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Several design guidelines and flexibility indices have been developed in the literature to inform the design of flexible production networks. In this paper, we propose additional flexibility design guidelines for unbalanced networks, where the numbers of plants and products are not equal, by refining the well-known Chaining Guidelines. We study symmetric networks, where all plants have the same capacity and product demands are independent and identically distributed, and focus mainly on the case where each product is built at two plants. We also briefly discuss cases where (1) each product is built at three plants and (2) some products are built at only one plant. An extensive computational study suggests that our refinements work very well for finding flexible configurations with minimum shortfall in unbalanced networks.

The uncertainty of wind power generation brings problems in power system operation, such as requiring more reserves and possible frequency issues. In this paper, we propose an idea of combining concentrating solar power (CSP) plants with wind farms to reduce the overall uncertainty in the joint power output. Taking advantage of the dispatchability of CSP, the uncertainty of joint power generation is expected to decrease. Based on the operational model of CSP plants with thermal storage system, we search for the narrowest but robust bounds of the joint power output with a given uncertainty of the wind power output and solar power availability, and within operational constraints of CSP plants. The problem is formulated as an adaptive robust optimization (RO) problem, containing mixed-integer variables at the second stage. We introduce an algorithm that combines a nested column-and-constraint generation (C-CG) method and an outer approximation (OA) method to solve the problem. The case studies show that robust intervals for the joint power output can be obtained, and the obtained intervals can be significantly narrower than the original intervals of wind power.Index Terms-Adaptive robust optimization (RO), concentrating solar power (CSP), thermal energy storage, uncertainty, wind power. NOMENCLATUREA. Indices, parameters, and sets E th min , E th max Minimum and maximum storage levels of the TES system. E w , E w − Upper and lower bounds of the total energy of the uncertain wind power in the period of consideration. N w Number of wind farms. N CSP Number of CSP plants. P c max , P d max Maximum charge and discharge rates of the TES system. P e min , P e max Minimum and maximum electrical power output of the CSP plants. P th SU Thermal power required when the steam turbine starts up. P solar t Solar thermal power at time t. P w t , P w t Upper and lower bounds of the wind power at time t. RU CSP max , RD CSP max Maximum upward and downward ramping rate of electrical power from the CSP plants. T Number of time intervals under consideration. T CSP MinOFF , T CSP MinON Minimum ON and OFF times of the steam turbine in the CSP plants. Δt Time interval between two adjacent time points. ε Optimization tolerance. γ Dissipation factor of the TES system. η e Efficiency of thermoelectric conversion. η c Efficiency coefficient of charging the TES. η d Efficiency coefficient of discharging the TES. U Uncertainty set of wind power. V Uncertainty set of solar power. Ω CSP The variable set of a CSP plant. B. Variables b c , b d ∈ {0, 1} Charging and discharging state variables of CSP plants. E th Thermal energy stored in the TES system. P d1 , P d2 Slack variables in the slackness form of the RO problem. P e Active power output of the CSP plants. P set , P set Upper and lower bounds for the joint power output. 1949-3029

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