vahidreza ghezavati

Logistics in upstream oil industry is a critical task as rigs need consistent support for ongoing production. In this paper, a multi-period, multi-product and multi-hub routing and scheduling model is presented for offshore logistics problem. As rigs can be served in specific time intervals, time windows constraints are considered in the proposed model. Despite classic VRP models, vessels are not forced to return hubs at the end of duty days. Also, a vessel may leave and return back to hubs several times during the planning horizon. Moreover, the model determines which vessels are applied in each day. In other words, a vessel may be applied in some days and be inactive in other days of planning horizon. To develop a compromise model, fueling issue is considered in the model. As a rig can be supplied by different vessels in real world cases, the proposed model is split delivery. Based on these challenges and contributions, this research deploys an integrated optimization of routing and scheduling of vessels for offshore logistics. This paper deals with a combinatorial optimization model which is NP-hard. Hence, Genetic Algorithm is applied as the solution approach. The average gap between objective functions of GAMS and GA is only 1.18 percent while saving CPU time in GA is much more than GAMS (about 78.16 percent on average). The results confirm the applicability and efficiency of the GA.

Airlines try to reduce costs by improving the quality of their operational schedules. However, numerous uncontrollable factors make disruptions inevitable. A flight delay or cancellation caused by disruption may spread throughout the network and increase the operational costs by affecting the schedule of other flights, including aircraft, crew, and passengers’ itineraries. While previous researchers have focused on one of these aspects or sequential approaches, the resulted solutions cannot lead to a reliable operational solution due to the complex relationships between these factors in practice. Therefore, integrated recovery approaches are highly essential. The main objective of this research is to provide a fully integrated recovery model that contains various recovery scenarios to tackle the disruption and delay propagation with more flexibility and acceptable solution time. So, an integrated model for crew, aircraft, and passenger recovery problem is proposed in this paper. The proposed model is formulated as MILP, based on individual flight legs to achieve a more accurate schedule with better recovery solution. Options such as aircraft reassignment, crew swapping, reassignment of passengers, and ticket refunds are considered as alternatives to face disruption. Moreover, the considerations related to crew rest-time and maintenance requirements are also included in the model. Due to the NP-Hard nature of the problem, the Genetic algorithm is used as the solution approach successfully for the real-world data to limit delay propagation on various random flights.

A new mixed-integer multi-objective mathematical model is developed to optimize sustainable inventory-routing decisions in products agri-chain. The first aim is to optimize the network total revenue besides noticing logistics decisions related to the distribution and collection of perishable products. Also, the economical, social and environmental factors have been integrated in the proposed model. The first objective function considers some traditional terms and novel issues (e.g., postharvest biological behavior of agricultural products), which is related to deviation from ideal quality (customer's dissatisfaction) and the costs of expired products. Because old products have significant environmental impacts and require recycling, the reverse logistics framework is used to collect and bring products back to recycling. A function is applied to compute the level of deviation from suitable maturity and customer's dissatisfaction costs. A numerical example is analyzed to indicate the model's applicability by applying the ε-constraint methodology to show the opposite pattern between the two objectives. Results show that a lower level of accidents leads to lower revenue or higher costs of the supply chain. Remarking the NP-hardness of the presented model, two multi-objective meta-heuristic algorithms, namely the Non-dominated Sorting Genetic Algorithm (NSGA-II) and Multi-Objective Dragonfly Algorithm (MODA) are used to explore near-optimal solutions for medium and large-sized problems. Results show a better performance of the NSGA-II. Furthermore, the sensitivity analysis is presented and explained in four parts to show the trend of the proposed model by fluctuations on important parameters.

The purpose of this paper is to identify and classify the main factors implementing the Cloud Manufacturing Systems (CMS) in the internet service providers company by Fuzzy Cognitive Map (FCM) methodology. Through expert opinions, 20 main factors were identified and classified based on the importance and then a FCM approach was applied for obtaining the relationship between the factors, and all of the impact factors are outputs of expert opinion. The outcomes of the study highlighted those three factors, including customer scoring, R&D, and method development were the most important factors impressing the implementation CMSs. Present practices for implementation CMS are and the relationship between the main factors also impressing CMS by employing the FCM approach in the Iranian internet service provider company. The model obtained in this study guides the managers to identify and classify the important factors of the cloud manufacturing and finally implement it successfully.

At the time of natural disasters occurrence, prompt responding and providing required items to affected areas is the most urgent priority. Moreover, given a stochastic nature of the crisis severity and the number of the affected areas,effective planning is a crucial task. In this study, two major steps in the disaster management cycle,namely preparation and response phases, are formulated using a multi-objective mathematical model under uncertainty. In the preparation phase, the optimum location of relief distributions, medical centers and inventories of relief goods to storage items received from suppliers are determined. Also, in the second step or response phase, the amount of relief goods transported from supply points to relief distribution centers and from these centers to affected areas as well as the number of injured people transferred to medical centers and hospitals through ambulances and aerial transportationare determined. Moreover, regarding the problem nature, its key parameters (e.g., demand and the number of injured people) are considered to be uncertain. Furthermore, given that the failureof facilities in both supplier and distributor sections can adverselyaffect their service provision, this issueisconsidered in the model. To efficiently solve the model, the non-dominated sorting genetic algorithm II (NSGA-II) and the multi-objective grey wolf optimizer (MOGWO) areused. Comparison of the results obtained from the proposed meta-heuristics with the exact solution method indicates that these algorithms can provide acceptable solutions in a reasonable amount of computational time.

One of the goals of financial institutions is to strengthen the economic infrastructure in developing the financial sphere. In this regard, financial institutions should take the necessary planning to increase their incomes, and if they do not pay attention, the consequences can be predicted for this group of economic activists Increasing income and reducing the risk of bankruptcy are among the most important goals for financial institutions and enterprises. Therefore, considering the increase of income and the integration approach based on the selection of partners in the field of banking, this paper presents a mathematical model based on reducing the risk of bankruptcy. The multi-objective genetic algorithm method has been used to solve and optimize the model. The proposed method was implemented on real data related to ten Iranian banks and the results led to the formation of a financial firm with a combination of banks to maximize the income and minimize the bankruptcy risk.

We aim to plan better scheduling for movement of shuttle trains on the single-line route of inter-city railway network to decrease the delays due to the trains blocking in successive crowded stations. A MINLP model is examined to increase capacity efficiency of the stations using the queuing theory considering blocking. We propose an optimal schedule for moving trains which minimizes the blocking probability to raise the profit gained on a two-way railway. The results show that we have achieved the best scheduling with lowest delays considering the constraints of the track number inside stations. Queuing models are applicable because the trains’ departure scheduling can be evaluated with the aid of the performance criteria obtained by the queuing model. To validate the model, an optimal schedule is proposed for a real case-study in Iran. Finally, the benefits of the model and sensitivity analysis are conducted using GAMS v24.9.1, with BARON solver.

Crisis is an inevitable fact of the human’s life. Fortunately, science and technology development has highlycontributed to the reduction of losses and casualties, but it has not reduced the happenings or damages to zero.Crisis management is mentioned as one of the most important scientific-practical issues nowadays that everycountry stray toward it. This paper targeted the response phase of crisis management that is considered as the mostimportant crisis management phase. The basic operations such as relief and rescue, evacuation of the injured andvictims, and relief commodities distribution are carried out in this phase. In this study, the locating of temporarydepots and routing of vehicles were taken into account by considering the reliability of the roads and allocatingthe distribution centers. The model is multi-objective and aimed at achieving the following goals: 1) Minimizingthe maximum shortage of the disaster points. 2) Minimizing the maximum time of the vehicles by considering thevelocity and normal speed of vehicles. The proposed method augmented Epsilon Constraint generalized modelfor Case study in Sichuan, China. The results showed the effectiveness and applicability of the proposed modelwas reliable for product distribution centers and making decisions about allocation and assignment of temporaryaccommodation centers in different parts of logistics network in conditions of crisis .

In this study, we aim to present a new model for the resource-constrained project scheduling problem (RCPSP) considering a working calendar for project members and determined the skill factor of any member using the efficiency concept. For this purpose, the recyclable resources are staff resources where any person with multiple skills can meet the required skills of activities in a given time. Then, considering uncertainty condition for parameters, it provided a fuzzy scheduling model and validated models by solving different examples. The proposed mathematical programming model optimizes the allocation of limited resources to project activities for scheduling purposes in an essential activity in the real condition of scheduling problems. Moreover, the proposed model can decrease the risk of deviation from scheduling by allocating members with higher skill factors to critical activities. Then, considering uncertainty condition for parameters, it provided a fuzzy scheduling model and validated models by solving different examples. Considering fuzzy conditions for the calendar of the project and multi-skill operators are firstly considered in this paper. Also, the recyclable resources are staff resources which are being considered for the model concurrently in response to the risks of availability to resources and delay in completing the project under uncertainty. The results derived from the model solved by CPLEX indicated a decreased need for employment and shortened project completion duration. Assuming the uncertainty of available resource capacity at any time, the results obtained from the fuzzy model for the value of objective function were evaluated under the influence of the resource calendar and showed the benefits. Effect of the multi-skill members with calendar constraints on the model is tested, and the advantages are determined.

Banking is one of the main components of any system and government, and proper management and proper promotion are one of the key factors in the country's economic growth. Banks are exposed to multiple risks as well as lack of control over bank charges; in this regard, appropriate strategies have to be adopted to improve banks' performance in this regard. One of these methods is the selection of partners to divide and reduce risk and share costs, so that they can reduce the Insolvency Risk of Banks and reduce the bank's share of cost control and lead to the bank's growth in financing and ultimately, economic growth in the country. In this research, a multi-objective model for selecting partners in the field of banking has been presented and further optimized using a multi-objective genetic algorithm.In this research, a multi-objective model for selecting partners in the field of banking has been presented and further optimized using a multi-objective genetic algorithm.

A Cellular Manufacturing System (CMS) is the practical use of Group Technology (GP) in a production environment, which has received attention from researchers in recent years. In this paper, a mathematical model for the design of a cell production system is presented with consideration of Production Planning (PP). Consideration of environmental factors such as energy consumption and waste generated by machines in the proposed model is considered. Also, the problem of scheduling component processing in the presented model has been considered. Due to the complexity of the model presented in this paper, a hierarchical approach is proposed for solving the model. At first, the proposed model is analyzed without considering the scheduling topic using the GAMS software and the results are analyzed. Then an Imperialist Competitive Algorithm (ICA) was used to solve the scheduling problem. To evaluate the performance of the proposed model, numerical examples are used in small, medium, and large dimensions. In addition, the ICA presented in this paper is compared with the methods available in the literature as well as the genetic algorithm and its quality is confirmed.

Stochastic flexible flow shop scheduling problem (SFFSSP) is one the main focus of researchers due to the complexity arises from inherent uncertainties and also the difficulty of solving such NP-hard problems. Conventionally, in such problems each machine’s job process time may encounter uncertainty due to their relevant random behaviour. In order to examine such problems more realistically, fixed interval preventive maintenance (PM) and budget constraint are considered.PM activity is a crucial task to reduce the production efficiency. In the current research we focused on a scheduling problem which a job is processed at the upstream stage and all the downstream machines get busy or alternatively PM cost is significant, consequently the job waits inside the buffers and increases the associated holding cost. This paper proposes a new more realistic mathematical model which considers both the PM and holding cost of jobs inside the buffers in the stochastic flexible flow shop scheduling problem. The holding cost is controlled in the model via the budget constraint. In order to solve the proposedmodel, three hybrid metaheuristic algorithms are introduced. They include a couple of well-known metaheuristic algorithms which have efficient quality solutions in the literature. The two algorithms of them constructed byincorporationof the particle swarm optimization algorithm (PSO) and parallel simulated annealing (PSA) methods under different random generation policies. The third one enriched based on genetic algorithm (GA) with PSA. To evaluate the performance of the proposed algorithms, different numerical examples are presented. Computational experiments revealed that the proposed algorithms embedboth desirable accuracy and CPU time. Among them, the PSO-PSAП outperforms than other algorithms in terms of makespan and CPU time especially for large size problems.

A project portfolio is a crucial decision-making process used to prepare an optimum collection of vast alternative projects. In most of the previous modeling methods, the focus is directed towards maximizing project efficiency and so, the role of risky aspects in selecting appropriate projects has been neglected. This paper presents an integrated multi-objective mathematical programming (MOMP) based on efficiency-risk for selecting a project portfolio using various techniques including data envelopment analysis (DEA), risk priority number (RPN) and non-dominated sorting genetic algorithm (NSGA-ΙΙ). The proposed model can support both the capability to nominate mutually exclusive projects (conflicting projects that only one of them can be done) or any type of predecessor projects (doing a project depends on another project) and concurrent projects (need to be done at the same time) selection. Another advantage of the model is that the hyper heuristic solutions can be found in the form of several non-dominated cases and it is possible for organization’s experts to choose the best and the most suitable solutions.  In the competitive world, intelligent optimum decision making is a vital task in the success of large systems. Due to lack of resources, it is not always possible to fully evaluate all proposed developmental projects. In this context, it is important to make an optimal portfolio of desired projects. The present article aimed to identify an applied methodology for the selection of project portfolios with regard to efficiency and risk assessment and the alignment of the projects’ purposes with the organization’s goals, while also considering the existing resource limitations and regarding risk as a main indicator. The efficiency of the projects is examined with regard to the resources used. The present paper seeks to respond to the following main questions:ü  How can an optimal project portfolio be selected for an organization with maximum efficiency and minimum risk?
ü  Does project risk assessment in view of the two criteria of impact and probability sufficiently address the economic conditions and the complexity of the projects in the majority of research and development projects?
ü  What is the drawback of current risk assessment methods for project portfolios?
Responding to these questions can help organization managers select optimal project portfolios and achieve their strategic organizational objectives. Many studies have been conducted on the selection of project portfolios and most of them follow a qualitative and quantitative approach and use combination classification. One of the applied studies conducted on project selection is by Eilat et al. , (2008), in which projects were selected within the combinational framework of DEA and a balance score card was used to select proper research and development projects (Tahri, 2015) presented two numerical methods for mathematical optimization problems for both single and multiple objectives using two values (0 and 1) as the decision variable. (Huang et al. , 2016) discussed the joint problem of optimal project selection and scheduling in situations when the projects’ initial outlays and net cash inflows are determined by experts’ estimates due to the lack of historical data. A literature review reveals that there are a lot of optimization models available to prepare project portfolios. Most of them have one objective function to maximize project benefits or to minimize operating costs subject to operational constraints. In most modeling methods, the role of risk aspects in selecting appropriate projects has been neglected. A few of them have explored the aspect of model constraints. In other words, in the past, the main focus is directed towards economic projects while the sustainable factors (e. g. , environmental and social risks) have been neglected. For this purpose, this study presents an integrated MOMP based on efficiency-risk for selecting a project portfolio using various techniques including DEA, RPN and non-dominated sorting genetic algorithm (NSGA-ΙΙ). Step1) Preparing a list of candidate & feasible projects
Step2) Calculating efficiency of each project by using the DEA Step3) Calculating the risk priority number for each project
Step4) Developing a MOMP model to select the best projects
Step5) Solving the model using a Non-dominated Sorting Genetic Algorithm ΙΙ (NSGAΙΙ) One of the main advantages of NSGAII is that the at-hand solutions can be found in the form of several non-dominated cases and therefore, it is possible for organization’s experts to choose the best and the most suitable solutions. Stated differently, the expert’s knowledge and viewpoints can be considered due to flexibility and availability of different solutions. Besides, it is feasible to compute the adjusted efficiency and to select the solution (s) producing the maximum efficiency as the final optimal answer (s). This article used the concepts of DEA, RPN, MOMP and NSGAII modeling to propose an applied methodology for extracting an optimal portfolio of projects. In other words, we suggest the use of a Non-dominated Sorting Genetic Algorithm ΙΙ as a solution method for the presented multi-objective model in order to deduce the optimal projects portfolio. By comparing the results for the proposed algorithm and existing methods, it was concluded that the previous methods can give portfolio of projects with suitable profit but these solutions face high risk and low reliability. Thus, such solutions are not acceptable by managers in organizations. The lack of attention to risk aspects leads to the non-realization of the estimated profit due to high probability of risk. Therefore, the valuable resources will be wasted. Whereas, by adjusting profit with the risk numbers, it is indicated that the profit gained by our method is so better and higher than previous methods after risk. This can indicate novelty, applicability, and performance of our method.
References
Eilat, H. , Golany, B. & Shtub, A. (2008). R&D project evaluation: An integrated DEA and balanced scorecard approach. Omega, 36, 895-912.
Huang, X. , Zhao, T. & Kudratova, S. (2016). Uncertain mean-variance and mean-semivariance models for optimal project selection and scheduling. Knowledge-Based Systems, 93, 1-11.
Tahri, H. (2015). Mathematical Optimization Application in Project Portfolio Management. Procedia-Social and Behavioral Sciences, 210, 339-347.

Large-scale projects often have several activities which are performed by subcontractors with limited multi-resources. Project scheduling with limited resources is one of the most famous problems in the research operations and optimization cases. The resource-constraint project scheduling problem (RCPSP) is a NP-hard problem in which the activities of a project must be scheduled to reduce the project duration. Therefore, subcontractors of the construction projects join together to decrease the project time and finally increase the project profit. This is an incentive for the subcontractors to form coalitions. This study presents a model based on the resource leveling problem. Results of the proposed model show that the subcontractors can earn more profit by the cooperation rather than working individually. Moreover, it is demonstrated that techniques such as the Shapley Value, Max-Min Core, and Equal Profit Method are able to fairly allocate extra profit of the cooperation among the subcontractors.

One of the most important problems facing distribution companies is to find the best locations for depots and also proper routes for transportation vehicles in order to optimize their supply network. This study aims to examine the problem of location-routing for post offices in Tehran. To achieve this, a bi-objective location-routing problem is proposed. In order to make the problem more realistic, time constraints are taken into account. A suitable solution procedure on the basis of customized goal programming is developed to solve the proposed model. The proposed model and solution procedure are applied in post offices in Tehran, Iran. The results of proposed model show considerable savings in time and cost of planning in comparison with the current planning in the case. The proposed model can be applied in other cases such as location of garbage bins in city and routing of collecting vehicles. Other significant parameters in urban planning can be considered as uncertainty in this model in the future research. This model can be customized for whole of Iran and therefore, meta-heuristic methods can be used to solve the instances in large scale

The purpose of this research is to present a new mathematical modeling for a vehicle routing problem considering concurrently the criteria such as distance, weight, traffic considerations, time window limitation, and heterogeneous vehicles in the reverse logistics network for collection of expired products. In addition, we aim to present an efficient solution approach according to differential evolution (DE) procedure to solve such a complicated problem. By using mathematical modeling tools for formulating the environmental sensitivities in vehicle routing problems, the reverse logistics must be managed according to criteria such as cargo weight carried by the vehicle, the vehicle speed and the covered distance by the vehicle. This leads to optimization and reduction of transportation fuel consumption and hence reduction of air pollution and environment concerns. This concept has led to creation and study of the green vehicle routing problems in this paper.Numerical analysis indicates that performance of the proposed DE algorithm can be validated in terms of CPU run time and optimality gap for solving the proposed model. Furthermore, sensitivity analysis show that extending maximum travelling distance by each vehicle, and increasing capacity of vehicles lead to reduction of total cost in the problem.

The optimal routing for transferring the wounded and relief assistance is a major problem in the event of a crisis. At this time the importance of two factors, namely time and money, in order to help and rescue the injured is doubled. This paper aims to find the most optimal route from a rescue center to the crisis center. The presented mathematical model aims to minimize the time and cost of accessing a crisis center. We also consider some assumptions, such as multiple storages, multiple paths, multiple scenarios, split delivery, multiple products, heterogeneity of the vehicles and time. Given that the values of some parameters, such as demand and time of the travel are uncertain, in which we state them in respect to the former mentioned assumptions. Considering these parameters uncertain makes them closer to the real problem. Most of the issues raised in this field have not considered all assumptions at the same time and they have considered the mentioned parameters (time and demand) as definitive. Finally, in order to find accurate answers regarding to multiple objectives of the model and different phases of parameters (i.e., time and demand), we use ε-constraint method in small-scale problems. Then because this problem is NP-hard, two meta-heuristic algorithms, namely MOHS and NSGA-II, are used to solve 15 issues large-scale problems. The results numerically show that both algorithms have high potential in producing good solutions at the right time and they are used to solve the largest and most complex issue in less than 480 seconds. This model is very suitable and uncertain with multiple objectives.

One of the most important problems for distribution companies is to find the best locations for depots and to find proper routes for transportation vehicles and to optimize supply network. This study intends to develop a model for the problem of location-routing in post offices. So, a new Bi-Objective Location-Routing Problem for Locating Town Post Office and Routing Parcels is defined. This problem is modeled through mixed-integer mathematical programming. The aim of proposed model is to select potential post offices and to find optimal routes for transportation vehicles while time constraints are taken into account. The proposed model is applied in a real case study including eight main post area and 21 regional offices in Tehran, Iran. A goal programming approach is proposed to solve this bi-objective optimization model. The GAMS Software is used to code and solve the associated mathematical model. Some required parameters of the model such as demands are estimated using Geographical Information System (GIS) and simulation methods. The results of proposed model including the objective functions, decision variables, and proposed routing of vehicles have been compared with the existing practical solutions. Sensitivity analysis on main parameters of proposed models is accomplished and the results are analyzed. This comparison illustrate the efficacy and applicability of proposed approach.

Strategic decisions in a supply chain are the most important decisions for petroleum production systems. These decisions, due to high costs of transportation and storing, are costly and affected by the tactical and operational decisions in uncertain situations. In this article, we focus on designing a downstream segment for a supply chain of petroleum production systems. For this purpose, we will propose a two- stage approach considering a hierarchical structure, including the mathematical optimization model for determining strategic decisions in a leader problem and a simulation model for determining tactical and operational decisions in a follower problem. In the first stage, strategic decisions are made by solving a new mathematical model to obtain the location of depots and their capacities, transportation facilities, the volume of annual production, annual flow from refinery to depots and from depots to markets regions. In the second stage, we face some queuing systems where we aim to determine the number of loading and unloading platforms and order volume. Finally, the proposed model is applied in a real-world problem. The results show the suitable performance of the proposed model.

Closed Loop production systems attempt to economic improvement, deliver goods to customers with the best quality, decrease in the return rate of expired material and decrease environmental pollution and energy usage. In this study, we solve a multi product, multi-period closed loop supply chain network in Kalleh dairy company, considering the return rate under uncertainty. The objective of this paper is to develop a supply chain model including raw material suppliers, manufacturers, distributors and a recycle center for returned products. Solving this model helps us to make a good decision about providing materials, production, distribution and recovery. Our basic goal is to estimate optimum return rate of some products such as yoghurt, to production cycle. Once the products pass of their shelf life, they are returned to production cycle. For this study, we develop a linear programming model with a consideration of chance constraints. Finally, this model is implemented by Lingo software with using real data. The obtained results by our model show 9.5 % decrease for total cost in comparison with the current status.

In many practical distribution networks, managers face significant uncertainties in demand, local price of building facilities, transportation cost, and macro and microeconomic parameters. This paper addresses design of distribution networks in a supply chain system which optimizes the performance of distribution networks subject to required service level. This service level, which is considered for each arbitrary request arriving at a distribution center (facility), has a (pre-specified) small probability of being lost. In this mathematical model, customer’s demand is stochastic that follows uniform distribution. In this model, inter-depot transportation (transportation between distributions centers (DCs)), capacities of facilities, and coverage radius restrictions are considered. For this restriction, each DC cannot service all customers. The aim of this model is to select and optimize location of plants and DCs. Also, the best flow of products between DCs and from plants to DCs and from DCs to customers will be determined. The paper presents a mixed integer programming model and proposed an exact solution procedure in regard to Benders’ decomposition method.

An integrated model considers all parameters and elements of different deficiencies in one problem. This paper presents a new integrated model of a supply chain that simultaneously considers facility location, vehicle routing and inventory control problems as well as their interactions in one problem, called location-routing-inventory (LRI) problem. This model also considers stochastic demands representing the customers’ requirement. The customers’ uncertain demand follows a normal distribution, in which each distribution center (DC) holds a certain amount of safety stock. In each DC, shortage is not permitted. Furthermore, the routes are not absolutely available all the time. Decisions are made in a multi-period planning horizon. The considered bi-objectives are to minimize the total cost and maximize the probability of delivery to customers. Stochastic availability of routes makes it similar to real-world problems. The presented model is solved by a multi-objective imperialist competitive algorithm (MOICA). Then, well-known multi-objective evolutionary algorithm, namely anon-dominated sorting genetic algorithm II (NSGA-II), is used to evaluate the performance of the proposed MOICA. Finally, the conclusion is presented.

Clustering parts and machines into part families and machine cells is a major decision in the design of cellular manufacturing systems which is defined as cell formation. This paper presents a non-linear mixed integer programming model to design cellular manufacturing systems which assumes that the arrival rate of parts into cells and machine service rate are stochastic parameters and described by exponential distribution. Uncertain situations may create a queue behind each machine; therefore, we will consider the average waiting time of parts behind each machine in order to have an efficient system. The objective function will minimize summation of idleness cost of machines, sub-contracting cost for exceptional parts, non-utilizing machine cost, and holding cost of parts in the cells. Finally, the linearized model will be solved by the Cplex solver of GAMS, and sensitivity analysis will be performed to illustrate the effectiveness of the parameters.