Carlos Montoya

Petri nets and genetic algorithms for complex manufacturing systems scheduling

In this paper we propose the GAPN (genetic algorithms and Petri nets) approach, which combines the modelling power of Petri nets with the optimisation capability of genetic algorithms (GAs) for manufacturing systems scheduling. This approach uses both Petri nets to formulate the scheduling problem and GAs for scheduling. Its primary advantage is its ability to model a wide variety of manufacturing systems with no modifications either in the net structure or in the chromosomal representation. In this paper we tested the performance on both classical scheduling problems and on a real life setting of a manufacturer of car seat covers. In particular, such a manufacturing system involves features such as complex project-like routings, assembly operations, and workstations with unrelated parallel machines. The implementation of the algorithm at the company is also discussed. Experiments show the validity of the proposed approach.

Scheduling manufacturing systems with blocking: a Petri net approach

This paper introduces a Petri net-based approach for scheduling manufacturing systems with blocking. The modelling of the job routings and the resource and blocking constraints is carried out with the Petri net formalism due to their capability of representing dynamic, concurrent discrete-event dynamic systems. In addition Petri nets can detect deadlocks typically found in systems with blocking constraints. The scheduling task is performed with an algorithm that combines the classical A* search with an aggressive node-pruning strategy. Tests were conducted on a variety of manufacturing systems that included classical job shop, flexible job shop and flexible manufacturing scheduling problems. The optimisation criterion was makespan. The experiments show that the algorithm performed well in all types of problems both in terms of solution quality and computing times.

Branch-and-price approach for the multi-skill project scheduling problem

This work introduces a procedure to solve the multi-skill project scheduling problem (MSPSP) (Néron and Baptista, International symposium on combinatorial, optimization (CO’2002), 2002). The MSPSP mixes both the classical resource constrained project scheduling problem and the multi-purpose machine model. The aim is to find a schedule that minimizes the completion time (makespan) of a project, composed of a set of activities. In addition, precedence relations and resources constraints are considered. In this problem, resources are staff members that master several skills. Thus, a given number of workers must be assigned to perform each skill required by an activity. Practical applications include the construction of buildings, as well as production and software development planning. We present a column generation approach embedded within a branch-and-price (B&P) procedure that considers a given activity and time-based decomposition approach. Obtained results show that the proposed B&P procedure is able to reach optimal solutions for several small and medium sized instances in an acceptable computational time. Furthermore, some previously open instances were optimally solved.

A Petri Net-based framework for realistic project management and scheduling

This paper presents a real life Petri Net-based framework for integrated and collaborative project management in the Animation and Videogame (A&V) industry. This framework provides an all-in-one modeling, scheduling, and simulation tool. The purpose of the framework is twofold: First to facilitate the configuration (and eventual reconfiguration) of projects and second, provide appropriate analysis tools. The modeling of the project activities and the associated resources is accomplished via a new class of Petri Net denoted here as extended attribute Timed Place Petri Net. This Petri Net class combines the strengths of colored and ordinary Timed Petri Nets in terms of modeling and analysis. The offline project schedule is generated with a Graph Search algorithm which explores the Petri Net state space. The algorithm is also adapted to handle reworks that often occur due to multiple changes during execution. Several scenarios can be simulated along with the calculations of duration, cost and resource usage. The potential of the framework is illustrated with two short case studies. The results and deliverables of the approach have been confronted with managers of several companies involved in the project who provided valuable insight and gave favorable remarks. A real life Petri Net-based prototype for project management in the Animation and Videogame (A&V) industry.A computer application that covers the planning, scheduling and execution phases.A methodology that shows significant improvement on the A&V project estimationsA methodology that shows its validity for schedule regeneration.

Integrated Column Generation and Lagrangian Relaxation Approach for the Multi-Skill Project Scheduling Problem

This chapter introduces a procedure to solve the Multi-Skill Project Scheduling Problem. The problem combines both the classical Resource-Constrained Project Scheduling Problem and the multi-purpose machine model. The aim is to find a schedule that minimizes the completion time (makespan) of a project composed of a set of activities. Precedence relations and resources constraints are considered. In this problem, resources are staff members that master several skills. Thus, a given number of workers must be assigned to perform each skill required by an activity. Practical applications include the construction of buildings, as well as production and software development planning. We present an approach that integrates the utilization of Lagrangian relaxation and column generation for obtaining strong makespan lower bounds. Finally, we present the corresponding obtained results.

Applications of resource assignment and scheduling with Petri Nets and heuristic search

This paper introduces a new Petri Net based approach for resource allocation and scheduling. The goals are (i) minimize the number of required resources given a set of jobs, (ii) find both an assignment for all jobs in the span of a predefined shift and (iii) the sequence in which such jobs are executed. The studied problem was inspired from a complex real life manufacturing shop as described in this document. The modeling of the processes and jobs is carried out with Petri Nets due to their capability of representing dynamic, concurrent discrete-event dynamic systems. The resource assignment starts with an initial feasible solution (initial number of resources) and then follows with a re-optimization process aimed to further reduce the resource requirements. The algorithm is based on a modified Heuristic Search method previously presented. The algorithm was tested first on a number of instances from the literature and then on the aforementioned system (a car seat cover manufacturer). The proposed approach shows not only good results in terms of performance but also shows the potential of Petri Nets for modeling and optimizing real-life systems. An implementation phase at the first stages of the process is underway at the time of writing.