This paper addresses optimal locating healthcare facilities problem regarding the essential role of these systems on expense and equity at the strategic level to decision-makers. As a result, a multi-objective model with a hierarchical structure and congestion consideration is proposed for the location issue, which is the main contribution of this study. A mixed-integer non-linear programming (MINLP) model is developed to reduce overall system expenses, such as setup, operating, travel costs, and total waiting time at facility levels, while concurrently maximizing the number of covered patients. Furthermore, two M/M/1/K and M/M/C/K queue systems are utilized at facility levels. Then, two LP-metric and augmented epsilon-constraint methods are implied. Several examples are conducted and evaluated using statistical tests and the TOPSIS approach to assess the performance of the solution strategies. After that, a sensitivity analysis is carried out. The findings indicate that the proposed model may be used as a tool to assist decision-makers in the design of multi-level healthcare facilities.

Introduction: Locating hospitals and health care centers, thereby assigning clients to these centers is one of the major challenges encountered by managers and urban planners. The right decision in this area is so important that otherwise would increase costs of providing health services and cause irreparable damages to the individual and social health. The efficiency of such models is critical to decision-makers and has always been the source of making effective use of available resources.methods: In this paper, a multi objective linear programming model was developed based on simultaneous consideration of locating and allocating services in hospitals. Further, using data envelopment analysis in this model helped locate and assign services at maximum efficiency. The model was used for locating and allocating available services in Amol hospitals. The proposed model the weighting method and the augmented epsilon constraint approach were applied. The results showed that the augmented epsilon constraint has a better capability than the other method to solve this problem Results: The model enables decision makers to consider quality in addition to the cost in locating and allocating procedure. Increasing efficiency along with considering costs are achievements of proposed model for health decision makers.Conclusion: The Pareto results achieved from solving proposed model can be a suitable base for making decisions. Managers can compare obtained solutions and their optimality and make proper decisions. The present case study showed that the model has a proper performance in locating and allocating available services in Amol hospitals.

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.

Generation maintenance scheduling (GMS) is one of the most important and influential programs on short-term scheduling. On the other hand, the variability nature of distributed renewable resources is led to the need for a power system to provide flexibility. In order to achieve a flexible operation, it is essential to develop a flexible GMS framework. For this purpose, it has used the flexibility index of the system in order to evaluate the flexibility of the power system. In flexibility studies, modeling and predicting the variability of renewable resources is important. Gas-fired power plants are one of the most important suppliers of flexibility in the supply-side. Therefore, the reliable operation of electricity grids depend on the natural gas availability . Furthermore, gas demand is subject to various uncertainties, especially in cold seasons, which will have significant effects on power system. In this paper, the uncertainties of wind and gas load is considered through forecasting by ARIMA method in Python. In this paper, natural gas and electricity demand responses are implemented as flexibility provisions from demand-side resources. It is worth noting that the objectives of increasing flexibility, leveling the energy index of reliability and reducing emission and costs have been considered as the objectives of optimizing GMS . The proposed framework is implemented on a modified IEEE 24 bus. According to the results, the system flexibility has been improved without increasing costs. The flexibility index in proposed model has improved by about 19.11%, due to the use of DRRs.

One of the most challenging issues in multi-objective problems is finding Pareto optimal points. This paper describes an algorithm based on Benders Decomposition Algorithm (BDA) which tries to find Pareto solutions. For this aim, a multi-objective facility location allocation model is proposed. In this case, an integrated BDA and epsilon constraint method are proposed and it is shown that how Pareto points in multi-objective facility location model can be found. Results are compared with the classic form of BDA and the weighted sum method for demand uncertainty and deterministic demands. To do this, Monte Carlo method with uniform function is used, then the stability of the proposed method towards demand uncertainty is shown. In order to evaluate the proposed algorithm, some performance metrics including the number of Pareto points, mean ideal points, and maximum spread are used, then the t-test analysis is done which points out that there is a significant difference between aforementioned algorithms.

Supply Chain is a network of facilities and distribution centers that performs operation of preparation, conversion of raw materials into products and distribution of the final product to the customer. Recent technological, organizational and economic advances in comprehensive health systems have provided patients with more access to treatment. Despite this progress, improvements in health infrastructure and supply chain management are inevitable. Therefore, proper use of appropriate drugs with the right combination for the right patient at the right amount at the right time is essential for the safety and recovery of the disease. Therefore, in this paper, a drug supply chain network with considering discount on the green supply chain, including a pharmacy, a distribution center and a recycling center with a number of drugstores is studied, consisting of two homogeneous vehicle routing sections. A distribution center for medicines and a recycling center for pharmaceutical waste are set up. This research is solved by using the epsilon constraint method with software of GAMs and after sensitivity analysis it is determined that the most important parameters are demand and then lost unit cost and unit hold cost. In other words, GAMs can solve this model for up to 5 nodes and 11 periods.

In this paper, a new approach is proposed for optimal bidding of strategic units in day ahead energy market and market clearing process. This method describes the multi objective scheduling of strategic units that is going to maximize its profit in presence of rivals and minimize its emission. In order to achieve this goal, a bi-level mathematical optimization model with equilibrium constraints Is provided. The first level maximizes the profit of strategic units and the second level maximizes the level of social welfare. The bi-level model is converted to a mixed integer linear programming model using a duality theory and Karush-Kuhn-Tucker (KKT). Another goal is to solve the bi-level problem in a multi-objective method using augmented epsilon constraint method in order to maximize profit of linearized model and reduce the emission of strategic units. Finally, the best answer is selected using fuzzy decision method. The power transmission distribution factor (PTDF) method has been used to model the network structure.

Short life cycle products, especially food products, require a certain type of supply chain management due to their particular specifications such as perishability. On the other hand, the food distribution also requires special considerations and imparts more complexity compared with the distribution of other goods because in food distribution the quality of the food delivered to the customer should be considered as well as transportation costs. Therefore, in this paper, a new mathematical model is developed for integrating decisions regarding food supply and distribution under conditions of uncertainty (vehicles’ travel time) with aims to minimize purchase and transportation costs and maximize customer satisfaction. Customer satisfaction relies upon the quality of the food delivered to the customers. The multi-objective model proposed in this paper is NP-hard. Hence, a developed version of NSGA-II called Multi-Objective Time Travel to History (MOTTH) algorithm, inspired from the idea of traveling through history, is proposed to solve the problem. In order to validate the performance of the proposed algorithm, the results of MOTTH algorithm are compared with the results obtained from an exact augmented epsilon-constraint method. Furthermore, a comparison is provided between the NSGA-II and MOTTH algorithms, the results of which indicate the superiority of the MOTTH metaheuristic algorithm.

This paper develops a 0-1 integer-programming model for multi-model assembly line balancing and equipment selection problem. In the investigated model, parallel stations are allowed under zoning constraints. Under zoning constraints, assignment of different tasks to the same workstation may be forced (positive zoning constraint) or may be forbidden (negative zoning constraint). There are two objectives for the investigated problem: (1) Optimizing the number of workstations over the assembly line and (2) Minimizing the total equipment costs. An augmented ε-constraint method is proposed to solve the investigated problem. To illustrate effectiveness of the proposed model, a numerical example is conducted. Results show the performance of the proposed model.

In current study, multi objective programming (MOP) model was used for a representative farm in tropical zone of Dashtestan, Bushehr. Four goals were considered in the model namely, maximizing total gross margin (GM), minimizing irrigation water, risk, and used chemical fertilizer and pesticides. The model was solved by weighting and augmented e-constraint approaches in 18 and 42 various manners and a non-inferior solution obtained in each condition. The results indicated that, augmented e-constraint in comparison with weighting method had less inadequacy and richer representation of the efficient set. Moreover, comparison of non-inferior solutions with farmer actual plan indicated that solutions in which goals of total GM maximization and minimization of risk have been emphasized were closer to actual plan.