Improved design of CMS by considering operators decision-making styles

Cell formation is one of the oldest problems in cellular manufacturing systems (CMS) including assigning parts, machines and operators to cells. Cell manufacturing contains a number of cells where each cell is responsible for processing the family of similar parts. Another important aspect of cell formation is worker assignment to cells. Since operators work together in long periods, it is suggested to consider operators’ personal characteristics to increase their satisfaction and the productivity of system. This paper considers decision-making styles of operators (as an index of operator’s personal characteristics) and presents a new mathematical programming model for clustering parts, machines and workers simultaneously. The model includes two objectives; (1) minimization of intracellular movements and cell establishment costs, (2) minimization of decision-making style inconsistency among operators in each cell. The paper applies ε-constraint method for solving the problem and gathering non-dominated solutions such as Pareto optimal solutions. Furthermore, this paper uses common weighted multicriteria decision analysis (MCDA)-data envelopment analysis method to choose the best solution from the candidate Pareto optimal solutions that have been achieved by solving the mathematical model. A real case study is investigated to show the capability of the proposed model to design CMS in the assembly unit. The proposed design assists decision-makers to develop cellular systems with more operators’ satisfaction and productivity.     

Towards a psychologically consistent cellular manufacturing system

In cellular manufacturing systems (CMSs), an operator plays an important role. Because operators work for long-time periods in a production area, an increase in job satisfaction and system productivity occurs if the consistency of operators’ personal characteristics are considered in the design of CMSs. In a CMS, a cell formation problem (CFP) focuses on grouping and allocating machines, part families and operators to manufacturing cells. This paper considers a decision-making style (DMS) as an operator’s personal characteristic index in a CFP for designing a psychologically consistent CMS. DMS influences not only the interaction between two operators, but also the work that operator does on a machine. Hence, this paper develops a novel multi-objective mathematical model for the CFP considering consistency between each two operators in each cell and consistency between operator and his/her assigned machine(s). Because of possibility of a change in the primary DMS of a person to the backup one, this paper tackles this issue by applying a probabilistic procedure. Two hybrid meta-heuristic algorithms are developed for the large-sized test problems. In addition, the PROMETHEE-II method is applied to select the best Pareto solution. Finally, a real case study is presented to show the applicability of the developed approach.     

n jobs and m machines job-shop problems with sequence-dependent set-up times

This paper presents a mathematical model based on the branch-and-bound technique to solve static scheduling problems involving n jobs and m machines where the objective is to minimize the cost of setting up the machines. Set-up times are sequence dependent and not included in processing times. There is a finite non-zero cost associated with setting the machines which is different for each machine. It is further assumed that the routing may be different for different jobs and a job may return to a machine more than once.     

A hybrid algorithm for total tardiness minimisation in flexible job shop: genetic algorithm with parallel VNS execution

This paper addresses the flexible-job-shop scheduling problem (FJSP) with the objective of minimising total tardiness. FJSP is the generalisation of the classical job-shop scheduling problem. The difference is that in the FJSP problem, the operations associated with a job can be processed on any set of alternative machines. We developed a new algorithm by hybridising genetic algorithm and variable neighbourhood search (VNS). The genetic algorithm uses advanced crossover and mutation operators to adapt the chromosome structure and the characteristics of the problem. Parallel-executed VNS algorithm is used in the elitist selection phase of the GA. Local search in VNS uses assignment of operations to alternative machines and changing of the order of the selected operation on the assigned machine to increase the result quality while maintaining feasibility. The purpose of parallelisation in the VNS algorithm is to minimise execution time. The performance of the proposed method is validated by numerical experiments on several representative problems and compared with adapted constructive heuristic algorithms’ (earliest due date, critical ratio and slack time per remaining operation) results.     

Multi-objective fuzzy parallel machine scheduling problems under fuzzy job deterioration and learning effects

This paper investigates a multi-objective parallel machine scheduling problem under fully fuzzy environment with fuzzy job deterioration effect, fuzzy learning effect and fuzzy processing times. Due dates are decision variables for the problem and objective functions are to minimise total tardiness penalty cost, to minimise earliness penalty cost and to minimise cost of setting due dates. Due date assignment problems are significant for Just-in-Time (JIT) thought. A JIT company may want to have optimum schedule by minimising cost combination of earliness, tardiness and setting due dates. In this paper, we compare different approaches for modelling fuzzy mathematical programming models with a local search algorithm based on expected values of fuzzy parameters such as job deterioration effect, learning effect and processing times.     

Cash management in single and parallel machine scheduling

Traditional scheduling problems are usually focused on minimising time-based objectives. In this paper, we have examined the problems in single and parallel machine scheduling. We have incorporated cash management into the objective function of these problems. It is assumed that processing a given job involves incurring a total cost and receiving a total revenue. Each job also has its own temporal pattern of cost incurring and revenue receiving. Nonetheless, the total cost/revenue of processing a job is assumed to be incurred/received during its processing and not beyond it. We have defined five new objectives: (i) maximising average available cash; (ii) minimising revenue-cost duration; (iii) minimising average cash deficiency; (iv) minimising maximum cash deficiency; and (v) maximising minimum available cash. Based on the results achieved in this paper, the above patterns do not affect the optimal scheduling policy in regards to the first two objectives. For single machine models, all except one of the problems are solved in polynomial time. For parallel machines, all models are proved to be NP-hard. Some of the NP-hard models are convertible to equivalent traditional ones.     

Multi-objective cell formation and production planning in dynamic virtual cellular manufacturing systems

This article presents a fuzzy goal programming-based approach for solving a multi-objective mathematical model of cell formation problem and production planning in a dynamic virtual cellular manufacturing system. In a dynamic environment, the product mix and part demand change over a planning horizon decomposed into several time periods. Thus, the cell formation done for one period may be no longer efficient for subsequent periods and hence reconfiguration of cells is required. Due to the variation of demand and necessity of reconfiguration of cells, the virtual cellular manufacturing (VCM) concept has been proposed by researchers to utilise the benefits of cellular manufacturing without reconfiguration charges. In a VCM system, machines, parts and workers are temporarily grouped for one period during which machines and workers of a group dedicatedly serve the parts of that group. The only difference of VCM with a real CM is that machines of the same group are not necessarily brought to a physical proximity in VCM. The virtual cells are created periodically depending on changes in demand volumes and mix, as new parts accumulate during a planning horizon. The major advantage of the proposed model is the consideration of demand and part mix variation over a multi-period planning horizon with worker flexibility. The aim is to minimise holding cost, backorder cost and exceptional elements in a cubic space of machine–part–worker incidence matrix. To illustrate the applicability of the proposed model, an example has been solved and computational results are presented.     

Optimal job assignment considering operators’ walking costs and ergonomic aspects

The paper deals with the problem of assigning jobs to operators in contexts where the operators are not fixed on a single position, but rotate, by travelling on foot, between different stations. The objective is to jointly consider the need for minimising the operators’ walking costs, expressed as both unproductive times and physiological costs, and the ergonomic risk of the scheduled jobs and their combinations. A new optimisation-based methodology is presented by developing a systematic procedure for input data analysis and an original mixed-integer linear programming model which minimises the cost of walking (or the total metabolic cost) by considering workplace safety and physiological needs. Finally, the proposed optimisation approach has been applied to a case study from the plastic industry. The obtained results allow to draw some interesting conclusions about the impact of ergonomic aspects on the optimal assignment of jobs to operators. Moreover, the importance of reducing unproductive times (i.e. walking times) and, if possible, improving the design of manual tasks (e.g. lifting operations) is highlighted by showing that even small ergonomic investments may lead to significant cost savings.     

An ant colony optimization heuristic for an integrated production and distribution scheduling problem

Make-to-order or direct-order business models that require close interaction between production and distribution activities have been adopted by many enterprises in order to be competitive in demanding markets. This article considers an integrated production and distribution scheduling problem in which jobs are first processed by one of the unrelated parallel machines and then distributed to corresponding customers by capacitated vehicles without intermediate inventory. The objective is to find a joint production and distribution schedule so that the weighted sum of total weighted job delivery time and the total distribution cost is minimized. This article presents a mathematical model for describing the problem and designs an algorithm using ant colony optimization. Computational experiments illustrate that the algorithm developed is capable of generating near-optimal solutions. The computational results also demonstrate the value of integrating production and distribution in the model for the studied problem.     

A hybrid electromagnetism-like algorithm for two-stage assembly flow shop scheduling problem

This paper presents a study on the two-stage assembly flow shop scheduling problem for minimising the weighed sum of maximum makespan, earliness and lateness. There are m machines at the first stage, each of which produces a component of a job. A single machine at the second stage assembles the m components together to complete the job. A novel model for solving the scheduling problem is built to optimise the maximum makespan, earliness and lateness simultaneously. Two optimal operation sequences of jobs are determined and verified. As the problem is known to be NP-hard, a hybrid variable neighbourhood search – electromagnetism-like mechanism (VNS-EM) algorithm is proposed for its handling. To search beyond local optima for a global one, VNS algorithm is embedded in each iteration of EM, whereby the fine neighbourhood search of optimum individuals can be realised and the solution is thus optimised. Simulation results show that the proposed hybrid VNS-EM algorithm outperforms the EM and VNS algorithms in both average value and standard deviation.     

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.     

A method combining rules with genetic algorithm for minimizing makespan on a batch processing machine with preventive maintenance

This paper considers the problem of minimising makespan on a single batch processing machine with flexible periodic preventive maintenance. This problem combines two sub-problems, scheduling on a batch processing machine with jobs’ release dates considered and arranging the preventive maintenance activities on a batch processing machine. The preventive maintenance activities are flexible but the maximum continuous working time of the machine, which is allowed, is determined. A mathematical model for integrating flexible periodic preventive maintenance into batch processing machine problem is proposed, in which the grouping of jobs with incompatible job families, the starting time of batches and the preventive maintenance activities are optimised simultaneously. A method combining rules with the genetic algorithm is proposed to solve this model, in which a batching rule is proposed to group jobs with incompatible job families into batches and a modified genetic algorithm is proposed to schedule batches and arrange preventive maintenance activities. The computational results indicate the method is effective under practical problem sizes. In addition, the influences of jobs’ parameters on the performance of the method are analyzed, such as the number of jobs, the number of job families, jobs’ processing time and jobs’ release time.     

A discrete electromagnetism-like mechanism for parallel machine scheduling under a grade of service provision

We consider the problem of minimising total weighted tardiness on identical parallel machines with grade of service eligibility. Due to the essential complexity of the problem, we apply an electromagnetism-like mechanism (EM), which is a novel metaheuristic, to solve the problem. In the proposed EM, the particle is redesigned to represent a valid assignment of jobs to machines. A distance measure between particles, called ‘1A2B’ distance, is proposed by the concept of a number guessing game. Then, the new attraction and repulsion operators are developed to move a particle to the new particle. To verify the proposed EM, computational experiments are conducted to make a comparison with a recent genetic algorithm (GA). The results show that the proposed EM has a good performance and outperforms the GA for the considered problem.     

Simultaneous scheduling of production and maintenance tasks in the job shop

This paper deals with the job shop problem of simultaneous scheduling of production operations and preventive maintenance tasks. To solve this problem, we develop an elitist multi-objective genetic algorithm that provides a set of Pareto optimal solutions minimising the makespan and the total maintenance cost. A deep study was made to choose the best encoding, operators, and the different probabilities. Some lower bounds of the adopted criteria are developed. The computational experiments carried out on a set of published instances validate the efficiency of the proposed algorithm.     

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.     

Optimization-based manufacturing scheduling with multiple resources, setup requirements, and transfer lots

The increasing demand for on-time delivery of products and low production cost is forcing manufacturers to seek effective schedules to coordinate machines and operators so as to reduce costs associated with labor, setup, inventory, and unhappy customers. This paper presents the modeling and resolution of a job shop scheduling system for J. M. Products Inc., whose manufacturing is characterized by the need to simultaneously consider machines and operators, machines requiring significant setup times, operators of different capabilities, and lots dividable into transfer lots. These characteristics are typical for many manufacturers, difficult to handle, and have not been adequately addressed in the literature. In our study, an integer optimization formulation with a separable structure is developed where both machines and operators are modeled as resources with finite capacities. Setups are explicitly considered following our previous work with additional penalties on excessive setups. By analyzing transfer lot dynamics, transfer lots are modeled by using linear inequalities. The objective is to maximize on-time delivery of products, reduce inventory, and reduce the number of setups. By relaxing resource capacity constraints and portions of precedence constraints, the problem is decomposed into smaller subproblems that are effectively solved by using a novel dynamic programming procedure. The multipliers are updated using the recently developed surrogate subgradient method. A heuristic is then used to obtain a feasible schedule based on subproblem solutions. Numerical testing shows that the method generates high quality schedules in a timely fashion.     

Integrated production scheduling and vehicle routing problem with job splitting and delivery time windows

In this paper, we study a production scheduling and vehicle routing problem with job splitting and delivery time windows in a company working in the metal packaging industry. In this problem, a set of jobs has to be processed on unrelated parallel machines with job splitting and sequence-dependent setup time (cost). Then the finished products are delivered in batches to several customers with heterogeneous vehicles, subject to delivery time windows. The objective of production is to minimize the total setup cost and the objective of distribution is to minimize the transportation cost. We propose mathematical models for decentralized scheduling problems, where a production schedule and a distribution plan are built consecutively. We develop a two-phase iterative heuristic to solve the integrated scheduling problem. We evaluate the benefits of coordination through numerical experiments.     

Minimising total cost for training and assigning multiskilled workers in seru production systems

This paper investigates the multiskilled worker training and assignment (MWT&A) problem of the seru production system (SPS), which is a new type of assembly line configured as multiple assembly cells, or so-called serus. The configuration of the SPS emphasises production efficiency and flexibility, achieved by multiskilled workers (MWs) able to cope with the demand of high-variety and low-volume manufacturing. Well-arranged and trained MWs are viewed as a critical factor when it comes to enhancing the performance of SPSs. This paper studies the MWT&A problem in the SPS with the aim of minimising the total cost, specifically, the workers’ training cost and the balance cost of processing times of the MWs in serus. This study provides an applicable mathematical programming model and designs a two-phase heuristic, named the SAIG algorithm, to effectively and efficiently solve this problem. The performance of the proposed algorithm is demonstrated by a comparison with the state-of-the-art heuristic through a series of computational experiments.     

Iterative algorithms for batching and scheduling to minimise the total job tardiness in two-stage hybrid flow shops

This study considers the batching and scheduling problem in two-stage hybrid flow shops in which each job with a distinct due-date is processed through two serial production stages, each of which has identical machines in parallel. Under the fundamental trade-off that large batch sizes with less frequent changeovers may reduce setup costs and hence increase machine utilisation, while small batch sizes may reduce job flow times and hence improve scheduling performance, the problem is to determine the number of batches, the batch compositions, the allocation of batches to the parallel machines at each stage, and the sequence of the batches allocated to each machine for the objective of minimising the total job tardiness. A mixed integer programming model is developed for the reduced problem in which the number of batches is given, and then, three iterative algorithms are proposed in which batching and scheduling are done repeatedly until a good solution is obtained. To show the performance of the algorithms, computational experiments were done on a number of test instances, and the results are reported. In particular, we show that the number of batches decreases as the ratio of the batch setup time to the job processing time increases.     

Heuristics for minimizing total weighted tardiness in complex job shops

Semi-conductor manufacturing is arguably one of the most complex manufacturing processes in existence today. A semi-conductor wafer fabrication facility is comprised of batching machines, parallel machines, machines with sequence-dependent set-ups, and re-circulating product flow. The individual job release times and due dates combine with the other processing environment characteristics to form a ‘complex’ job shop scheduling problem. We first present a mixed-integer program (MIP) to minimize total weighted tardiness in a complex job shop. Since the problem is NP-hard, we compare a heuristic based on the MIP (MIP heuristic) with both a tuned version of a modified shifting bottleneck heuristic (SB heuristic) and three dispatching rules using random problem instances of a representative model from the literature. While the MIP heuristic typically produces superior schedules for problem instances with a small number of jobs, the SB heuristic consistently outperforms the MIP heuristic for larger problem instances. The SB heuristic's superior performance as compared to additional dispatching rules is also demonstrated for a larger, ‘real world’ dataset from the literature.