This paper presents a new mathematical model to solve cell formation problem in cellular manufacturing systems, where inter-arrival time, processing time, and Machine breakdown time are probabilistic. The objective function maximizes the number of operations of each part with more arrival rate within one cell. Because a queue behind each Machine; queuing theory is used to formulate the model. To solve the model, two metaheurstic algorithms such as modified particle swarm optimization and genetic algorithm are proposed. For the generation of initial solutions in these algorithms, a new heuristic method is developed, which always creates feasible solutions. Both metaheurstic algorithms are compared against global solutions obtained from Lingo software’s branch and bound (B&B). Also, a statistical method will be used for comparison of solutions of two metaheurstic algorithms. The results of numerical examples indicate that considering the Machine breakdown has significant effect on block structures of Machine-part matrixes.

The cell formation (CF) is one of the mostimportant steps in the design of a cellular manufacturingsystem (CMS), which it includes Machines’ grouping incells and part grouping as separate families, so that thecosts are minimized. The various aspects of the problemshould be considered in a CF. The Machine reliability andthe tool assigned to them are the most important problemswhich have to be modeled correctly. Another importantaspect in CMS is material handling costs that they consistof inter-cell and intra-cell movement costs. Moreover, setup and tool replacement costs can be effective in CFdecision making. It is obvious that CF cannot be completedwithout considering the number of demand. With consideringof all of the above aspects, an extended linear integerprogramming is represented for solving the cell formationproblem (CFP) in this study. The objective is to minimizethe sum of inter-cell movement, intra-cell movement, toolreplacement, Machine breakdown, and setup costs. In theother terms, for states that cost of movement is higher thantool-changing cost, although a part can have the inter-and/or intra-cell movements, the model tries to find a solutionwhich part is allocated to one cell and with changing thetools, processes of that part is completed. In addition, tovalidate the model and show its efficiency and performance, several examples are solved by branch and bound(B&B) method.

Most manufacturers use human-Machine systems to produce high-quality products. Dealing with human-Machine systems is very complicated since not only Machines should be utilized in proper condition but also appropriate environment should be provided for human resources. Most manufacturers have a maintenance plan for Machines but many of them do not have a proper work-rest schedule for human resources. Considering this fact, we emphasis on human role in human-Machine systems maintenance and propose a mathematical model that obtains the optimal work-rest schedule for humans based on fatigue-recovery models and the optimal maintenance policy for Machines based on reliability level. The performance of proposed model was examined by some instances and the obtained results indicate this model can provide effective maintenance policy for human-Machine systems.

The fundamental function of a cellular manufacturing system (CMS) is based on the definition and recognition of a type of similarity among parts that should be produced in a planning period. Cell formation (CF) and cell layout design are two important steps in implementation of the CMS. This paper represents a new nonlinear mathematical programming model for dynamic cell formation that employs the rectilinear distance notion to determine the layout in the continuous space. In the proposed model, Machines are considered unreliable with a stochastic time between failures. The objective function calculates the costs of inter- and intra-cell movements of parts and the cost due to the existence of exceptional elements (EEs), cell reconfigurations, and Machine breakdowns. Due to the problem’s complexity, the presented mathematical model is categorized in NP-hardness; thus, a genetic algorithm (GA) is used for solving this problem. Several crossover and mutation strategies are adjusted for GA and parameters are calibrated based on Taguchi experimental design method. The great efficiency of the proposed GA is then demonstrated by drawing a comparison between particle swarm optimization (PSO) and the optimum solution via GAMS considering several small/medium- and large-sized problems.