Job-shop scheduling: limits of the binary disjunctive formulation

Assembly and disassembly sequences were planned and assessed independently. However, as eco-friendly product design has been enforced by government regulation, it is needed to plan assembly and disassembly sequence at the same time in early product design stage. This paper aims to propose a sequence structure design method by integrating both assembly and disassembly sequence planning. First, graphs represent feasible assembly sequence with components. Second, adjacency matrices are developed to accumulate the sequence information for computational analysis. Third, a black box diagram is applied to understand and consider the functions of a product during assembly and disassembly operations. Finally, factors are determined to overcome gaps between each assembly and disassembly sequence structure. By considering product architecture with Design Structure Matrix (DSM), we can determine modular design for selective disassembly and interface type for assembly. A case study is performed with two coffee makers to demonstrate the effectiveness of the proposed method.

The goal of assembly sequencing is to plan a feasible series of operations to construct a product from its individual parts. Previous research has thoroughly investigated assembly sequencing under the assumption that parts have nominal geometry. This paper considers the case where parts have toleranced geometry. Its main contribution is an efficient procedure that decides if a product admits an assembly sequence with infinite translations that is feasible for all possible instances of the components within the specified tolerances. If the product admits one such sequence, the procedure can also generate it. For the cases where there exists no such assembly sequence, another procedure is proposed which generates assembly sequences that are feasible only for some values of the toleranced dimensions. If this procedure produces no such sequence, then no instance of the product is assemblable. Finally, this paper analyzes the relation between assembly and disassembly sequences in the presence of toleranced parts. This work assumes a simple, but non-trivial tolerance language that falls short of capturing all imperfections of a manufacturing process. Hence, it is only one step toward assembly sequencing with toleranced parts.

The importance of job shop scheduling as a practical problem has attracted the attention of many researchers. However, most research has focused on special cases such as single machine, parallel machine, and flowshop environments due to the “hardness” of general job shop problems. In this paper, a hybrid algorithm based on an integration of a genetic algorithm and heuristic rules is proposed for a general job shop scheduling problem with sequence-dependent setups (Jm|sjk|Cmax ). An embedded simulator is employed to implement the heuristic rules, which greatly enhances the flexibility of the algorithm. Knowledge relevant to the problem is inherent in the heuristic rules making the genetic algorithm more efficient, while the optimization procedure provided by the genetic algorithm makes the heuristic rules more effective. Extensive numerical experiments have been conducted and the results have shown that the hybrid approach is superior when compared to recently published existing methods for the same problem.

This paper addresses the parameter modelling and optimisation issues in the application of a bio-inspired model for the scheduling of dynamic flexible job shop with sequence-dependent setups. The study sets the model parameters using two steps, termed mapping and tuning. Mapping establishes a set of coefficients to link the model parameters with the scheduling problem characteristics. Tuning determines good values of these coefficients and is then used to compute the model parameters. Such a tuning procedure is accomplished by extensive computational experiments and statistical analyses. A data set from semiconductor manufacturing was used to show the effectiveness of the parameter setting approach. The performance of the proposed multiagent model was compared with that of another scheduling method which is based on dispatching rules. It is concluded that the proposed parameter setting method is effective and worth considering when applying bio-inspired division of labour to dynamic manufacturing scheduling. [Received 5 October 2006; Revised 2 January 2007; Accepted 1 March 2007]

The theoretical research literature on Manufacturing Schedule Optimisation has yielded few applications of dynamic schedule optimisation to actual manufacturing situations. This is particularly true of the classical job-shop scheduling model. Conventional job-shop scheduling problem (JSP) approaches were found to be based on an over simplified assumption set and a single optimisation objective. Most JSP algorithms neglect issues such as sequence-dependent set-ups, and parallel resources. An actual job-shop scheduling problem in a case study firm is used to identify the deficiencies in the traditional JSP solution approaches. A more realistic scheduling model was formulated and addressed using Constraint Satisfaction Problem (CSP) formulation and heuristic techniques. This combined heuristic and CSP approach was found in practice to be able to deal with an industrial scale problem and achieved superior plant performance in terms of order tardiness and machine utilisation. This approach represented much more effectively the real world manufacturing problem than the conventional approach.

In this study, a new and simple alternate routing heuristics, which would be superior to the conventional routing strategies in terms of various system performance measures and easier to apply practically, was presented. Because of the high investment costs of FMSs, it is also definitely worth choosing the best operating policy and system configuration by analyzing the system model, and adapting to changes over time. In future research, the heuristic rule base will be extended to include other supplementary constraints such as dynamic tool allocation and sequence dependent setup times. For practical implementation of the proposed decision support system, additional research in the area of human interfaces could be useful to develop more user friendly system which automatically constructs simulation model of the system from the knowledge base of a production system.

In order to effectively reduce the human-computer interaction (HCI) workload before the assembly process simulation in the digital assembly environment, and to enhance the intelligence of assembly sequence planning, we introduce the assembly constraint relationship into the automatic generation of assembly sequences and propose a practical assembly sequence planning method for intelligent assembly. Firstly, starting from the assembly geometry model, an assembly model liaison graph is constructed by combining the analysis of assembly constraint relationship and the definition of disassembly direction rules. Then, according to the liaison graph, disassembly priority constraint matrix based on constraint relationship is constructed, and the automatic generation and dynamic update of the disassembly priority diagram can be realized by the definition of disassembly doubly linked list. According to the diagram, the rationality of the disassembly sequence is determined through the interference check analysis, and then the assembly sequence is automatically generated from the reversed disassembly sequence. Finally, the method in the text is verified by an example case study.

Job-shop scheduling is a difficult problem, both theoretically and practically. This problem is a combinatorial optimization of considerable industrial importance. Although the job-shop scheduling problem has often been investigated, very little of this research is concerned with the uncertainty characterized by the imprecision in problem variables. In this paper, we investigate the job-shop scheduling problem with imprecise processing times. We first use triangular fuzzy numbers to represent imprecise processing times, and then construct a fuzzy job-shop scheduling model. Our work intends to extend the deterministic job-shop scheduling problem into a more generalized problem that would be useful in practical situations.KeywordsFuzzy NumberTriangular Fuzzy NumberMembership GradeFuzzy Processing TimeShifting BottleneckThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The authors propose the implementation of hybrid Fuzzy Logic-Genetic Algorithm (FL-GA) methodology to plan the automatic assembly and disassembly sequence of products. The GA-Fuzzy Logic approach is implemented onto two levels. The first level of hybridization consists of the development of a Fuzzy controller for the parameters of an assembly or disassembly planner based on GAs. This controller acts on mutation probability and crossover rate in order to adapt their values dynamically while the algorithm runs. The second level consists of the identification of the optimal assembly or disassembly sequence by a Fuzzy function, in order to obtain a closer control of the technological knowledge of the assembly/disassembly process. Two case studies were analyzed in order to test the efficiency of the Fuzzy-GA methodologies.

This study deals with the automatic determination of part specifications from assembly drawings, such as the assembly sequence and the distribution of tolerances. This paper describes a new algorithm for generating assembly/disassembly sequence of functional machine unit. The algorithm is based on a data model of assembly structure described by connective relations among parts. The algorithm for generating disassembly sequence can be divided into three stages. In the first stage, a set of parts are listed as candidates to be disassembled. In the second stage, one part is selected from the set according to the rules arranged in the order of the ease of disassembly. In the third stage, the selected part is actually disassembled using an appropriate procedure. These three stages are executed recursively until all parts are disassembled. This paper also discusses an optimal disassembly sequence to minimize the number of the changes of direction in disassembly and the number of tools changes. This algorithm is implemented as a rule based system in Prolog. Through the experiments on the machine units, including a headstock of eighty parts. The solutions are the same to those determined manually by skilled engineers.

Modern manufacturing environments seek adaptive solutions to integrate predictive maintenance into job shop scheduling. This paper conducts a comparative study of various Genetic Algorithm (GA) based approaches for Integrated Scheduling and Predictive Maintenance Planning (ISPMP). The study assesses the performance of four GAs across three job load conditions (i.e., Low, Medium, and High), considering both single and multiple machine breakdown scenarios. The results highlight the standard GA's potential for near-real-time scheduling solutions, emphasizing its adaptability and scalability. Bridging the theoretical innovations with practical applications, this research highlights an adaptive production planning paradigm, championing the role of GA-enabled simulation and decision support systems in the ever-evolving industrial landscape.

Preventive Maintenance and Job Shop Scheduling: An Approach to React to Unplanned Events and Minimizing Unused Time Slots in Production Control

Power generation and transmission systems face increasing challenges in coordinating maintenance planning under economic pressure and carbon emission constraints. This study proposes an optimization framework that integrates preventive maintenance scheduling with operational dispatch decisions, aiming to achieve both cost efficiency and emission reduction. A bi-layer scenario-based mixed-integer optimization model is formulated, where the upper layer determines annual preventive maintenance windows, and the lower layer performs hourly economic dispatch considering renewable generation and demand uncertainty. To manage the exposure to extreme carbon outcomes, a Conditional Value-at-Risk (CVaR) constraint is embedded, jointly controlling economic and environmental risks. A parallel cut-generation decomposition algorithm is developed to ensure computational scalability for large-scale systems. Numerical experiments on six-bus and IEEE 118-bus systems demonstrate that the proposed model reduces total carbon emissions by up to 32.1%, while maintaining cost efficiency and system reliability. The scenario analyses further show that adjusting maintenance schedules according to seasonal carbon intensity effectively balances operation and emission targets. The results confirm that the proposed optimization framework provides a practical and scalable approach for achieving low-carbon, reliable, and economically efficient power system maintenance planning.

mRNA translation is tightly regulated to preserve cellular homeostasis. Despite extensive biochemical, genetic, and structural studies, a detailed understanding of mRNA translation regulation is lacking. Imaging methodologies able to resolve the binding dynamics of translation factors at single-cell and single-mRNA resolution were necessary to fully elucidate regulation of this paramount process. Here live-cell spectroscopy and single-particle tracking were combined to interrogate the binding dynamics of endogenous initiation factors to the 5’cap. The diffusion of initiation factors (IFs) changed markedly upon their association with mRNA. Quantifying their diffusion characteristics revealed the sequence of IFs assembly and disassembly in cell lines and the clustering of translation in neurons. This approach revealed translation regulation at high spatial and temporal resolution that can be applied to the formation of any endogenous complex that results in a measurable shift in diffusion.

In this paper a main point of view is the exhausting of capacity in relation to a capacity focus at every node of the production graph. This exhausting process has a local and a global aspect. Optimality means a homogeneous reservation of the production nets and exhaustion of the capacity in the nodes close to the focus. Under weak conditions an optimal production sequence is achievable constructively. A classical field of application of this result is the assembly, but many other applications are possible.