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This paper presents a unit commitment formulation for micro-grid that includes a significant number of grid parallel Proton Exchange Membrane-Fuel Cell Power Plants (PEM-FCPPs) with ramping rate and minimum up/down time constraints. The aim of this problem is to determine the optimum size of energy storage like battery storages and use the efficient hydrogen and thermal energy storages and to schedule the committed units' output power while satisfying practical constraints and electrical/thermal load demand over one day with 15 min time step. In order to best use of multiple PEM-FCPPs, hydrogen storage management is carried out. Also, since the electrical and heat load demand are not synchronised, it could be useful to store the extra heat of PEM-FCPPs in the peak electrical load in order to satisfy delayed heat demands. Due to uncertainty nature of electrical/thermal load, photovoltaic and wind turbine output power and market price, a two-stage scenario-based stochastic programming model, where the first stage prescribes the here-and-now variables and the second stage determines the optima value of wait-and-see variables under cost minimization is implemented. For solving the problem, a new enhanced cuckoo optimisation algorithm is presented and successfully applied to two typical micro-grids. Quantitative results show its usefulness.

Changing the structure of supply chains to move towards less polluting industries and better performance has attracted many researchers in recent studies. Design of such networks is a process associated with uncertainties and control of the uncertainties during decision-making is of particular importance. In this paper, a two-stage stochastic programming model is presented for the design of a green closed-loop supply chain network. In order to reach the environmental goals, an upper bound of emission capability that would help governments and industries to control greenhouse gas emissions was considered. During the reverse logistics of this supply chain, waste materials were returned to the forward flow by the disassembly centers. To control the uncertainty of strategic decisions, demand and the upper bound of emission capacity with three possible scenarios were considered. To solve the model, a new accelerated Benders decomposition algorithm along with Pareto-optimal-cut was used. The efficiency of the proposed algorithm was compared with the regular Benders algorithm. The effect of different numerical values of parameters and probabilities of scenarios on the total cost was also examined.

When a disaster strikes, there is always a demand for life-supporting commodities, whose slow and ineffective delivery can result in huge human and financial losses. Warehouse location and the storage of necessary relief commodities (RCs) before a disaster, and the proper distribution of RCs among affected people following a disaster can improve performance and reduce latency when responding to a given disaster. Hence, many researchers have focused on these fields while overlooking some crucial actual conditions as a result of the complexity of the problem. Consequently, this study develops a location-inventory-distribution problem in disaster relief supply chain (DRSC) considering the gradual injection of the limited pre-disaster budgets, the time value of money, and various evaluation criteria for locating warehouses. In this regard, a novel multi-objective two-stage scenario-based stochastic programming model under a pre-disaster multi-period planning time horizon (PTH) is presented. In each period, pre-disaster warehouse location and inventory management are addressed in the first stage, and the post-disaster distribution of the stocked RCs is planned in the second stage. Utilizing new priority-weighted service utility and balance measures, the model strives to optimize deprivation cost, demand coverage, and fair service. The maximization of warehouses’ utility is done according to various criteria and using a data envelopment analysis (DEA) model integrated with the model. The applicability and performance of the model are validated via a real-world case study followed by various tests and sensitivity analyses. The outcomes show that the model significantly improves logistics and deprivation costs, satisfied demands, fair service, and warehouses’ utility.

This paper focuses on the capacity uncertainty in water supply chains that occurs when facilities face disruption. A combination of scenario-based two-stage stochastic programming with the min-max robust optimization approach is proposed to optimize the water supply chain network design problem. In the first stage, the decisions are made on locations and capacities of reservoirs and water-treatment plants while recourse decisions including amount of water extraction, amount of water refinement, and consequently amount of water held in reservoirs are made at the second stage. The proposed robust two-stage stochastic programming model can help decision makers consider the impacts of uncertainties and analyze trade-offs between system cost and stability. The literature reveals that most exact methods are not able to tackle the computational complexity of mixed integer non-linear two-stage stochastic problems at large scale. Another contribution of this study is to propose two metaheuristics - a particle swarm optimization (PSO) and a bat algorithm (BA) - to solve the proposed model in large-scale networks efficiently in a reasonable time. The developed model is applied to several hypothetical cases of water resources management systems to evaluate the effectiveness of the model formulation and solution algorithms. Sensitivity analyses are also carried out to analyze the behavior of the model and the robustness approach under parameters variations.