic models provide a rigorous problem statement in the language of set theory and are typical of the more abstract development of scheduling theory in mathematics and computer science. Mathematical programming models rely on familiar concepts of nonlinear optimization and are generally the most accessible. Network models (disjunctive graphs) are best suited to the development of solution approaches and figure prominently in discussions of algorithm design and analysis. In this tutorial, it is shown how the minimum-makespan job-shop problem (n/m/G/C(max)) is realized in each of these three model forms. A common notation is developed and how the underlying structure and fundamental difficulty of the problem are expressed in each model is demonstrated

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