Stochastic and robust optimizations have been considered as two different views of stochastic problems. While robust optimization takes optimization in the worst case, stochastic optimization regards no conservative view and merely focuses on expected value. However, a unilateral view of stochastic problems does not apply to most real problems. In this article, a hybrid robust and stochastic approach is proposed for optimization problems under uncertainty. Our major contribution is presenting different conservative levels in solving an optimization problem using a Hybrid Robust and Stochastic Optimization approach. To this end, we cluster uncertain parameters into different clusters using Latin Hypercube Sampling and k-Means clustering tools; having established various numbers of clusters of uncertain parameters, different clustering criteria and a Multi-Criteria Decision Making (MCDM) tool is employed to determine the optimal number of clusters of uncertain parameters. Then, a hybrid energy optimization model under uncertainty is applied to coordinate the scheduling of natural gas-fired electricity generation units and gas supply units (gas refinery) under natural gas and electricity demand uncertainty, with known probability distribution and uncertain parameters having different levels of conservatism. The results indicate that while no special trend is evident in the execution time as the number of clusters increases, the optimal value is decreased.

Considering the cognitive, random, uncertain, and flexible constraints, a robust, stochastic, possibilistic, and flexible chance-constrained model was developed based on credibility measurement. The ultimate aim was closedloop supply chain network design. Different attitudes of decision-makers were answered by more flexible measurements of optimistic and pessimistic parameters in the form of credibility measurement. The model has been able to reduce the possible deviation, stochastic deviations, nonfulfillment of demand and capacity constraints, and violation of flexible constraints, which simultaneously include cognitive and random uncertainties and flexibility of constraints in the model. To apply the model, a case study was conducted to design the closed-loop supply chain network of multi-product and multi-period stone paper. The results of implementing the model showed that in different situations and according to the importance of decision makers' opinions, using the range of optimism and pessimism, the number, location of facilities, optimal flow of products and materials between centers in the stone paper supply chain network can be determined. The proposed model was evaluated using robustness and sensitivity analysis, and its performance was evaluated using nominal data in the realization model, which results showed the appropriate performance of the model.

Finding the location for plans like factories or warehouses for any organization is an important and strategic decision. Costs of transportation which are the main part of the price of the goods, is the function of the location of these projects. to find the optimum location of these projects, there have been various methods proposed which are usually defined (not random). In reality and in dealing with real world conditions, taking into account influential and effective parameters leads to unexpected results. In this research, while introducing these defined algorithms, it been tried to random location model based on the existing models. Regarding this, by studying the models taken in random location we tried to propose an efficient and effective model. For this purpose, by using randomized planning and randomized constrained planning, we turn random model to defined model, which is solvable by using the last algorithm or standard planning methods.

In recent years, the complexity of the environment, the intense competition of organizations, the pressure of governments on producers to manage waste products, environmental pressures and most importantly, the benefits of recycling products have added to the importance of designing a closed loop supply chain network. Also, the existence of inherent uncertainties in the input parameters is another important factor that the lack of attention them can affect the strategic, tactical and operational decisions of organizations. Given these reasons, this research aims to design a multi-product and multi period closed loop supply chain network model in uncertainty conditions. To this aim, first a mixed-integer linear programming model is proposed to minimize supply chain costs. Then, for considering model hybrid uncertainties effectively, randomness and epistemic uncertainty, a novel robust stochastic-possibilistic programming (RSPP) approach is proposed. Furthermore, several varieties of RSPP models are developed and their differences, weaknesses, strengths and the most suitable conditions for being used are discussed. Finally, usefulness and applicability of the RSPP model are tested via the real case study in an edible oil industry.