augmented epsilon constraint

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.

The last decade has seen numerous studies focusing on the closed-loop supply chain. Accordingly, the uncertainty conditions as well as the environmental impacts of facilities are still open issues. This research proposes a new bi-objective mixed-integer linear programming model to design a closed-loop supply chain tire remanufacturing network considering environmental issues that improve performance in conditions of uncertainty associated with the tire industry. This model seeks to maximize the total profits of the network, including customer centers, collection centers, recycling centers, manufacturing/remanufacturing plants, distribution centers, and on the other hand, is looking to minimize environmental impact all over the supply chain network. Another novelty of the proposed model is in the solution methodology. By using an exact approach, the augmented ε‑constraint method, and meta-heuristic algorithm, a well-known Grasshopper Optimization Algorithm (GOA), optimal and Pareto solutions have been obtained for medium and large size sample problems. We analyze the effectiveness of these meta-heuristics through numerical experiments. Also, sensitivity analysis has been provided for some parameters of the model. Finally, the results and suggestions for future research are presented.

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.

Assembly lines are flow-oriented production systems that are of great importance in the industrial production of standard, high-volume products and even more recently, they have become commonplace in producing low-volume custom products. The main goal of designers of these lines is to increase the efficiency of the system and therefore, the assembly line balancing to achieve an optimal system is one of the most important steps that have to be considered in the design of assembly lines. The purpose of the assembly line balancing is to assign tasks to the workstation called the station, so that prerequisite relationships, cycle times, and other assembly line constraints to be met and a number of line performance criteria to be optimized. In this study, considering the social responsibility related objective function, a mathematical model is proposed for scheduling and balancing the cost-oriented assembly line that has resource constraints with cost uncertainty. The box set robust optimization is applied and the obtained model is solved with the augmented epsilon constraint in the GAMS and some test problems and their results are presented. Finally, the cost parameter has been changed in a robust optimization approach and the obtained results have been analyzed for different costs.