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.

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.

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.

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.