## 1. INTRODUCTION

Today, production planning is important because of the increasing influence of the role of customers in the production economy as well as the high market demand variability. In fact production planning is the process of planning and controlling the various aspects of all production activities in order to supply customer demand. The purpose of production planning is the best use of human resources and equipment (Zurich, 1975).

Manufacturing systems depending on the pro-duction volume and product diversity can be divided into fixed and process systems, and product and cellular systems (Süer *et al*., 2010). In fixed manufacturing system, product is fixed and equipment and machinery are carried out around the product in order to make the product. In process manufacturing system, machines can be grouped together as stations to perform similar operations. In the type of manufacturing system, machines are on the order of the operation of a particular product that may lead to arrangement in several specific production lines. In cellular manufacturing system (CMS), parts with similar oper-ations are arranged into families, which, are performed by the same machines in each cell, and in the end will be processed (Wemmerlov and Johnson, 1997.( Group Technology (GT) is called a set of techniques whose purpose is to group parts and components of production in order to provide various production needs. In fact, the problem of a CMS is the application of the updated philosophy of GT, which aims to classify parts and machines such that both intercellular and intracellular movements of the parts are minimized. Therefore, one of the most important applications of GT is a CMS (Pinedo, 2012). CMSs are looking for the flexible of manufacturing systems (FMSs) in a workshop and a high efficiency production system (Luong *et al*., 2002). Taking into account the similarity between parts and processes and grouping parts and machinery accordingly provide the basis for optimal design and production (Burbidge, 1975).

The primary goal of a CMS is, like group tech-nology, to classify machinery and components in such a way that the intercellular and intracellular part move-ments minimize, which is the sole purpose of the tradi-tional and primary purpose of this production method and over time, taking into account goals such as operation sequences, multi-period models, alternative production row (Arkat *et al*., 2007), many other assumptions and characteristics of CMSs upgrade and improve.

The advantages of CMS include: (1) Reducing parts handling, (2) reducing equipment, (3) reducing time setup, (4) reduction of acceleration, (5) decrease in the current inventory, (6) decrease in the use of work space, (7) improving operator use, (8) improving expertise and employing human resources. Some of the disadvantages of CMS include: (1) increased investment, (2) Less machine operation (Greene and Sadowski, 1984).

Cell formation, cell layout, and cell scheduling are three important steps that must be considered in the successful design of a CMS. The cell formation involves determining the family of parts and machine cells with the goal of reducing intra-cell handling time. Cell layout design consists of two parts: (1) determining the layout of the cells at the workshop level; and (2) specifying the layout of machines in each cell. Both aimed at reducing the time of displacement, and ultimately, the management of the cell in planning issues such as Cell scheduling. In cell scheduling, the scheduling of the family of components and each individual part is taken into consideration. Relationship among these three decisions play an important role in the design of a CMS (Graham *et al*., 1979).

The issue of a DCMS in which the planning horizon is divided into several dynamic periods (year, month, or week) and demand products at any given time are known to be not necessarily equal to the amount of demand for other courses product demand forecasting methods are usually determined, as the forecast error increases for long period of time, these courses are divided into smaller periods.

In previous studies, many researchers have been focused on the planning of CMSs in the framework of mathematical models. Moreover, the researchers were initially planned CMSs in a static and definitive environment, but with the passing of time and technological progress, many manufacturing organizations were encountered uncertainty in demand for their products. In addition, in today’s competitive world, in most manufacturing organizations, production planning patterns which integrates processes in terms of uncertain demand, and manufacturing organizations require that integration for creating all operational processes in your production cycle. Therefore, CMS was planned in uncertain and dynamic conditions.

Given that the study of the properties of the mathematical models for the design in layout in a DCMS can be useful for researchers in this field, this paper would review the various features of most articles in this regard. These features will be further reviewed improvements and the achievements in the field of mathematical models of CMS and in the final section to present the results, the conceptual model and future suggestions and slots reviews.

### 1.1 Research Design and Method Data Col-lection

The nature of the present research is qualitative. Therefore, the grounded theory method (GTM), which was developed by Glaser and Strauss (1967) in 1961, has been used. In recent years, the systematicity of this method has been taken into consideration in recent years (Nonaka and Konno, 1998). Furthermore, this method has been widely used for analyzing (mainly) qualitative data in the social science field (Goldkuhl and Cronholm, 2010).

In the GTM, there are three main factors comprising concepts, classes, and propositions or arguments to concepts of the main analysis because they result from the conceptualization and understanding of input information (Pandit, 1996). The main classes in this method are latent concepts in the study, the conceptual groups are formed by discovering their relationship with each other. This work up the saturation stage which no longer can be understood or a new article is added (Corbin and Strauss, 1990).

GTM, there are five phases: (1) research plan, (2) information gathering, (3) information organization, (4) information analysis, and (5) comparison of information.

In the method of theoretical development after the organization of information, it has been analyzed by coding, which is one of the most important steps to ex-tract concepts, stripes and theories from information obtained in previous steps.

The coding process is of three types: free coding, axial coding and selective coding free encryption with classification and tagging information creates concepts and classes. So the free encoding of information and class is formed.

In axial coding, the use of information obtained is to develop the main classes, as well as the relationship between them. Selective coding also applies to the class integrity of the theoretical framework, it forms the primary communications between the main classes (Pandit, 1996). Figure 1 shows the general framework of the methodology of GTM.

### 1.2 The Main Research Question

What are the main gaps in the mathematical model of the cell manufacturing system in dynamic conditions?

## 2. DATA ANALYSIS

In this section of the paper, along with all infor-mation obtained from a collection of articles on the mathematical models for the design in a DCMS from the authoritative databases (1996-2017), efforts have been made to extract the main, free coding, axial and selective cod-ing and a conceptual model has been presented.

This study attempted to separate them by free coding, by discovering the differentiation of the issues, and similar ones under a categorized title. By presenting previous articles in the field of DCMS, this study have been attempted to provide a proper theoretical framework. The four main components of mathematical models in previous articles are the objectives, assumptions, constraints and stages for the design of CMS. The design of CMS, its three main components including cell formation, cell layout, cell scheduling, are described below.

The Cell formation is the sorting of parts and machines based on the operations and similarities of production and the formation of the family of components. The cell layout is the selection and design of the machine layout within each cell as well as the layout of the cells optimally or nearly optimally. The cell scheduling is scheduling of the family of parts so that it ends in the shortest possible time of production operations

The goals that have been taken into account in previous studies in the field of DCMS include the maxi-mum use of labor capacity, minimize the total cost of the production system such as cost of handling parts (intra and inter-cell handling), fixed and operating costs of the machine, the cost of the machine relocation, setup cost, machine purchase cost, machines failure cost, reduce unemployment of the machine, production planning cost, internal production, outsourcing, inventory hold, back orders, operator’s costs (hiring, firing, training, salary), intra and inter-cell balance, overtime cost and maximizing operator performance.

The assumptions that were notable in previous research include multiple processing row, multi-skill ma-chines, machine repeats, sequencing operations, multi-disciplinary human, non-demanded (fixed-demand, uncertain demand), re-configuration, multi-period planning. Limitations in these models include cell capacity, machine capacity, time available to labor and social criteria.

In the central coding, the relationship between the main concepts derived from the articles is determined by selective coding, then a theoretical framework has been devised. The following is a follow-up study:

Rheault *et al*. (1996) for the first time in the field of cell manufacturing introduced the concept of dynamics. Results from this study show that a DCMS has the flexibility and efficiency in the technology system increases the group.

Tavakkoli-Moghaddam *et al*. (2005) developed a mathematical model for solve the dynamic cell formation problem. Their proposed mathematical model, in addition to DCMS, machine flexibility and alternative routes and relocation machines are also taken into account. Model objectives include minimizing investment, depreciation, and relocation, operational costs of the machines, intra and inter-cell costs. To solve the model, the lingo software and the Genetic Algorithm, Simulated Annealing Algorithm and Tabu Search Algorithm have been used.

Defersha and Chen (2006) examined the effect of production planning goals on dynamic cell formation. The proposed model goals were to minimize operational costs of machine, reconfigured costs, outsourcing of parts, cost of tools and setup costs, and load balancing of cells. Lingo software is used to solve the model.

Safaei *et al*. (2008) presented a fuzzy program-ming approach for the problem of the cell formation in a dynamic and uncertain condition. In their study, according to the considerations obtained from the dynamic system, a multi-period planning horizon and the combination of demand and product can be varied in each period. Also in production systems, some parameters such as processing time, demand, fixed cost and machine variables per period, the batch of intra and inter-cell handling in each period are fuzzy. The purpose function of the proposed model is nonlinear, and the objectives include determining the optimal configuration of the cell in each period with the maximum desirability of the target fuzzy, fixed and variable costs of the machine, the costs of intra and inter-cell handling.

Defersha and Chen (2008) used the genetic algorithm to solve the math model of the dynamic cell formation. Their model objectives include minimizing intercellular motivation costs, operational costs of machine, cost of outsourcing, intracellular balance. They plan assumptions in the proposed model such as a multi-period planning, reconfiguration, operation sequence and alter-native processing paths.

Ahkioon *et al*. (2009) introduced a more com-prehensive model to design a DCMS. In this model, pro-duction planning and reconfiguration of the system is considered simultaneously. The features considered in this model include the operation sequence, machinery duplicate, machine capacity. This model was validated and solved using the Cplex software.

Safaei and Tavakoli-Moghaddam (2009) pre-sented an integrated math model with a multi-period production planning in a dynamic environment. In this model, the goals include machine reduction, balance of work, intra and intercellular movements, reconfiguration, inventory cost and outsourcing.

Wang *et al*. (2009) examined changes in demand and fluctuations in the business environment, one-period consideration of production cannot be reduced help costs. They presented a mathematical model for the formation of dynamic cells, whose objectives include maximizing the use of machine capacity, configuration reducing the cell, minimizing the cost of the machine relocation and the cost of intracellular material handling, and intracellular bal-ance.

Ahkioon *et al*. (2009) presented a mathematical model for a DCMS. In their proposed model, they sought to minimize the costs of intra and inter-cellular transfers, inventory cost, re-configuration, fixed and variable costs of the machine.

Mahdavi *et al*. (2010) because workers play an important role in working on machines, the assignment of workers to cells is an important step in using the complete a DCMS. Therefore, an integer mathematical model for a DCMS by taking into account production planning and worker allocation has been designed. Multi-period production planning, dynamic system, reconfiguration, duplicate machines, machine capacity, time in workers access and workers assignment are based on model assumptions. Their model goals reduce machine costs (fixed, operational, setup), reduced machine relocation costs and human resource costs (hiring, firing, salary and wage) and intercellular material handling costs, keeping inventory costs, back Order costs.

Deljoo *et al*. (2010) presented a mathematical model for dynamic cell formation and used a genetic algorithm to solve the model. Their proposed model includes the costs of the machinery such as the cost of investment and purchase and depreciation, operating costs such as the cost of processing for production parts, the cost of intra/inter-cell material handling, the cost of machine relocation from one cell to another. Ghotboddini *et al*. (2011) presented a comprehensively model for design and formatin of cells in a dynamic state. They used the bender analysis method to solve the model. They made the proposed model is multi-objective, and its objectives include minimizing fixed and variable costs of the machine, the costs of intra and inter-cell material handling, overtime, salary and labor costs, machine costs, and GAMS software is used to solve the model.

Soolaki (2012) presented a mathematical model for the design of a multi-objective integrated DCMS, which is based on the model of operator allocation and planning production and reconfiguration of cells are also considered the model’s objectives include minimizing the cost of machine relocation, the cost of maintenance and overheads, backorder costs, Costs of outsourcing, Inventory Maintenance, machine purchase, cost salary and wages, the cost of firing and hiring the worker, and the genetic algorithm has been used to solve the model.

Kia *et al*. (2012) presented a group layout design model of a DCMS, and demand varies over different periods in this model, the problem of cell formation and group layout is considered simultaneously. Assumptions such as alternative paths, sequence of operations, time processing, volume of parts production, machine purchase, duplicate machines, machine capacity, intracellular layout, intercellular layout, reconfiguration, Multi-row layout are considered, the model objectives include minimizing the total cost of intracellular and intercellular handing, machine relocation, purchasing new machine, machine overhead, machine processing. To validate the model, the lingo software is used and to optimal solution obtained from the Refrigeration simulation algorithm is used.

Dalfard (2013) presents a new model for DCMS based on the number and length of inter- cell and intra- cell transportation his research goals include minimizing the fixed cost of the purchase of machines and the cost of the machine's operation, the cost of intercellular handling. To solve the model, the simulated annealing algorithm embedded in branch and cut (SAAEBB) has been used that is a method depends on a combination.

Rafiei and Ghodsi (2013) presented a dual-mode mathematical model to the problem of the cell formation in a DCMS. In this model the first goal is to minimize costs (the cost of purchase and moving machinery, variable costs of machinery, the cost of inter- cell and intra- cell, the cost of overtime, and the second goal is to maximize the use of labor. To solve the model, the Ant Colony Optimization (ACO) algorithm and genetic algorithm are used.

Kia *et al*. (2013) presented a novel mixed integer non-linear programming multi- model for designing group layout in DCMS. Integrated decision making in group layout and cell formation was one of the important features of their model. The first goal is to minimize the total costs of intra and inter-cell material handling, machines relocation, purchasing new machines, machine overhead, machine processing.

Kia *et al*. (2014) presented a mixed-integer pro-gramming model for multi-level layout design model for a DCMS. In the proposed model the problem of cell formation and group layout is simultaneously considered in a multi-period planning horizon. The model objectives include minimizing the cost of intra and inter-cell material handling between different floors, machine purchase costs, machine overhead, machine processing and machine relocation, multi-rows layout of equal area facilities in each cell, flexible reconfigurations of cells during successive periods, distance-based material handling cost and machine depot keeping idle machines is based on model assumptions. The genetic algorithm is used to solve the proposed model optimally.

Bagheri and Bashiri (2014) developed a mathematical model for solving the problem of cell formation and the allocation of human resources and the cells layout in a dynamic state. The goal of this study was to minimize inter-cell material handling, the cost of machine relocation, training costs, operators’ hiring and firing costs, operator’s salary and wages.

Deep and Singh (2015) presented a mathematical model for a DCMS to this model, a comprehensive mathematical model is proposed for designing robust machine cells for dynamic part production in which one of the most important features of this model was considered multiple processing routes and incorporates machine cell configuration design problem bridged with the machines allocation problem. The purpose of this model is to minimize machines purchase costs, operating costs, production costs and cost of the intercellular and intracellular movements.

Nouri (2016) by the developing of the Bacteria foraging optimization Algorithm (BFO), presented a model for DCMS and considered issues such as machine assignment, inter/intra-cell material handling, workload balancing based on operational time and operation sequence. The objectives of this model include fixed and variable costs of the machine, the cost of intra and inter- cell transportation, the cost of reconfiguring, cost of outsourcing, delayed cost of service, inventory cost, hiring and firing, salary and wages of workers, after solving with algorithm the proposed Multi-Objective Matrix Based Bacteria foraging optimization Algorithm Traced Constraints (MOMBATCH), the results showed that it hsd a higher efficiency than the genetic algorithm.

Niakan *et al*. (2016a) developed a new multi-objective mathematical model for the Formation of dynamic cells under demand and cost taking account of uncertainty in social criteria. In this study, for the first time, social criteria and social uncertainty conditions are taken into consideration. The objectives of this model are to reduce the fixed and variable costs of the machine, the cost of inter/inter- cell transportation, and the cost of salaries and Wages while maximizing societal issues (e.g. potential machine hazards are minimized, while job opportunities are maximized) and maximizing career opportunities. They used robust optimization theory in model. To solve this model, the non-dominated sorting Genetic Algorithm (NSGA-II) as a meta-heuristic method has been used and the results shows that optimal solution is obtained from the uncertainty mode of all levels.

Niakan *et al*. (2016b) presented a DCMS model with skill-based assignment. In this study, a bi-objective model is considered with taking into consideration of environmental and social criteria. The first goal in this model is to minimize production costs and costs worker while minimizing waste of final production (e.g. Energy, chemicals, raw materials, CO2 emissions, etc.) In this model, limited social criteria are considered. Finally, the combination of MOSA and NSGA-II algorithms has been used to solve this model.

Sakhaii *et al*. (2016) presented a robust optimization model for an integrated DCMS and production planning with unreliable machines. This model, includes features such as dynamic cell formation, intercellular layout, machine reliability, operator assignment, alternative process routings and production planning concepts, intra and inter-cellular transportation, and to counteract the uncertainty of the processing time of parts from the robust optimization approach is used because it can evaluate the system at various levels of uncertainty. The purpose of this research is to minimize the cost of machine failure, the machine relocation, the training of the worker and hiring, the intra-and inter-cellular handling, and the backorder and inventory.

Zohrevand *et al*. (2016) presented a multi-objective model for a DCMS with a stochastic program-ming approach. The first goal of this model is to mini-mize the total cost of machine layout, machine relocation, inter-cell moves, overtime, hiring and firing of workers, moving workers between cells, and the second goal is to maximize the efficiency of the CMS. To solve this model, the Hybrid Tabu Search-Genetic Algorithm (TS-GA) and GAMS software have been used.

Mehdizadeh and Rahimi (2016) presented an integrated model for solving the problem of cell formation in dynamic conditions, taking into account the allocation of operators and the layout inside and intercellular. The objectives of the proposed model include minimizing inter-and inter-cellular displacements and machine displacements, minimizing costs machines and operators, and ultimately maximizing forward flow rates. In order to solve the model after validation of the model, multi-objective simulated annealing algorithms (MOSA) and multi-objective vibration damping optimization (MOVDO) algorithm have been used.

Mehdizadeh *et al*. (2016) used a vibration damping optimization algorithm for solving a new multi-objective dynamic cell formation problem with workers training. In the model presented assumptions and constraints such as reconfiguration, multi-period production planning, sequencing operations, alternative routes, flexibility of operators and machines, machine capacity limitations and machine repeat, availability time constraints operators have been used. The purposes that are considered in the model include minimizing intra and inter-cell costs, Costs of reconfirming the machine and removing and adding the machine, the cost of set up, the cost of production planning (inventory, shortage, Outsourcing, the cost of firing , hiring, training and salary of workers and, finally, minimizing unemployment of machinery. Given that the proposed model is NP-hard, to solve the model, the multi-objective evolutionary algorithms (MOEA) of NRGA and NSGA-II and Movdo is used.

Delgoshaei *et al*. (2016) presented a multi-period scheduling scheme for a DCMS in spite of uncer-tain costs. Purposeful functions this model involves re-ducing the costs of installing, operating, purchas-ing/removing machinery and the cost of planning re-production, outsourcing costs, sentence represents backorder costs, the cost of intra/inter-cell material transport. The costs mentioned in the proposed model have an inflation rate that causes inflation uncertainty in costs.

Bayram and Şahin (2016) introduced a comprehensive model for DCMS and sought to minimize internal displacement, and inter-cell materials, re-configuring, fixed and variable costs of a machine. Expenditures that are considered in the model include machine reps, machine capacity, operational sequence, Alternate Paths. To optimize the model, refrigeration simulation algorithms of SA and GA have.

Azadeh *et al*. (2017) designed a DCMS with taking into consideration of human factors and which developed by two meta- heuristic algorithms of NSGA-II and MOPSO, as optimal solution for the proposed model. In this model, the human factors are considered in terms of reliability and decision-making process in the model. The objectives of this model are to minimize the total costs such as fixed and variable machine cost, purchase cost, second-hand machine sales income, machine failure costs, re-configuration cost, the cost of intra and inter-cell material handling, human resources costs such as training to increase operators’ skills, minimizing non-compliance of the operators and the system, minimizing the difference between the percentage of use of all operators in the whole system and the percentage of their use in each the cell.

## 3. THE CONCEPTUAL FRAMEWORK

As described above, by analyzing the data col-lected from the previous review of the DCMS using the GT method, main concepts have been extracted, while coding is free, axial and selective, a conceptual frame-work is emerged Figure 2.

The core of the conceptual framework is the design steps, consisting of three parts of cell formation, cell layout, and cell scheduling. In addition to the core of the conceptual framework, limitations and assumptions is fully described in the previous sections. Finally, beside the design of the three parts of the design steps, the limi-tations and assumptions will be achieved by the objec-tives of the model. The point to be noted is that a re-searcher can use the research and models presenting on a number of objectives, assumptions, constraints, and design steps of the conceptual framework should be focused on them used in his research.

Regarding the past review of DCMS, the goals, assumptions and limitations of the mathematical models presented since the year 1996 to 2017, which is fully described in Figure 2. For further assistance to researchers in future studies, a summary of the review of the literature is in the Table 1.

## 4. DISCUSSION AND CONCLUSION

DCMS is one of the most up-to-date and effi-cient manufacturing systems of today. This system at-tempts to categorize machines and similar parts of the production cells (CF) to minimize intracellular travelling and correct cell alignment (CL) of one attempt to reduce intercellular travelling, therefore, the position of the cells and their distance from each other when forming the CMS is important. In the cell scheduling (CS), the timing of the family of parts and each individual part is considered, so the connections between these three decision making (CF, CL, CS) plays an important role in the design of a CMS. The point is the dynamic debate. Due to the extreme changes that occur in production technology, a static CMS model has been considered. It can create problems in facing real world issues. Therefore, the problem is considered under dynamic conditions.

In the present study, using grounded theory (GT) method, the previous research on DCMS was discussed. This method uses three steps encoding (free, axial, and selective), and attempts were made to extract the most important information from the review of previous arti-cles. In free encoding, the distinction between issues identified and information was categorized. In the axial coding, we tried to find the link between the discovered objects in the previous step and in ultimately, using selective coding, the class integrity that forms the theoretical framework is also addressed.

From the review of previous research, using the GT method approach to the critical gap in mathematical models of a DCMS, it can be noted that despite the importance of communication between the three phases (CF, CL, CS) of the design of a DCMS, previous researchers have only developed one or two stages of the design of a DCMS as a gap in the design of a DCMS, DCMS design can be ignored at the same time.

In order to obtain an optimal solution, in addi-tion to solving the model by the gams and lingo software, researchers have used heuristic and meta-heuristic algorithms that are effective. Over time, the dimensions of the models presented for DCMS have increased in previous research, which has led to NP-hardation of models which makes use of the heuristic and meta-heuristic algorithm to solve the model. Special attention of researchers in past research has been to workforce and issues such as (hiring, firing, training, and salary and labor costs) and costs related to the machine in a DCMS. But the goals and assumptions that are less widely considered in the past are: Maximum use labor, maximum use of car capacity, cost of failure, depreciation and setup of machinery, production planning, balancing inter-cellular work, uncertain demand, multipurpose machine, multi-skill labor, ma-chine repeat, cell and machinery reconfiguration.

Future studies and comprehensive DCMS mod-els are suggested for researchers to focus more on cell scheduling (CS) and they attempt to provide a compre-hensive DCMS model taking into account all three design steps (CF, CL, CS). Also, due to a wide range of issues related to human resources other different dimensions, such as work teamwork, labor skills, optimal number of human resources, and multiple assignment machines can be considered for an operator, etc. Furthermore, the goals and assumptions that are less widely considered in previous research put up. In order to solve the optimal proposed models in future studies, it is suggested that by studying the heuristic and meta-heuristic algorithm used in previous studies, the proposed new algorithms for solving the model would yield better results.