The present study aimed to design a bi-Objective bi-level mathematical model for multi-dimensional cellular manufacturing system. Minimizing the total number of voids and balancing the assigned workloads to cells are regarded as two Objectives of the upper level of the model. However, the lower level attempts to maximize the workers' interest to work together in a special cell. To this aim, two nested bi-level metaheuristics including particle swarm optimization (NBL-PSO) and a population-based simulated annealing algorithm (NBL-PBSA) were implemented to solve the model. In addition, the goal programming approach was utilized in the upper level procedure of these algorithms. Further, nine numerical examples were applied to verify the suggested framework and the TOPSIS method was used to find the better algorithm. Furthermore, the best weights for upper level Objectives were tuned by using a weight sensitivity analysis. Based on computational results, all three Objectives were different from their ideal goals when decisions about inter and intra-cell layouts, and cell formation to balance the assigned workloads by considering voids and workers' interest were simultaneously madeby considering a wide assumption-made problem closer to the real world. Finally, NBL-PBSA could perform better than NBL-PSO, which confirmed the efficiency of the proposed framework.

When a region is hit by a natural or man-made disaster, planning people evacuation is one of the most challenging issues. Since relief vehicles represent a scarce resource in the disaster situations, their efficient usage plays a major role. In this paper, a simultaneous routing and scheduling of relief vehicles model are proposed to transport evacuees from affected areas to shelters. Our model has introduced two Objectives. The first Objective function measures the total transportation time. The second Objective function represents routes reliability. We apply the augmented epsilon constraint method to determine the Pareto solutions. During the people evacuation, issues such as the feasibility of serving each affected area with multiple vehicles, heterogeneous fleet of relief vehicles and capacity constraint for shelters has been regarded. In order to represent the proposed model efficiency, we selected a random example, ran the model on it, and present solution results.

In recent years, many industries in developed countries have integrated the important process of reverse logistics into their supply chain for different reasons, including growing environmental concerns. Given fish as perishable food, re-employing unused products and waste in each step of the chain constitute a major concern for the decision-makers. The present study is conducted to maximize responsiveness to customer demand and minimize the cost of the fish closed-loop supply chain (CLSC) by proposing a novel mathematical model. To solve this model, the epsilon-constraint method and Lp-metric were employed. Then, the solution methods were compared with each other based on the performance metrics and a statistical hypothesis. The superior method is ultimately determined using the TOPSIS method. The model application is tested on a case study of the trout CLSC in the north of Iran by performing a sensitivity analysis of demand. This analysis showed the promising results of using the proposed solution method and model.

The problem of maximal hub covering as a challenging problem in operation research. Transportation programming seeks to find an optimal location of a set of hubs to reach maximum flow in a network. Since the main structure's parameters of the problem such as origin-destination flows, costs and travel time, change periodically in the real world applications, new issues arise in handling it. In this paper, to deal with the periodic variations of parameters, a bi-Objective mathematical model is proposed for the single allocation multi-period maximal hub covering problem. The ε-constraint approach has been applied to achieve non-dominated solutions. Given that the single-Objective problem found in the ε-constraint method is computationally intractable. Benders decomposition algorithm by adding valid inequalities is developed to accelerate the solution process. Finally, the proposed method is carried out by CAB data set, and the results confirm the efficiency of it regarding optimality and running time.

Nowadays, with the increasing pressure of the competitive business environment and demand for diverse products, manufacturers are force to seek for solutions that reduce production costs and rise product quality. Cellular manufacturing system (CMS), as a means to this end, has been a point of attraction to both researchers and practitioners. Limitations of cell formation problem (CFP), as one of important topics in CMS, have led to the introduction of virtual CMS (VCMS). This research addresses a bi-Objective dynamic virtual cell formation problem (DVCFP) with the Objective of finding the optimal formation of cells, considering the material handling costs, fixed machine installation costs and variable production costs of machines and workforce. Furthermore, we consider different skills on different machines in workforce assignment in a multi-period planning horizon. The biObjective model is transformed to a single-Objective fuzzy goal programming model and to show its performance; numerical examples are solved using the LINGO software. In addition, genetic algorithm (GA) is customized to tackle large-scale instances of the problems to show the performance of the solution method.

The nurse scheduling in a hospital is a complex and timeconsuming problem which considers assigning nurses to shifts for each day of a planning horizon while ensuring meeting the demand of hospital units. In developing countries, there is usually a shortage of nursing sta,in health centers' therefore, the nurse scheduling problem is one of the most important issues in human resource management in clinical units. In this research, a mathematical model is developed so that constraints are classi , ed into two types of hard and soft and the weight of soft ones is obtained using the pairwise comparison matrix. In the proposed model, two Objective functions are considered to maximize nurses' preferences and minimize the deviations from soft constraints for nursing scheduling problems. The nurses' preferences represent a very important issue in nurses' satisfaction. As a novelty of this paper, three factors used to calculate the nurses' preferences based on the data envelopment analysis (DEA) method are as follows: nurses' preferential ratings, data related to the preferences of past scheduling periods, and the work experience of nurses. Hospital nurses are also divided into two groups: , xed shift work and rotational shift work. Also, a fair allocation is considered for night and weekend shifts for nurses. The proposed model was solved by an improved version of the augmented epsilon constraint method (AUGMECON2) using the data for a case study in the Intensive Care Unit (ICU) in Loghman Hakim Hospital in Tehran, Iran. Comparing the results of the solution of the proposed model with the current method shows that there is a signi, cant improvement in preparing the nursing timetable and responding to nurses' preferences. The computational results of the mathematical model show that the nurses' mandatory overtime is reduced' therefore, the hospital costs are decreased. Also, a sensitivity analysis is presented for the deviations from soft constraints with respect to maximum working hours.

Each year, many people around the world are affected by a variety of natural disasters. It also costs a lot of helping time for injured people. Relief logistics is considered to be as the principal of all of relief operations and aid, and it is one of the main subsystems of logistics and supply chain management. One of the problems existed in relief logistics is unpredictable events that cause some uncertain parameters. This paper presented a bi-Objective model that includes several supply centers, distribution centers and demand (vulnerable) centers. The first Objective is minimizing the total cost and the second one is maximizing satisfaction of applicants (injury victims). The first step, the proposed model is determined by using robust optimization method. In the second step, the bi-Objective model is solved by goal programing method. Finally a comprehensive example is solved and analyzed which can be a help to understand real problems.

In this paper, robust optimization of a bi-Objective mathematical model in a dynamic cell formation problem considering labor utilization with uncertain data is carried out. The robust approach is used to reduce the effects of fluctuations of the uncertain parameters with regards to all the possible future scenarios. In this research, cost parameters of the cell formation and demand fluctuations are subject to uncertainty and a mixed-integer programming (MIP) model is developed to formulate the related robust dynamic cell formation problem. Then the problem is transformed into a bi-Objective linear one. The first Objective function seeks to minimize relevant costs of the problem including machine procurement and relocation costs, machine variable cost, inter-cell movement and intra-cell movement costs, overtime cost and labor shifting cost between cells, machine maintenance cost, inventory, holding part cost. The second Objective function seeks to minimize total man-hour deviations between cells or indeed labor utilization of the modeled.

There are di, erent factors, including economic development and population explosion, causing the rapid increase in municipal solid waste generation rates. In today's municipal solid waste management, a considerable amount of , nancial and human resources is spent on collection and transportation, and little attention has been paid to production, storage in place, recycling, and disposal. As proper collection and transportation are important issues in municipal solid waste system, creation of energy from waste as well as recycling and disposal are also signi, cant, attention must be paid to the optimal usage of dirty gold (i. e. municipal solid wastes) for pollution reduction. Moreover, determining suitable locations for transfer stations and waste disposal facilities is a very complex problem, needing a comprehensive review and evaluation process accounting for the requirements of municipal, environmental, and governmental regulations. In this context, it is vital to develop an e, ective and e, cient approach for designing and planning a waste management system. In order to realize this goal, a three-level network consisting of customers, transfer stations, and disposal facilities (recycling, composting, waste incinerator, and land, ll centers) was considered in the present paper. A bi-Objective mixed-integer linear mathematical programming model was presented for location and allocation of municipal solid waste. model goals were minimizing waste disposal cost and greenhouse gas emission. Other points taken into consideration were a variety of products derived from recycling waste, transferring them to sales areas, and the limitations of number and capacity for transfer stations and waste disposal facilities. Districts 1 to 8 and District 22 of Tehran were selected as a case study for measuring model performance. The results of the case study and sensitivity analysis demonstrated that the optimal solution requires the location of disposal facilities in different districts of Tehran, although these facilities incur considerable costs.