Machine Loading Problem Research Articles

A robust cardinality-constrained model to address the machine loading problem

Abstract Several deterministic models have been proposed in the literature to solve the machine loading problem (MLP), which considers a set of product types to be produced on a set of machines using a set of tool types, and determines the quantity of each product type to be produced at each time period and the corresponding machine tool loading configuration. However, processing times are subject to random increases, which could impair the quality of a deterministic solution. Thus, we propose a robust MLP counterpart, searching for an approach that properly describes the uncertainty set of model parameters and, at the same time, ensures practical application. We exploit the cardinality-constrained approach, which considers a simple uncertainty set where all uncertain parameters belong to an interval, and allows tuning the robustness level by bounding the number of parameters that assume the worst value. The resulting plans provide accurate estimations on the minimum production level that a system achieves even in the worst conditions. The applicability of the robust MLP and the impact of robustness level have been tested on several problem variants, considering single- vs multi-machine and single- vs multi-period MLPs. We also consider the execution of the plans in a set of scenarios to evaluate the practical implications of MLP robustness. Results show the advantages of the robust formulation, in terms of improved feasibility of the plans, identification of the most critical tools and products, and evaluation of the maximum achievable performance in relation to the level of protection. Moreover, low computational times guarantee the applicability of the proposed robust MLP counterpart.

Model of decision support for the configuration of manufacturing system

Abstract Manufacturing enterprises today have to face the volatility of markets, characterized by a decreasing production volume and an increasing number of product variants to meet customer expectations. Traditional dedicated manufacturing lines (DML) have been replaced by flexible manufacturing systems (FMS) and, recently, by the systems that combine features of DML and FMS, i.e., by reconfigurable manufacturing systems (RMS). Appropriate manufacturing support and optimization systems for FMS and RMS will advance the quality and effectiveness of reconfigurable manufacturing. This paper proposes an original mixed integer linear programming (MILP) model for decision support in configuration and reconfiguration of the manufacturing system. The modeled problem is a certain development of the known machine loading problem MLP. In this approach, we generate a highly parameterized model based on a set of constraints and a set of questions. Different mathematical programming (MP) - based solvers are proposed to solve this model.

A Cardinality-constrained Approach for Robust Machine Loading Problems

The Machine Loading Problem (MLP) refers to the allocation of operative tasks and tools to machines for the production of parts. Since the uncertainty of processing times might affect the quality of the solution, this paper proposes a robust formulation of an MLP, based on the cardinality-constrained approach, to evaluate the optimal solution in the presence of a given number of fluctuations of the actual processing time with respect to the nominal one. The applicability of the model in the practice has been tested on a case study.

Solving machine loading problem of flexible manufacturing systems using a modified discrete firefly algorithm

Solving machine loading problem of flexible manufacturing systems using a modified discrete firefly algorithm

An Improved Particle Swarm Optimization Approach for Solving Machine Loading Problem in Flexible Manufacturing System

Machine loading problem in flexible manufacturing system is considered as a vital pre-release decision. Loading problem is concerned with assignment of necessary operations of the selected jobs to various machines in an optimal manner to minimize system unbalance under technological constraints of limited tool slots and operation time. Such a problem is combinatorial in nature and found to be NP-hard; thus, finding the exact solutions is computationally intractable and becomes impractical as the problem size increases. To alleviate above limitations, a meta-heuristic approach based on particle swarm optimization (PSO) has been proposed in this paper to solve the machine loading problem. Mutation, a commonly used operator in genetic algorithm, has been introduced in PSO so that trapping of solutions at local minima or premature convergence can be avoided. Logistic mapping is used to generate chaotic numbers in this paper. Use of chaotic numbers makes the algorithm converge fast toward global optimum and hence reduce computational effort further. Twenty benchmark problems available in open literature have been solved using the proposed heuristic. Comparison between the results obtained by the proposed heuristic and the existing methods show that the results obtained are encouraging at significantly less computational effort.

Optimisation of a machine loading problem using a genetic algorithm-based heuristic

In the present work, apart from operating on the structure of a conventional genetic algorithm (GA), a heuristic which uses techniques like differential mutation probability, elitism and local search is used to produce near optimal solutions for large machine loading problems with less computational intensity. Two variants of the machine loading problem are analysed in the present work: single batch model and the multiple batch models. The sensitivity of the problem with respect to the tool capacity constraint is evaluated to find that moderately restricted problems requiring greater computational resources in comparison to lesser restricted and tightly restricted class of problems. The performance of various dispatching rules was compared to infer that the least slack principle fares better than the other tested dispatching rules. It is observed from the results, that the proposed heuristic is efficient in handling large and complex machine loading problems.

A Critical Review of Machine Loading Problem in Flexible Manufacturing System

Production planning is the foremost task for manufacturing firms to deal with, especially adopting Flexible Manufacturing System (FMS) as the manufacturing strategy for production seeking an optimal balance between productivity-flexibility requirements. Production planning in FMS provides a solution to problems regarding part type selection: machine grouping, production ratio, resource allocation and loading problem. These problems need to be solved optimally for maximum utilization of resources. Optimal solution to these problems has been a focus of attention in production and manufacturing, industrial and academic research since a number of decades. Evolution of new optimization techniques, software, technology, machines and computer languages provides the scope of a better optimal solution to the existing problems. Thus there remains a need of research to solve the problem with latest tools and techniques for higher optimal use of available resources. As an objective, the researchers need to reduce the computational time and cost, complexity of the problem, solution approach viz. general or customized, better user friendly communication with machine, higher freedom to select the desired objective(s) type(s) for optimal solution to the problem. As an approach to the solution to the problem, a researcher first needs to go for an exhaustive literature review, where the researcher needs to find the research gaps, compare and analyze the tools and techniques used, number of objectives considered for optimization and need, and scope of research for the research problem. The present study is a review paper analyzing the research gaps, approach and techniques used, scope of new optimization techniques or any other research, objectives considered and validation approaches for loading problems of production planning in FMS.

A hybrid algorithm optimization approach for machine loading problem in flexible manufacturing system

The production planning problem of flexible manufacturing system (FMS) concerns with decisions that have to be made before an FMS begins to produce parts according to a given production plan during an upcoming planning horizon. The main aspect of production planning deals with machine loading problem in which selection of a subset of jobs to be manufactured and assignment of their operations to the relevant machines are made. Such problems are not only combinatorial optimization problems, but also happen to be non-deterministic polynomial-time-hard, making it difficult to obtain satisfactory solutions using traditional optimization techniques. In this paper, an attempt has been made to address the machine loading problem with objectives of minimization of system unbalance and maximization of throughput simultaneously while satisfying the system constraints related to available machining time and tool slot designing and using a meta-hybrid heuristic technique based on genetic algorithm and particle swarm optimization. The results reported in this paper demonstrate the model efficiency and examine the performance of the system with respect to measures such as throughput and system utilization.

Optimum loading of machines in a flexible manufacturing system using a mixed-integer linear mathematical programming model and genetic algorithm

Machine loading problem in a flexible manufacturing system (FMS) encompasses various types of flexibility aspects pertaining to part selection and operation assignments. The evolution of flexible manufacturing systems offers great potential for increasing flexibility by ensuring both cost-effectiveness and customized manufacturing at the same time. This paper proposes a linear mathematical programming model with both continuous and zero-one variables for job selection and operation allocation problems in an FMS to maximize profitability and utilization of system. The proposed model assigns operations to different machines considering capacity of machines, batch-sizes, processing time of operations, machine costs, tool requirements, and capacity of tool magazine. A genetic algorithm (GA) is then proposed to solve the formulated problem. Performance of the proposed GA is evaluated based on some benchmark problems adopted from the literature. A statistical test is conducted which implies that the proposed algorithm is robust in finding near-optimal solutions. Comparison of the results with those published in the literature indicates supremacy of the solutions obtained by the proposed algorithm for attempted model.

Integration of part selection, machine loading and machining optimisation decisions for balanced workload in flexible manufacturing system

This paper demonstrates the importance of incorporating and solving the machining optimisation problem jointly with part selection and machine loading problems in order to avoid unbalanced workload in the FMS. Unbalanced workload renders to ineffective FMS such that some machines on the manufacturing shop floor become more occupied than others. Since CNC machine tools employed in the FMS are rather expensive, it is mostly important to balance the workload so that all machines can be effectively utilised. Therefore, in this study, two mathematical models are presented and solved in efforts to balance the workload and improve the performance of the FMS. A two-stage sequential approach is adopted whereby the first stage deals with the maximum throughput objective while the second stage deals with the minimum production cost objective. The results show that when part selection, machine loading and machining optimisation problems are jointly solved, more practical decisions can be made and a wide range of balanced workload in the FMS can be realised with minimum production cost objective. The results also show that the available machine time and tooling budget have enormous effects on throughput and production cost.

A hybrid simulated annealing-tabu search algorithm for the part selection and machine loading problems in flexible manufacturing systems

Part selection and machine loading are two major problems in the production planning phase of the flexible manufacturing systems. The problems have a combinatorial structure and usually, in practice, it is difficult to deal with this kind of problems using a mathematical programming model. In this paper, the above problems are formulated as a mixed-integer programming model which is handled sequentially and solved by a diversification-strategy-added version of the hybrid tabu search/simulated annealing algorithm of Zhang et al. (Comput Oper Res 35:282–294, 2008) presented in 2008. The performance of the algorithm is tested on eight random-generated problems with different sizes. The results are compared with those of the mathematical programming model, the original version of Zhang et al.’s (Comput Oper Res 35:282–294, 2008) algorithm and also a tabu search algorithm developed earlier by the authors.

An efficient hybrid evolutionary heuristic using genetic algorithm and simulated annealing algorithm to solve machine loading problem in FMS

In this paper, a machine loading problem in a flexible manufacturing system (FMS) is discussed, with bi-criterion objectives of minimising system imbalance and maximising system throughput in the occurrence of technological constraints such as available machining time and tool slots. A mathematical model is used to select machines, assign operations and the required tools in order to minimise the system's imbalance while maximising the throughput. An efficient evolutionary algorithm by hybridising the genetic algorithm (GA) and simulated annealing (SA) algorithm called GASA is proposed in this paper. The performance of the GASA is tested by using 10 sample dataset and the results are compared with the heuristics reported in the literature. The influence of genetic operators on the evolutionary search in GASA is studied and reported. Two machine selection heuristics are proposed and their influence on the quality of the solution is also studied. Extensive computational experiments have been carried out to evaluate the performance of the proposed evolutionary heuristics and the results are presented in tables and figures. The results clearly support the better performance of GASA over the algorithms reported in the literature.

Incorporating dynamism in traditional machine loading problem: an AI-based optimisation approach

Machine breakdowns have been recognised in flexible manufacturing systems (FMS) as the most undesirable characteristic adversely affecting the overall efficiency. In order to ameliorate product quality and productivity of FMS, it is necessary to analyse, as well as to minimise the effect of breakdowns on the objective measures of various decision problems. This paper addresses the machine loading problem of FMS with a view to maximise the throughput and minimise the system unbalance and makespan. Moreover, insufficient work has been done in the domain of machine loading problem that considers effect of breakdowns. This motivation resulted in a potential model in this paper that minimises the effect of breakdowns so that profitability can be augmented. The present work employs an on-line machine monitoring scheme and an off-line machine monitoring scheme in conjunction with reloading of part types to cope with the breakdowns. The proposed model bears similarity with the dynamic environment of FMS, hence, termed as the dynamic machine loading problem. Furthermore, to examine the effectiveness of the proposed model, results for throughput, system unbalance and makespan on different dataset from previous literature has been investigated with application of intelligence techniques such as genetic algorithms (GA), simulated annealing (SA) and artificial immune systems (AIS). The results incurred under breakdowns validate the robustness of the developed model for dynamic ambient of FMS.

An improved metaheuristic approach for solving the machine loading problem in flexible manufacturing systems

Production planning in Flexible Manufacturing Systems (FMSs) requires several hierarchical issues to be resolved sequentially or simultaneously. Loading is one of the vital issues in FMS production planning. It deals with the assignment of the necessary operations and tools among various machines in an optimal manner to minimise system unbalance under technological constraints. Such a problem is combinatorial in nature and found to be NP-complete; thus, finding the exact solutions is computationally intractable for large-scale problems. Therefore, in this study, a metaheuristic approach based on Particle Swarm Optimisation (PSO) has been proposed to solve the machine loading problem. Mutation has been introduced in PSO in a novel way so that the trapping of solutions at local minima can be avoided. The comparative study of the proposed algorithm with existing methods for ten benchmark instances available in the literature suggests that the results obtained in the proposed algorithm are quite encouraging.

Optimal job sequence determination and operation machine allocation in flexible manufacturing systems: an approach using adaptive hierarchical ant colony algorithm

In this paper, an Adaptive Hierarchical Ant Colony Optimization (AHACO) has been proposed to resolve the traditional machine loading problem in Flexible Manufacturing Systems (FMS). Machine loading is one of the most important issues that is interlinked with the efficiency and utilization of FMS. The machine loading problem is formulated in order to minimize the system unbalance and maximize the throughput, considering the job sequencing, optional machines and technological constraints. The performance of proposed AHACO has been tested over a number of benchmark problems taken from the literature. Computational results indicate that the proposed algorithm is more effective and produces promising results as compared to the existing solution methodologies in the literature. The evaluation and comparison of system efficiency and system utilization justifies the supremacy of the algorithm. Further, results obtained from the proposed algorithm have been compared with well known random search algorithm viz. genetic algorithm, simulated annealing, artificial Immune system, simple ant colony optimization, tabu search etc. In addition, the algorithm has been tested over a randomly generated problem set of varying complexities; the results validate the robustness and scalability of the algorithm utilizing the concepts of ‘heuristic gap’ and ANOVA analysis.

Part-selection and machine-loading problems in a flexible manufacturing system environment: a heuristic approach based on reallocation paradigm

In this research, an exact and efficient heuristic-based solution methodology has been formulated, which covers three segments of the machine-loading problem, i.e., part-type sequence determination, operation allocation decision and reallocation of part-type in a flexible manufacturing environment. An iterative reallocation procedure has been devised to ensure minimum positive system unbalance and maximum throughput. The proposed heuristic aims to achieve these objectives in the presence of constraints posed by availability of machining time and tool slot in a given planning horizon. Computational results on test problems indicate the supremacy of proposed heuristic which shows a significant improvement over existing methods.

Modified particle swarm optimization for solving machine-loading problems in flexible manufacturing systems

In flexible manufacturing systems (FMSs), the loading problem is considered as a vital pre-release decision because its operational effectiveness largely depends on a good quality solution to the loading problem. Difficulties arise in obtaining optimal solutions to such problems because of its combinatorial and NP-hard nature. In the past, numerous techniques have been suggested and found to be efficient, but they take long computational times when the problem size increases. In order to address the above issues, a meta-heuristic approach based on particle swarm optimization (PSO) has been proposed in this paper to improve the solution quality and reduce the computational effort. However, PSO has the tendency to suffer from premature convergence. Therefore, the PSO algorithm has been modified through the introduction of a mutation operator to improve efficiency of the algorithm. The proposed algorithm attempts to minimize the system unbalance while satisfying the technological constraints, such as the availability of machining time and tool slots. The proposed algorithm produces promising results in comparison to existing methods for ten benchmark instances available in the FMS literature.

Fast clonal algorithm

The aim of this paper is to design an efficient and fast clonal algorithm for solving various numerical and combinatorial real-world optimization problems effectively and speedily, irrespective of its complexity. The idea is to accurately read the inherent drawbacks of existing immune algorithms (IAs) and propose new techniques to resolve them. The basic features of IAs dealt in this paper are: hypermutation mechanism, clonal expansion, immune memory and several other features related to initialization and selection of candidate solution present in a population set. Dealing with the above-mentioned features we have proposed a fast clonal algorithm (FCA) incorporating a parallel mutation operator comprising of Gaussian and Cauchy mutation strategy. In addition, a new concept has been proposed for initialization, selection and clonal expansion process. The concept of existing immune memory has also been modified by using the elitist mechanism. Finally, to test the efficacy of proposed algorithm in terms of search quality, computational cost, robustness and efficiency, quantitative analyses have been performed in this paper. In addition, empirical analyses have been executed to prove the superiority of proposed strategies. To demonstrate the applicability of proposed algorithm over real-world problems, Machine-loading problem of flexible manufacturing system (FMS) is worked out and matched with the results present in literature.

Modified immune algorithm for job selection and operation allocation problem in flexible manufacturing systems

The advent of automated manufacturing systems and the variability in demand pattern have forced the manufacturers to increase the flexibility and efficiency of their automated systems to stay competitive in the dynamic market. Loading decisions play an important role in determining the efficiency of manufacturing systems. Machine loading problems in flexible manufacturing systems (FMSs) are known to be NP-hard problems. Although some NP-hard problems could still be optimized for very small instances, machine loading complexity is so extensive that even small problems take excessive computational time to reach the optimal solution. To ease the tedious computations, and to get a good solution for large problems, this paper develops a special Immune Algorithm (IA) named ‘Modified immune algorithm (MIA)’. IA is a suitable method due to its self learning capability and memory acquisition. This paper improves some issues inherent in existing IAs and proposes a more effective immune algorithm with reduced memory requirements and reduced computational complexity. In order to verify the efficacy and robustness of the proposed algorithm, the paper presents comparisons to existing immune algorithms with benchmark functions and standard data sets related to the machine loading problem. In addition proposed algorithm has been tested at different noise level to examine the efficiency of algorithm on different platforms. The comparisons show consistently that the proposed algorithm outperforms the existing techniques. For all machine loading dataset proposed algorithm has shown good results as compared to the best results reported in the literature.

Solving machine-loading problem of a flexible manufacturing system with constraint-based genetic algorithm

Machine-loading problem of a flexible manufacturing system is known for its complexity. This problem encompasses various types of flexibility aspects pertaining to part selection and operation assignments along with constraints ranging from simple algebraic to potentially very complex conditional constraints. From the literature, it has been seen that simple genetic-algorithm-based heuristics for this problem lead to constraint violations and large number of generations. This paper extends the simple genetic algorithm and proposes a new methodology, constraint-based genetic algorithm (CBGA) to handle a complex variety of variables and constraints in a typical FMS-loading problem. To achieve this aim, three new genetic operators—constraint based: initialization, crossover, and mutation are introduced. The methodology developed here helps avoid getting trapped at local minima. The application of the algorithm is tested on standard data sets and its superiority is demonstrated. The solution approach is illustrated by a simple example and the robustness of the algorithm is tested on five well-known functions.