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As a relatively emerging topic in optimization, green routing could reduce the fixed and variable costs induced by different parts of a routing and transportation system and the costs imposed by pollution. This study proposes green transportation routing with a time window under confirmed stable conditions that consider transportation capacity restrictions, speed and time of delivery, and allocation of authorized drivers. This being the case, the goals of selecting the shortest route to goods transfer with the lowest costs caused by pollution, overdue fines, and maintenance of costs could be attained. Accordingly, the Lagrangian relaxation algorithm was employed, and the mathematical model of mixed-integer was developed to address the problem. Lagrange coefficient takes advantage of subgradient methods and closed methods. Lagrangian relaxation is applied separately to address two restrictions. The algorithm saves time by immediate problem solving than the Baron approach. These papers seek to simultaneously use complex restrictions close to actual incidents and could be more similar to natural conditions than other developed models.

Today due to the significance of environmental pollutants and the increase of global standards for the environment, more attention has been paid to the design of closed-loop supply chain networks with green considerations. On the other hand, the direct and inverse chains affect each other in terms of the efficiency rate. As a result, the performance of each chain has its own effect on other chains and on the entire supply chain. In this research, we design a mathematical model for the green closed-loop heavy-duty supply chain network, which considers products under conditions of uncertainty with the concept of economic pricing. Economic pricing in this issue increases economic profitability. The designed mathematical model has a fuzzy basis and pursues two objectives. The first goal is to minimize costs and the second goal is to minimize environmental pollutants. The decisions made in this model include determining the optimal location of each center based on potential locations, the optimal amounts of production, distribution, collection and recycling, and also the reproduction of products. Furthermore, a two-sample independent t-test is used to validate the results of the definite and indefinite models. To solve the two-objective function model, the ε-constraint method is used so that the problem can guarantee strong Pareto optimal solutions and prevent weak Pareto solutions. Finally, to evaluate the efficiency of the proposed method, a case in the field of heavy tires is studied, solved and implemented to produce and present valuable management results.

The nurse scheduling in a hospital is a complex and time-consuming 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 staff 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 classified 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: fixed 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 significant 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.

In recent years, the location of mobile facilities has been highly regarded in design of health system. One of the important areas in this field is design of blood collection and distribution systems. Since blood is as perishable and vital goods and donation of blood is a voluntary work, supply blood and blood products is one of the most challenging issues in the supply chain in emergency and non-emergency situation. In this paper, we propose a four-echelon two-stage stochastic model to supply whole blood and its products in disaster. The hospitals, regional blood centers, local blood centers and bloodmobile facilities are considered as main elements of blood supply chain. It is assumed that the blood collection from the donors just done in bloodmobile facilities and local blood centers. Also, processing operation of blood products from collected whole blood are done only in the regional blood centers. In the designed supply network in this paper, every hospital could provide needed blood products from other near hospitals in the emergency situation as well as other fixed and mobile blood centers. One of the most important issues in the blood supply in disasters is delivery time of blood, so here; we consider an upper bound to blood delivery time to the affected areas and the objective of our presented model is blood supply in the standard time so that the total supply cost be minimized. In the other hand, the time solution is very important to obtain an acceptable solution in a reasonable time. We present a heuristic approach based on genetic algorithm and exact method to solve the proposed MIP model. The locations of fixed and mobile facility are computed through genetic algorithm then other variables are calculated by solve model with CPLEX. In order to validate the proposed approach, we generate 8 examples with different sizes and numerical results are presented. Also the results of comparison our approach with exact and metaheurisitc method are presente.