Makespan minimization in a job shop with a batch processing machine

A job shop with one batch processing and several discrete machines is analyzed. Given a set of jobs, their process routes, processing requirements, and size, the objective is to schedule the jobs such that the makespan is minimized. The batch processing machine can process a batch of jobs as long as the machine capacity is not violated. The batch processing time is equal to the longest processing job in the batch. The problem under study can be represented as Jm:batch:Cmax. If no batches were formed, the scheduling problem under study reduces to the classical job shop scheduling problem (i.e. Jm:: Cmax), which is known to be NP-hard. This research extends the scheduling literature by combining Jm::Cmax with batch processing. The primary contributions are the mathematical formulation, a new network representation and several solution approaches. The problem under study is observed widely in metal working and other industries, but received limited or no attention due to its complexity. A novel network representation of the problem using disjunctive and conjunctive arcs, and a mathematical formulation are proposed to minimize the makespan. Besides that, several algorithms, like batch forming heuristics, dispatching rules, Modified Shifting Bottleneck, Tabu Search (TS) and Simulated Annealing (SA), were developed and implemented. An experimental study was conducted to evaluate the proposed heuristics, and the results were compared to those from a commercial solver (i.e., CPLEX). TS and SA, with the combination of MWKR-FF as the initial solution, gave the best solutions among all the heuristics proposed. Their results were close to CPLEX; and for some larger instances, with total operations greater than 225, they were competitive in terms of solution quality and runtime. For some larger problem instances, CPLEX was unable to report a feasible solution even after running for several hours. Between SA and the experimental study indicated that SA produced a better average Cmax for all instances. The solution approaches proposed will benefit practitioners to schedule a job shop (with both discrete and batch processing machines) more efficiently. The proposed solution approaches are easier to implement and requires short run times to solve large problem instances.

'Investigating Artificial Immune Systems For Job Shop Rescheduling In Changing Environments'

ABSTRACT Artificial immune system can be used to generate schedules in changing environments and it has been proven to be more robust than schedules developed using a genetic algorithm. Good schedules can be produced especially when the number of the antigens is increased. However, an increase in the range of the antigens had somehow affected the fitness of the immune system. In this research, we are trying to improve the result of the system by rescheduling the same problem using the same method while at the same time maintaining the robustness of the schedules.

'Investigating Artificial Immune Systems For Job Shop Rescheduling In Changing Environments'

ABSTRACT Artificial immune system can be used to generate schedules in changing environments and it has been proven to be more robust than schedules developed using a genetic algorithm. Good schedules can be produced especially when the number of the antigens is increased. However, an increase in the range of the antigens had somehow affected the fitness of the immune system. In this research, we are trying to improve the result of the system by rescheduling the same problem using the same method while at the same time maintaining the robustness of the schedules.

Heuristics for Job-Shop Scheduling

Two methods of obtaining approximate solutions to the classic General Job-shop Scheduling Program are investigated. The first method is iterative. A sampling of the solution space is used to decide which of a collection of space pruning constraints are consistent with "good" schedules. The selected space pruning constraints are then used to reduce the search space and the sampling is repeated. This approach can be used either to verify whether some set of space pruning constraints can prune with discrimination or to generate solutions directly. Schedules can be represented as trajectories through a Cartesian space. Under the objective criteria of Minimum maximum Lateness family of "good" schedules (trajectories) are geometric neighbors (reside with some "tube") in this space. This second method of generating solutions takes advantage of this adjacency by pruning the space from the outside in thus converging gradually upon this "tube." One the average this methods significantly outperforms an array of the Priority Dispatch rules when the object criteria is that of Minimum Maximum Lateness. It also compares favorably with a recent relaxation procedure.

A hyper-heuristic ensemble method for static job-shop scheduling.

We describe a new hyper-heuristic method NELLI-GP for solving job-shop scheduling problems (JSSP) that evolves an ensemble of heuristics. The ensemble adopts a divide-and-conquer approach in which each heuristic solves a unique subset of the instance set considered. NELLI-GP extends an existing ensemble method called NELLI by introducing a novel heuristic generator that evolves heuristics composed of linear sequences of dispatching rules: each rule is represented using a tree structure and is itself evolved. Following a training period, the ensemble is shown to outperform both existing dispatching rules and a standard genetic programming algorithm on a large set of new test instances. In addition, it obtains superior results on a set of 210 benchmark problems from the literature when compared to two state-of-the-art hyperheuristic approaches. Further analysis of the relationship between heuristics in the evolved ensemble and the instances each solves provides new insights into features that might describe similar instances.

An Extension to the Tactical Planning Model for a Job Shop: Continuous-Time Control

We develop an extension to the tactical planning model (TPM) for a job shop by the third author. The TPM is a discrete-time model in which all transitions occur at the start of each time period. The time period must be defined appropriately in order for the model to be meaningful. Each period must be short enough so that a job is unlikely to travel through more than one station in one period. At the same time, the time period needs to be long enough to justify the assumptions of continuous workflow and Markovian job movements. We build an extension to the TPM that overcomes this restriction of period sizing by permitting production control over shorter time intervals. We achieve this by deriving a continuous-time linear control rule for a single station. We then determine the first two moments of the production level and queue length for the workstation.

Escalonamento de um Job Shop : análise de um algoritmo com regras heurísticas

O presente trabalho visa definir um modelo de alocação dos recursos da produção para centros de trabalho em sistemas baseados em job shop, usando a abordagem heurística para garantir uma boa alocação dos recursos. São levados em conta a complexidade de um ambiente de produção, seus aspectos temporais e os modelos de Job Shop Scheduling atualmente em uso. Com isso são examinados os aspectos conceituais deste ambiente e proposto um modelo de alocação de recursos para auxiliar no planejamento operacional do mesmo. Pode-se definir os recursos como todos os elementos necessários à execução das diversas atividades de um processo produtivo, tais como equipamentos, máquinas, mão-de-obra, etc. Por sua vez, os recursos são limitados por natureza, quanto à quantidade de unidades disponíveis, às suas funcionalidades e à capacidade produtiva. O processo de alocação dos recursos pressupõe a designação dos recursos mais satisfatórios para a execução de cada uma das atividades que fazem parte de um projeto. O modelo proposto é baseado no uso de heurísticas para resolver o escalonamento nos centros de trabalho, também chamados de células de produção, usando restrições e regras entre as ordens de fabricação (peças) e as máquinas, para encontrar uma solução satisfatória ao problema. O resultado final é uma ferramenta de apoio à decisão no processo de manufatura, permitindo a visualização do melhor escalonamento de produção, visando a redução do ciclo e setup de produção no processo, com base nas informações locais do ambiente fabril. O sistema está implementado numa empresa de componentes hidráulicos, inicialmente no centro de trabalho de corte, composto por quatro máquinas que realizam o corte de diversos tipos de matérias-primas.

Um modelo de projeto de layout para ambientes job shop com alta variedade de peças baseado nos conceitos da produção enxuta

Segundo Canem e Williamson (1998), o planejamento do layout é importante, pois normalmente representa os maiores e mais caros recursos da organização. Além disso, a localização e disposição física dos equipamentos no chão de fábrica têm impacto em diversos fatores como nível de estoque em processo, tamanho dos lotes de transferência, dificuldade no gerenciamento das atividades, movimentação de pessoas e produtos, entre outros. Portanto, o estudo de conceitos de arranjo físico e o desenvolvimento de modelos de projeto do layout, que visem a otimização dos recursos de produção, são de vital importância na busca pela melhoria dos sistemas produtivos. Neste contexto, este artigo apresenta um novo modelo de projeto de layout, para ambientes job shop com ampla variedade de peças. O modelo foi desenvolvido durante uma pesquisa de doutorado e foi aplicado em algumas empresas do setor metal mecânico. Os resultados obtidos comprovaram a eficiência do modelo projetado. O objetivo do modelo consiste em conduzir a equipe de projeto de layout a desenvolver alternativas de arranjo físico que estejam em consonância com conceitos e princípios da filosofia de produção enxuta. Vale ressaltar novamente que o modelo foi desenvolvido para ambientes com alta variedade de peças, ambientes esses em que, devido à dificuldade em se projetar o arranjo físico, as empresas terminam por adotar o layout funcional, conceito esse de arranjo físico que apresenta sérios problemas como excesso de transporte, altos níveis de estoques em processo, etc.

Algoritmi esatti per il Job Shop Scheduling: approcci Mathematical Programming

In questa tesi ci occuperemo di fornire un modello MIP di base e di alcune sue varianti, realizzate allo scopo di comprenderne il comportamento ed eventualmente migliorarne l’efficienza. Le diverse varianti sono state costruite agendo in particolar modo sulla definizione di alcuni vincoli, oppure sui bound delle variabili, oppure ancora nell’obbligare il risolutore a focalizzarsi su determinate decisioni o specifiche variabili. Sono stati testati alcuni dei problemi tipici presenti in letteratura e i diversi risultati sono stati opportunamente valutati e confrontati. Tra i riferimenti per tale confronto sono stati considerati anche i risultati ottenibili tramite un modello Constraint Programming, che notoriamente produce risultati apprezzabili in ambito di schedulazione. Un ulteriore scopo della tesi è, infatti, comparare i due approcci Mathematical Programming e Constraint Programming, identificandone quindi i pregi e gli svantaggi e provandone la trasferibilità al modello raffrontato.

Design and implementation of a web based shop floor control system to maintain schedule feasibility in a dynamic job shop environment

The effective control of production activities in dynamic job shop with predetermined resource allocation for all the jobs entering the system is a unique manufacturing environment, which exists in the manufacturing industry. In this thesis a framework for an Internet based real time shop floor control system for such a dynamic job shop environment is introduced. The system aims to maintain the schedule feasibility of all the jobs entering the manufacturing system under any circumstance. The system is capable of deciding how often the manufacturing activities should be monitored to check for control decisions that need to be taken on the shop floor. The system will provide the decision maker real time notification to enable him to generate feasible alternate solutions in case a disturbance occurs on the shop floor. The control system is also capable of providing the customer with real time access to the status of the jobs on the shop floor. The communication between the controller, the user and the customer is through web based user friendly GUI. The proposed control system architecture and the interface for the communication system have been designed, developed and implemented.