Efficient algorithm for cell formation with sequence data,machine replications and alternative process routings

Cell formation is an important problem in the design of a cellular manufacturing system. Despite a large number of papers on cell formation being published, only a handful incorporate operation sequence in intercell move calculations and consider alternative process routings, cell size, production volume and allocating units of identical machines into different cells. Modelling the above factors makes the cell formation problem complex but more realistic. The paper develops a model and solution methodology for a problem of cell formation to minimize the sum of costs of intercell moves, machine investment and machine operating costs considering all the factors mentioned above. An algorithm comprised of simulated annealing and local search heuristics has been developed to solve the model. A limited comparison of the proposed algorithm with an optimal solution generated by complete enumeration of small problems indicates that the algorithm produces a solution of excellent quality. Large problems with 100 parts and 50 machine types are efficiently solved using the algorithm.     

Manufacturing cells' design in consideration of various production factors

A cell formation problem is introduced that incorporates various real-life production factors such as the alternative process routing, operation sequence, operation time, production volume of parts, machine capacity, machine investment cost, machine overload, multiple machines available for machine types and part process routing redesigning cost. None of the cell formation models in the literature has considered these factors simultaneously. A similarity coefficient is developed that incorporates alternative process routing, operation sequence, operation time and production volume factors. Although very few studies have considered the machine capacity violated issue under the alternative process routing environment, owing to the difficulties of the issue discussed here, these studies fail to deal with the issue because they depend on some unrealistic assumptions. Five solutions have been proposed here and are used to cope with this difficulty. A heuristic algorithm that consists of two stages is developed. The developed similarity coefficient is used in stage 1 to obtain basic machine cells. Stage 2 solves the machine-capacity violated issue, assigns parts to cells, selects process routing for each part and refines the final cell formation solution. Some numerical examples are used to compare with other related approaches in the literature and two large size problems are also solved to test the computational performance of the developed algorithm. The computational results suggest that the approach is reliable and efficient in either the quality or the speed for solving cell formation problems.     

Multiple routeings and capacity considerations in group technology applications

This paper addresses the problem of manufacturing cell formation, given multiple part routeings, and multiple functionally similar workcentres. Cellular manufacturing is intended to facilitate production, and thus should be based on projected production requirements. The originality of the approach lies in considering both the manufacturing system as well as projected production, and distributing the demand among alternate routeings in order to obtain a better manufacturing cell design. The suggested choice of part routeings favours the decomposition of the manufacturing system into manufacturing cells in a way that minimizes part traffic, along with satisfying the part demand and workcentre capacity constraints. We show that the problem can be formulated as a linear programming type problem which simultaneously addresses two problems: (i) routeing selection, and (ii) cell formation. The common objective is to minimize the inter-cell traffic in the system. The proposed algorithm iteratively solves two problems. The first problem is formulated as a linear-programming problem, while the latter is approached by an existing heuristic bottom-up aggregation procedure, known as Inter-Cell Traffic Minimization Method (ICTMM), enhanced appropriately.     

Machine cell formation using a mathematical model and a genetic-algorithm-based heuristic

This paper presents a comprehensive mathematical model and a genetic-algorithm-based heuristic for the formation of part families and machine cells in the design of cellular manufacturing systems. The model incorporates dynamic cell configuration, alternative routings, sequence of operations, multiple units of identical machines, machine capacity, workload balancing among cells, operation cost, subcontracting cost, tool consumption cost, set-up cost and other practical constraints. To solve this model efficiently, a two-phase genetic-algorithm-based heuristic was developed. In the first phase, independent cells are formed which are relatively simple to generate. In the second phase, the solution found during the first phase is gradually improved to generate cells optimizing inter-cell movement and other cost terms of the model. A number of numerical examples of different sizes are presented to demonstrate the computational efficiency of the heuristic developed.     

Cell design and multi-period machine loading in cellular reconfigurable manufacturing systems with alternative routing

This paper deals with the design and loading of Cellular Reconfigurable Manufacturing Systems in the presence of alternative routing and multiple time periods. These systems consist of multiple reconfigurable machining cells, each of which has Reconfigurable Machine Tools and Computer Numerical Control (CNC) machines. Each reconfigurable machine has a library of feasible auxiliary machine modules for achieving particular operational capabilities, while each CNC machine has an automatic tool changer and a tool magazine of a limited capacity. The proposed approach consists of two phases: the machine cell design phase which involves the grouping of machines into machine cells, and the cell loading phase that determines the routing mix and the tool and module allocation. In this paper, the cell design problem is modelled as an Integer Linear Programming formulation, considering the multiple process plans of each part type as if they were separate part types. Once the manufacturing cells are formed, a Mixed Integer Linear Programming model is developed for the cell loading problem, considering multi-period demands for the part types, and minimising transportation and holding costs while keeping the machine and cell utilisations in each period, and the system utilisation across periods, approximately balanced. An illustrative problem and experimental results are presented.     

Production and subcontracting control for an unreliable manufacturing system with setups

This paper deals with the problem of joint production, setup and subcontracting control of unreliable manufacturing systems producing two product types. The production requires setups each time it switches from one product type to another. Subcontracting is an integral part of the decision-making process due to limited production capacity in existing facility. The objective is to propose an effective control policy for the considered system which simultaneously manages production, setup and subcontracting activities. The complexity of the problem lies in the interaction between internal manufacturing decisions and subcontracting that outsource a part of the production, in a dynamic and stochastic environment. An experimental optimisation approach is adopted to determine the optimal control parameters which minimise the average total cost. Extensive sensitivity analyses are performed to illustrate the robustness and the usefulness of the adopted approach. An in-depth study comparing five control policies across a wide range of system parameters is also conducted. Extended cases closer to reality are also investigated considering elements such as the preventive maintenance and the production of non-conforming products. The best control policy in terms of economic performance is then obtained. Valuable insights providing a better understanding of interactions involving production, setup, and subcontracting are discussed.     

Cellular manufacturing system design considering machines reliability and parts alternative process routings

Cell formation is an important problem in the design of cellular manufacturing systems (CMS). Most cell formation methods appeared in the literature assume that each part has one process plan, and all machines are 100% reliable with unlimited capacity. However, this is not realistic in manufacturing systems. Considering machines reliability in addition to machines capacity and machine duplicates during the part route selection process help to obtain better machine grouping and minimum total cost for CMS. Considering these factors in addition to operations sequence and production volumes makes the problem more complex but more realistic. Most of the methods appeared in the literature to solve such problems use mathematical programming procedures that take large amount of computational efforts. Procedures using similarity coefficient method are more flexible in incorporating various important production data and lend easily to computer applications. A new similarity coefficient equation that incorporates all these production factors is developed. Also, a procedure that captures the similarity between machine groups and minimises the total CMS cost is developed. The procedure utilises functional cells to eliminate intercellular moves and achieve ‘one-piece flow’ practise. The methodology is compared with other methods in the literature and found to be more effective.     

基于多条工艺路线单元构建的遗传算法

单元化制造系统的建立可简单划分为单元构建和单元组织两大部分,其中单元构建算法是一个典型的ＮＰ问题．本文设计了单元构建的基于多条工艺路线的算法,同时就遗传算法如何应用于考虑多条工艺路线的单元构建问题进行探讨,并开发了相应的基于Ｍａｔｌａｂ的软件,举例验证了其有效性．     

Formation of independent manufacturing cells with the consideration of multiple identical machines

Cellular manufacturing is a manufacturing philosophy with the goal to produce low-medium volume products with high variety, while maintaining the high productivity of large-scale production. It is recognised as one of the most powerful management innovations in job-shop and batch production. Among the problems of designing a cellular manufacturing system, cell formation is the central and foremost issue. In the present paper, we investigate the formation of independent manufacturing cells with the consideration of multiple identical machines, in which inter-cell movements are completely eliminated by allocating identical machines in different manufacturing cells. Incorporating many real-life production factors including processing time, set-up time, alternative processing routes, machine capacity, batch size and cell size, we formulate a bi-objective mathematical model to minimise workload imbalance among manufacturing cells. Then, a genetic algorithm based on non-dominated sorting genetic algorithm II is developed to solve it. The computational results of numerical examples and the comparison analysis validated the performance of the proposed algorithm.     

A new approach to the cell formation problem with alternative processing routes and operation sequence

Cellular manufacturing (CM) is an important application of group technology in manufacturing systems. One of the crucial steps in the design of CM is the identification of part families and manufacturing cells. This problem is referred to as cell formation problem (CFP) in the literature. In this article, a solution approach is proposed for CFP, which considers many parameters such as machine requirement, sequence of operations, alternative processing routes, processing time, production volume, budget limitation, cost of machines, etc. Due to the NP-hardness of CFP, it cannot be efficiently solved for medium- to large-sized problems. Thus, a genetic algorithm (GA) is proposed to solve the formulated model. Comparison of the results obtained from the proposed GA to the globally optimum solutions obtained by Lingo Software and those reported in the literature reveals the effectiveness and efficiency of the proposed approach.     

A two-phase heuristic algorithm for cell formation problems considering alternative part routes and machine sequences

In this paper, we deal with the multi-objective machine cell formation problem. This problem is characterized as determining part route families and machine cells such that the total sum of inter-cell part movements and maximum machine workload imbalance are simultaneously minimized. Together with the objective function, alternative part routes and the machine sequences of part routes are considered in grouping part route families. Also, it is assumed that the number of machine cells is not pre-defined. Owing to the complexity of the problem, a two-phase heuristic algorithm is proposed. Computational experiments were conducted to verify the performance of the algorithm. Throughout the computational experiments, we verified that the two-phase heuristic algorithm is effective for large-scale machine cell formation problems.     

Fuzzy ART/RRR-RSS: a two-phase neural network algorithm for part-machine grouping in cellular manufacturing

In this paper an efficient methodology adopting Fuzzy ART neural network is presented to solve the comprehensive part-machine grouping (PMG) problem in cellular manufacturing (CM). Our Fuzzy ART/RRR-RSS (Fuzzy ART/ReaRRangement-ReaSSignment) algorithm can effectively handle the real-world manufacturing factors such as the operation sequences with multiple visits to the same machine, production volumes of parts, and multiple copies of machines. Our approach is based on the non-binary production data-based part-machine incidence matrix (PMIM) where the operation sequences with multiple visits to the same machine, production volumes of parts, and multiple identical machines are incorporated simultaneously. A new measure to evaluate the goodness of the non-binary block diagonal solution is proposed and compared with conventional performance measures. The comparison result shows that our performance measure has more powerful discriminating capability than conventional ones. The Fuzzy ART/RRR-RSS algorithm adopts two phase approach to find the proper block diagonal solution in which all the parts and machines are assigned to their most preferred part families and machine cells for minimisation of inter-cell part moves and maximisation of within-cell machine utilisation. Phase 1 (clustering phase) attempts to find part families and machines cells quickly with Fuzzy ART neural network algorithm which is implemented with an ancillary procedure to enhance the block diagonal solution by rearranging the order of input presentation. Phase 2 (reassignment phase) seeks to find the best proper block diagonal solution by reassigning exceptional parts and machines and duplicating multiple identical machines to cells with the purpose of minimising inter-cell part moves and maximising within-cell machine utilisation. To show the robustness and recoverability of the Fuzzy ART/RRR-RSS algorithm to large-size data sets, a modified procedure of replicated clustering which starts with the near-best solution and rigorous qualifications on the number of cells and duplicated machines has been developed. Experimental results from the modified replicated clustering show that the proposed Fuzzy ART/RRR-RSS algorithm has robustness and recoverability to large-size ill-structured data sets by producing highly independent block diagonal solution close to the near-best one.     

Cell formation problem with consideration of both intracellular and intercellular movements

The cellular manufacturing system (CMS) is a well-known strategy which enhances production efficiency while simultaneously cutting down the system-wide operation cost. Most of the researchers have been focused on developing different approaches in order to identify machine-cells and part-families more efficiently. In recent years, researchers have also focused their studies more scrupulously by collectively considering CMS with production volume, operation sequence, alternative routing or even more. However, very few of them have tried to investigate both the allocation sequence of machines within the cells (intra-cell layout) and the sequence of the formed cells (inter-cell layout). Solving this problem is indeed very important in reducing the total intracellular and intercellular part movements which is especially significant with large production volume.

In this paper, a two-phase approach has been proposed to tackle the cell formation problem (CFP) with consideration of both intra-cell and inter-cell part movements. In the first phase, a mathematical model with multi-objective function is formed to obtain the machine cells and part families. Afterwards, in the second phase, another mathematical model with single-objective function is presented which optimizes the total intra-cell and inter-cell part movements. In other words, the scope of problem has been identified as a CFP together with the background objective of intra-cell and inter-cell layout problems (IAECLP). The primary assumption for IAECLP is that only linear layouts will be considered for both intra-cell and inter-cell. In other words, the machine within cells and the formed cells are arranged linearly. This paper studies formation of two mathematical models and used the part-machine incidence matrix with component operational sequence.

The IAECLP is considered as a quadratic assignment problem (QAP). Since QAP and CFP are NP-hard, genetic algorithm (GA) has been employed as solving algorithm. GA is a widespread accepted heuristic search technique that has proven superior performances in complex optimization problems and further it is a popular and well-known methodology. The proposed algorithms for CFP and IAECLP have been implemented in JAVA programming language.     

Optimisation of production and subcontracting strategies

We consider the problem of optimising production and subcontracting decisions in a supply chain manufacturing engineered products. The supply chain manager can use a combination of internal production capacities, available capacity at qualified subcontractors, make capital investments and process improvements to minimise costs associated with production and penalties for not meeting desired operational metrics. We formulate this as an optimisation problem that requires simultaneous solution of a mathematical programming problem and queuing network model. We propose an efficient iterative approach to solve this problem and conduct numerical studies to demonstrate the effectiveness of the approach.     

Development of a hybrid negotiation scheme for multi-agent manufacturing systems

A hybrid inter-agent negotiation mechanism based on currency and a pre-emption control scheme is proposed to improve the performance of multi-agent manufacturing systems. The multi-agent system considered consists mainly of four types of agents: machine, clone, part and mediator. The machine agent controls the scheduling and the execution of a task. The clone agent aims to maximize the utilization rate by attracting relevant work to the machine. The part agent communicates with the machine agent or clone agent to acquire necessary production resources in order to get the required processing done, and the mediator agent contains the status of the part that will be processed by the subcontracting machine agent. The primary objective is to design decentralized control protocols for discrete part manufacturing systems to enhance the efficiency of the system and to allocate dynamically the resources to critical jobs based on the dynamic search tree. This research incorporates both the currency and the pre-emption schemes within a common framework. Currency functions are used to help the agents meet their individual objectives, whereas the pre-emption scheme is used to expedite the processing of parts based on their due dates. A dynamic search algorithm for the best route selection of different operations based on the job completion time is also proposed and it is implemented on a small manufacturing unit.     

A parallel genetic algorithm for dynamic cell formation in cellular manufacturing systems

Instead of using expensive multiprocessor supercomputers, parallel computing can be implemented on a cluster of inexpensive personal computers. Commercial accesses to high performance parallel computing are also available on the pay-per-use basis. However, literature on the use of parallel computing in production research is limited. In this paper, we present a dynamic cell formation problem in manufacturing systems solved by a parallel genetic algorithm approach. This method improves our previous work on the use of sequential genetic algorithm (GA). Six parallel GAs for the dynamic cell formation problem were developed and tested. The parallel GAs are all based on the island model using migration of individuals but are different in their connection topologies. The performance of the parallel GA approach was evaluated against a sequential GA as well as the off-shelf optimization software. The results are very encouraging. The considered dynamic manufacturing cell formation problem incorporates several design factors. They include dynamic cell configuration, alternative routings, sequence of operations, multiple units of identical machines, machine capacity, workload balancing, production cost and other practical constraints.     

Cellular manufacturing systems design with routing flexibility,machine procurement,production planning and dynamic system reconfiguration

This paper investigates the problem of designing cellular manufacturing systems with multi-period production planning, dynamic system reconfiguration, operation sequence, duplicate machines, machine capacity and machine procurement. An important aspect of this problem is the introduction of routing flexibility in the system by the formation of alternate contingency process routings in addition to alternate main process routings for all part types. Contingency routings serve as backups so as to effectively address the reality of part process routing disruptions (in the main routings) owing to machine breakdowns and allow the cellular manufacturing system to operate in a continuous manner even in the event of such breakdowns. The paper also provides in-depth discussions on the trade-off between the increased flexibility obtained versus the additional cost to be incurred through the formation of contingency routings for all parts. Some sensitivity analysis is also performed on some of the model parameters. The problem is modelled and solved through a comprehensive mixed integer programming formulation. Computational results presented by solving some numerical examples show that the routing and process flexibilities can be incorporated within the cellular manufacturing system design without significant increase in the system cost.     

Decision-making on multi-mould maintenance in production scheduling

The reliability of a critical tool like a mould on a machine affects the productivity seriously in many manufacturing firms. In fact, its breakdown frequency is even higher than machines. The decision-making on when mould maintenance should be started become a challenging issue. In the previous study, the mould maintenance plans were integrated with the traditional production schedules in a plastics production system. It was proven that considering machine and mould maintenance in production scheduling could improve the overall reliability and productivity of the production system. However, the previous model assumed that each job contained single operation. It is not workable in other manufacturing systems such as die stamping which may contain multiple operations with multiple moulds in each job. Thus, this study models a new problem for multi-mould production-maintenance scheduling. A genetic algorithm approach is applied to minimise the makespan of all jobs in 10 hypothetical problem sets. A joint scheduling (JS) approach is proposed to decide the start times of maintenance activities during scheduling. The numerical result shows that the JS approach has a good performance in the new problem and it is sensitive to the characteristic of the setup time defined.     

A PSO-based approach to cell formation problems with alternative process routings

Group technology (GT) has been extensively applied to cellular manufacturing system (CMS) design for decades due to many benefits such as decreased number of part movements among cells and increased machine utilisation in cells. This paper considers cell formation problems with alternative process routings and proposes a discrete particle swarm optimisation (PSO) approach to minimise the number of exceptional parts outside machine cells. The approach contains two main steps: machine partition and part-routing assignment. Through inheritance and random search, the proposed algorithm can effectively partition machines into different cells with consideration of multiple part process routings. The computational results are compared with those obtained by using simulated annealing (SA)-based and tabu search (TS)-based algorithms. Experimental results demonstrate that the proposed algorithm can find equal or fewer exceptional elements than existing algorithms for most of the test problems selected from the literature. Moreover, the proposed algorithm is further tailed to incorporate various production factors in order to extend its applicability. Four sample cases are tested and the results suggest that the algorithm is capable of solving more practical cell formation problems.     

Non-Cooperative Game of Coordinated Scheduling of Parallel Machine Production and Transportation in Shared Manufacturing

Given the challenges of manufacturing resource sharing and competition in the modern manufacturing industry, the coordinated scheduling problem of parallel machine production and transportation is investigated. The problem takes into account the coordination of production and transportation before production as well as the disparities in machine spatial position and performance. A non-cooperative game model is established, considering the competition and self-interest behavior of jobs from different customers for machine resources. The job from different customers is mapped to the players in the game model, the corresponding optional processing machine and location are mapped to the strategy set, and the makespan of the job is mapped to the payoff. Then the solution of the scheduling model is transformed into the Nash equilibrium of the non-cooperative game model. A Nash equilibrium solution algorithm based on the genetic algorithm (NE-GA) is designed, and the effective solution of approximate Nash equilibrium for the game model is realized. The fitness function, single-point crossover operator, and mutation operator are derived from the non-cooperative game model’s characteristics and the definition of Nash equilibrium. Rules are also designed to avoid the generation of invalid offspring chromosomes. The effectiveness of the proposed algorithm is demonstrated through numerical experiments of various sizes. Compared with other algorithms such as heuristic algorithms (FCFS, SPT, and LPT), the simulated annealing algorithm (SA), and the particle swarm optimization algorithm (PSO), experimental results show that the proposed NE-GA algorithm has obvious performance advantages.