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.

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.

Making decisions for allocating locations and determining the optimal route for vehicles will result in saving the number of transportation costs. In this paper, A Multi-Period Multi-Objective Routing-Locating of Heterogeneous Vehicles (MPMORLHVP) is proposed for determining the route and allocating the visit location for heterogeneous vehicles. The MPMORLHVP model can help optimize the routing and locating decisions for heterogeneous vehicles in a multi-period setting. It aims to find the most efficient and effective transportation plan, considering the specific context of a two-echelon supply chain and the possibility of facility breakdowns. Therefore the main contribution of the current study is to provide a strategy for transporting heterogeneous vehicles over periods of time for handling and distribution in a sustainable supply chain. For this purpose, presented a multi-objective mixed integer linear programming (MOMIP) that two objective functions formulated to improve efficiency and effectiveness. The first objective is to minimize the total cost per path. The second goal is to minimize the total repair time of vehicles to visit all areas. The Epsilon Constraint (EC) Method has been used to solve the proposed model. The applicability of the proposed model is shown via a numerical problem. The results obtained from solving the proposed model are compared with the routing plan. Based on the obtained results, the lowest allocation cost and duration of vehicle repairs have been calculated separately in each period. In the first period, the lowest and in the second period, the highest amount of cost has been calculated. In addition, in the second period, the lowest and in the third period, the maximum service time of vehicles has been determined. In addition, the results of this study can provide an advantage to decision-makers so that they consider appropriate strategies for disaster response.

Many Important problems In Artificial Intelligence can be defined as Constralnt Satisfaction Problems (CSP). These types of problems are defined by a limited set of variables, each having a limited domain and a number of Constralnts on the values of those variables (these problems are also called Consistent Labelling Problems (CLP), in which "Labeling" nuans assigning a value to a variable.) Solution to these problems is a set of unique values for variables such that all the problem constralnts are satisfied. Several search algorithms have been proposed for solving these problems, som of which reduce the need for bacJctracklng by doing some sort of looking to future, and produce more efficient solutions. These are the so-called Forward Checking (FC), Partialiy Lookahead (PL), and Fully Lookahead (FL) algorithms. They are different In terms of the amount of looking to the future, number of backtracks thaJ are performed, and the quality of the solution that they find. In this paper, wepropose a new search algorithm we call Modified Fully Lookahead (MFL) which is Shown to be more efficient than the original Fully Lookahead algorithm

The goal of theory of Constraints (TOC) is to maximize output, which is achieved by identifying and managing the critically constrained resources. To manage the Constraints, Goldratt proposed five focusing steps (5FS). If we increase constrained output, the output of system will be increased. In this paper, we focus on step four of the 5FS and use the remained capacity of nonConstraint to elevate the system’s Constraint.

In this paper, a fuzzy multi-objective sustainable model is presented to select and allocate the order to supplier in uncertainty conditions and in a multi-period, multi-source, and multi-product cases at two levels of supply chain with pricing considerations. First objective function considered in this study as the measures to evaluate the suppliers are the purchase, transportation, and ordering costs. Second objective function considered employment rate and third objective function considered pollution rate. Employment and pollution rate parameters in the model are considered as uncertain and random triangular fuzzy number. A case study in engine oil industry in Zanjan province considered and the Epsilon-Constraint Method is used to solve the small size of this problem and sensitivity analysis is conducted to examine the accuracy and validity of the proposed Method.

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.

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.

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.