Job Shop Scheduling Problem: an Overview

The Job-shop scheduling is one of the most important industrial activities, especially in manufacturing planning. The problem complexity has increased along with the increase in the complexity of operations and product-mix. To solve this problem, numerous approaches have been developed incorporating discrete event simulation methodology. The scope and the purpose of this paper is to present a survey which covers most of the solving techniques of Job Shop Scheduling (JSS) problem. A classification of these techniques has been proposed: Traditional Techniques and Advanced Techniques. The traditional techniques to solve JSS could not fully satisfy the global competition and rapidly changing in customer requirements. Simulation and Artificial Intelligence (AI) have proven to be excellent strategic tool for scheduling problems in general and JSS in particular. The paper defined some AI techniques used by manufacturing systems. Finally, the future trends are proposed briefly

A survey of scheduling problems with setup times or costs

Author name used in this publication: C. T. NgAuthor name used in this publication: T. C. E. Cheng2007-2008 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

Flow shop scheduling with earliness, tardiness and intermediate inventory holding costs

We consider the problem of scheduling customer orders in a flow shop with the objective of minimizing the sum of tardiness, earliness (finished goods inventory holding) and intermediate (work-in-process) inventory holding costs. We formulate this problem as an integer program, and based on approximate solutions to two di erent, but closely related, Dantzig-Wolfe reformulations, we develop heuristics to minimize the total cost. We exploit the duality between Dantzig-Wolfe reformulation and Lagrangian relaxation to enhance our heuristics. This combined approach enables us to develop two di erent lower bounds on the optimal integer solution, together with intuitive approaches for obtaining near-optimal feasible integer solutions. To the best of our knowledge, this is the first paper that applies column generation to a scheduling problem with di erent types of strongly NP-hard pricing problems which are solved heuristically. The computational study demonstrates that our algorithms have a significant speed advantage over alternate methods, yield good lower bounds, and generate near-optimal feasible integer solutions for problem instances with many machines and a realistically large number of jobs

Lagrangian approach to minimize makespan of non-identical parallel batch processing machines

Advisors: Purushothaman Damodaran.Committee members: Omar Ghrayeb; Murali Krishnamurthi; Christine Nguyen.Batch Processing Machines (BPMs) are commonly used in electronics manufacturing, semi-conductor manufacturing, and metal-working - to name a few. Scheduling these machines are not an easy task; practical considerations and the exponential number of decision variables involved impede schedulers (or decision makers) from making good decisions. This research focuses on minimizing the makespan of a set of non-identical parallel batch processing machines. In order to schedule jobs on these machines, two decisions are to be made. The first decision is to group jobs to form batches such that the machine capacity is not exceeded. The second decision is to sequence the batches formed on the machines such that the makespan is minimized. Both the decisions are intertwined as the processing time of the batch is determined by the composition of the jobs in the batch. The problem under study is shown to be NP-hard. A mathematical model from the literature is adopted to develop a solution approach which would help the decision maker to make meaningful decisions.Lagrangian Relaxation approach has been shown to be very effective in solving scheduling problems. Using this decomposition approach, the mathematical model is decomposed and a sub-gradient approach was used to update the multipliers. Two sets of constraints were relaxed to consider two Lagrangian Relaxation models. Experiments were conducted with data sets from the literature. The solution quality of the proposed approach was compared with meta-heuristics (i.e. Particle Swarm Optimization (PSO) and Random Key Genetic Algorithm (RKGA)) published in the literature and a commercial solver (i.e. IBM ILOG CPLEX). On smaller instances (i.e. 10 and 20 jobs), the proposed approach outperformed PSO and RKGA. However, the proposed approach and CPLEX report the same results. On larger instances (i.e. 50, 100 and 200 job instances) with two and four-machines, the proposed approach was better than PSO whenever the variability in the processing times were smaller. The proposed approach generally outperformed RKGA and CPLEX on larger problem instances. Out of 200 experiments conducted, the proposed approach helped to find new improved solution on 34 instances and comparable on 105 instances when compared to PSO. The PSO approach was much faster than all other approaches on larger problem instances. The experimental study clearly identifies the problem instances on which the proposed approach can find a better solution. The proposed Lagrangian Relaxation solution approach helps the schedulers to make more informed decisions. Minor modifications can be made to use the proposed solution approach for other practical considerations (e.g. job ready times, tardiness objective, etc.) The main contribution of this research is the proposed solution approach which is effective in solving a class of non-identical batch processing machine problems with better solution quality when compared to existing meta-heuristics.M.S. (Master of Science

Unified Concept of Bottleneck

The term `bottleneck` has been extensively used in operations management literature. Management paradigms like the Theory of Constraints focus on the identification and exploitation of bottlenecks. Yet, we show that the term has not been rigorously defined. We provide a classification of bottleneck definitions available in literature and discuss several myths associated with the concept of bottleneck. The apparent diversity of definitions raises the question whether it is possible to have a single bottleneck definition which has as much applicability in high variety job shops as in mass production environments. The key to the formulation of an unified concept of bottleneck lies in relating the concept of bottleneck to the concept of shadow price of resources. We propose an universally applicable bottleneck definition based on the concept of average shadow price. We discuss the procedure for determination of bottleneck values for diverse production environments. The Law of Diminishing Returns is shown to be a sufficient but not necessary condition for the equivalence of the average and the marginal shadow price. The equivalence of these two prices is proved for several environments. Bottleneck identification is the first step in resource acquisition decisions faced by managers. The definition of bottleneck presented in the paper has the potential to not only reduce ambiguity regarding the meaning of the term but also open a new window to the formulation and analysis of a rich set of problems faced by managers.

Use of Excel worksheets with user-friendly interface in batch process (PSBP) to minimize the makespan

In the chemical industry, the necessity for scheduling is becoming more pronounced, especially in batch production mode. Nowadays, planning industrial activities is a necessity for survival. Intense competition requires diversified products and delivery in accordance with the requirements of consumers. These activities require quick decision making and the lowest possible cost, through an efficient Production Scheduling. So, this work addresses the Permutation Flow Shop scheduling problem, characterized as Production Scheduling in Batch Process (PSBP), with the objective of minimizing the total time to complete the schedule (Makespan). A method to approach the problem of production scheduling is to turn it into Mixed Integer Linear Programming- MILP, and to solve it using commercial mathematical programming packages. In this study an electronic spreadsheet with user-friendly interface (ESUFI) was developed in Microsoft Excel. The ease of manipulation of the ESUFI is quite evident, as with the use of VBA language a user-friendly interface could be created between the user and the spreadsheet itself. The results showed that it is possible to use the ESUFI for small problems

A hybrid genetic approach to solve real make-to-order job shop scheduling problems

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro TecnologicoProcedimentos de busca local (ex. busca tabu) e algoritmos genéticos têm apresentado excelentes resultados em problemas clássicos de programação da produção em ambientes job shop. No entanto, estas abordagens apresentam pobres habilidades de modelamento e poucas aplicações com restrições de ambientes reais de produção têm sido publicadas. Além disto, os espaços de busca considerados nestas aplicações são nomlalmente incompletos e as restrições reais são poucas e dependentes do problema em questão. Este trabalho apresenta uma abordagem genética híbrida para resolver problemas de programação em ambientes job shop com grande número de restrições reais, tais como produtos com vários níveis de submontagem, planos de processamento altemativos para componentes e recursos alternativos para operações, exigência de vários recursos para executar uma operação (ex., máquina, ferramentas, operadores), calendários para todos os recursos, sobreposição de operações, restrições de disponibilidade de matéria-prima e componentes comprados de terceiros, e tempo de setup dependente da sequência de operações. A abordagem também considera funções de avaliação multiobjetivas. O sistema usa algoritmos modificados de geração de programação, que incorporam várias heurísticas de apoio à decisão, para obter um conjunto de soluções iniciais. Cada solução inicial é melhorada por um algoritmo de subida de encosta. Então, um algoritmo genético híbrido com procedimentos de busca local é aplicado ao conjunto inicial de soluções localmente ótimas. Ao utilizar técnicas de programação de alta perfomlance (heurísticas construtivas, procedimentos de busca local e algoritmos genéticos) em problemas reais de programação da produção, este trabalho reduziu o abismo existente entre a teoria e a prática da programação da produção

Scheduling Hybrid Flow Lines of Aerospace Composite Manufacturing Systems

Composite manufacturing is a vital part of aerospace manufacturing systems. Applying effective scheduling within these systems can cut the costs in aerospace companies significantly. These systems can be characterized as two-stage Hybrid Flow Shops (HFS) with identical, non-identical and unrelated parallel discrete-processing machines in the first stage and non-identical parallel batch-processing machines in the second stage. The first stage is normally the lay-up process in which the carbon fiber sheets are stacked on the molds (tools). Then, the parts are batched based on the compatibility of their cure recipe before going to the second stage into the autoclave for curing. Autoclaves require enormous capital investment and maximizing their utilization is of utmost importance. In this thesis, a Mixed Integer Linear Programming (MILP) model is developed to maximize the utilization of the resources in the second stage of this HFS. CPLEX, with an underlying branch and bound algorithm, is used to solve the model. The results show the high level of flexibility and computational efficiency of the proposed model when applied to small and medium-size problems. However, due to the NP-hardness of the problem, the MILP model fails to solve large problems (i.e. problems with more than 120 jobs as input) in reasonable CPU times. To solve the larger instances of the problem, a novel heuristic method along with a Genetic Algorithm (GA) are developed. The heuristic algorithm is designed based on a careful observation of the behavior of the MILP model for different problem sets. Moreover, it is enhanced by adding a number of proper dispatching rules. As its output, this heuristic algorithm generates eight initial feasible solutions which are then used as the initial population of the proposed GA. The GA improves the initial solutions obtained from the aforementioned heuristic through its stochastic iterations until it reaches the satisfactory near-optimal solutions. A novel crossover operator is introduced in this GA which is unique to the HFS of aerospace composite manufacturing systems. The proposed GA is proven to be very efficient when applied to large-size problems with up to 300 jobs. The results show the high quality of the solutions achieved by the GA when compared to the optimal solutions which are obtained from the MILP model. A real case study undertaken at one of the leading companies in the Canadian aerospace industry is used for the purpose of data experiments and analysis

The dynamic, resource-constrained shortest path problem on an acyclic graph with application in column generation and literature review on sequence-dependent scheduling

This dissertation discusses two independent topics: a resource-constrained shortest-path problem (RCSP) and a literature review on scheduling problems involving sequence-dependent setup (SDS) times (costs). RCSP is often used as a subproblem in column generation because it can be used to solve many practical problems. This dissertation studies RCSP with multiple resource constraints on an acyclic graph, because many applications involve this configuration, especially in column genetation formulations. In particular, this research focuses on a dynamic RCSP since, as a subproblem in column generation, objective function coefficients are updated using new values of dual variables at each iteration. This dissertation proposes a pseudo-polynomial solution method for solving the dynamic RCSP by exploiting the special structure of an acyclic graph with the goal of effectively reoptimizing RCSP in the context of column generation. This method uses a one-time âÂÂpreliminaryâ phase to transform RCSP into an unconstrained shortest path problem (SPP) and then solves the resulting SPP after new values of dual variables are used to update objective function coefficients (i.e., reduced costs) at each iteration. Network reduction techniques are considered to remove some nodes and/or arcs permanently in the preliminary phase. Specified techniques are explored to reoptimize when only several coefficients change and for dealing with forbidden and prescribed arcs in the context of a column generation/branch-and-bound approach. As a benchmark method, a label-setting algorithm is also proposed. Computational tests are designed to show the effectiveness of the proposed algorithms and procedures. This dissertation also gives a literature review related to the class of scheduling problems that involve SDS times (costs), an important consideration in many practical applications. It focuses on papers published within the last decade, addressing a variety of machine configurations - single machine, parallel machine, flow shop, and job shop - reviewing both optimizing and heuristic solution methods in each category. Since lot-sizing is so intimately related to scheduling, this dissertation reviews work that integrates these issues in relationship to each configuration. This dissertation provides a perspective of this line of research, gives conclusions, and discusses fertile research opportunities posed by this class of scheduling problems. since, as a subproblem in column generation, objective function coefficients are updated using new values of dual variables at each iteration. This dissertation proposes a pseudo-polynomial solution method for solving the dynamic RCSP by exploiting the special structure of an acyclic graph with the goal of effectively reoptimizing RCSP in the context of column generation. This method uses a one-tim

Minimizing the makespan in a flexible flowshop with sequence dependent setup times, uniform machines, and limited buffers

This research addresses the problem of minimizing the makespan in a flexible flowshop with sequence dependent setup times, uniform machines, and limited buffers. A mathematical model was developed to solve this problem. The problem is NP-Hard in the strong sense and only very small problems could be solved optimally. For exact methods, the computation times are long and not practical even when the problems are relatively small. Two construction heuristics were developed that could find solutions quickly. Also a simulated annealing heuristic was constructed that improved the solutions obtained from the construction heuristics. The combined heuristics could compute a good solution in a short amount of time. The heuristics were tested in three different environments: 3 stages, 4 stages, and 5 stages. To assess the quality of the solutions, a lower bound and two simple heuristics were generated for comparison purposes. The proposed heuristics showed steady improvement over the simple heuristics. When compared to the lower bounds, the heuristics performed well for the smaller environment, but the performance quality decreased as the number of stages increased. The combination of these heuristics defiantly shows promise for solving the problem