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Optimization of the Integrated Downstream Processing of Microalgae for Biomolecule Production
Published in Kalyan Gayen, Tridib Kumar Bhowmick, Sunil K. Maity, Sustainable Downstream Processing of Microalgae for Industrial Application, 2019
Soumyajit Sen Gupta, Yogendra Shastri, Sharad Bhartiya
The study on production of biodiesel as the sole product having provided us with insights about the trade-offs in decision making, we investigated the modeling aspect in order to ensure a realistic representation of the system in terms of parameters and variables to the maximum possible extent. Thus, a few of the entities which were considered parameters in the base model were redesigned as variables. This led to terms involving the multiplication of variables, thereby introducing non-convexity. Accordingly, different standard techniques available in the literature (Harjunkoski et al. 1999) were applied for a test case of our model. The most efficient one was followed in the advanced model formulation, as has been discussed in Section 11.2.2.
A novel approach for the identification of critical nodes and transmission lines for mitigating voltage instability in power networks
Published in Nnamdi Nwulu, Mammo Muchie, Engineering Design and Mathematical Modelling, 2020
Akintunde Samson Alayande, Nnamdi Nwulu
Another solution to the problem is the placement of reactive power supports such as reactors or FACTs devices at various locations within the system where their influence would be most effective. Traditionally, generating stations are usually located far away from load centres due to health and developmental reasons. However, since it is not an easy task to transport reactive power over a long distance, there is a need to find an alternative way of compensating the transmission lines adequately in order to increase the efficiency of the transmission network (Taylor 2011). In order to reduce the overall investment cost of installing VAR sources, it is important to install them in such locations, where the least VAR amount is needed to ensure system voltage security against all severe contingencies. In addition, optimal design and operation of power systems are usually faced with the determination of suitable locations of reactive power devices within the networks. The basic AC power-flow equations on which most of the power system solutions depend are mathematically complex and nonlinear in nature. This makes convergence to the real solution practically impossible in most large-sized and radial power networks. This, however, compounds the challenge of identifying a suitable location for the reactive power resources such as SVC, capacitor banks, etc. Although, this approach is found helpful in resolving the issue, to some extent, its main bottleneck is how to quickly identify suitable locations where the effect of such reactive power supports could be most effective. Conventionally, most authors, in the open literature, have formulated the problem as a nonlinear optimization problem, which is subjected to certain system constraints (Ginarsa, Soeprijanto, and Purnomo 2013). The main challenges in this case are indeed non-convexity of the models and computational difficulties in terms of time and computer memory space. This has posed a lot of challenging tasks and concerns for power system operators and planners. A quick and an efficient methodology for identifying such suitable locations where the reactive power supports could be placed in order to prevent voltage collapse, is therefore, of utmost importance. Moreover, effective identification of locations where reactive power support could be placed requires that all the influential links and nodes that could lead to violations of network integrity in terms of reliability and security be quickly identified and monitored (Ginarsa, Soeprijanto, and Purnomo 2013; Ziari et al. 2010).
From a rugged to a smooth supply chain performance landscape: a complementarity perspective
Published in Production Planning & Control, 2023
Javad Feizabadi, David Gligor, Somayeh Alibakhshi Motlagh
This whole idea of changing a set of interdependent choice variables rather than optimising a single variable induced some economists to deviate from some classic economic assumptions (e.g. Cyert and March 1963; Milgrom and Roberts 1988, 1990, 1995). The observations on how the production was organised by some firms, such as Lincoln Electric, Toyota, and Liz Claiborne, led to the relaxation of two major assumptions in classic economic analysis (Milgrom and Roberts 1995; Roberts 2004). First is the assumption of considering only two resources of capital and labour, which are relatively homogenous across the firms. Second is the assumption of infinite divisibility of elements in designing organisational systems, a concave curvature performance function describing the association among the design elements, and a convex constraint set among the elements. Both of these assumptions supported the idea of a unimodal production function with a global maximum in which any random local adaptation would ultimately help the firm reach the global peak. In the complementarity approach, firms are perceived as a set of interdependent heterogeneous resources and capabilities; the elements of the firm’s organisational system mutually reinforce each other through positive feedback loops and a virtuous cycle (i.e. a supermodular and discontinuous performance function). An important role is played by the property of non-convexity, which means investing in multiple complementarity activities would not create a diminishing marginal return.
Accurate estimation of cost function parameters for thermal power plants using a novel optimization approach
Published in Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 2018
Alireza Askarzadeh, Mahdi Gharibi
where Pk,min is the minimum power generation limit of unit k and ak, bk, ck, ek, and fk are the unknown parameters of the non-smooth model. Figure 1 illustrates the smooth and non-smooth input-output characteristics on one figure. Using a non-smooth cost function may increase the precision of the modeling but will result in having a non-convex cost function. In optimization, non-convexity increases the complexity of finding the global optimal.
A distributionally robust optimisation model for last mile relief network under mixed transport
Published in International Journal of Production Research, 2022
Peiyu Zhang, Yankui Liu, Guoqing Yang, Guoqing Zhang
In an uncertain post-disaster environment, we lack historical data and are unable to obtain accurate data about the disasters. The data we obtained are usually rough and incomplete. The data in RO do not have the random characteristic and it only provides a fixed area to limit the data. In this case, the much less information in uncertain-but-bounded model and the associated worse case solutions can be too conservative and thus impractical. While the SO model seem to be quite natural, it suffers from a severe difficulties. First, we usually need to determine the probability distribution P of uncertain parameters. As described by Tofighi, Torabi, and Mansouri (2016): ‘Due to special characteristics of disasters, in most cases there is not enough historical/objective data to model uncertain parameters within each scenario as random data’, thus SO approach is not suitable for the post-disaster scenes. Second, the SO model has a severely computationally intractable problem because it is difficult to estimate to probability P of chance constraint with high accuracy. Most importantly, the model is not often feasible due to its non-convexity. Therefore, Distributionally Robust Optimisation (DRO) is an emerging approach to describe the random variables based on the partial distribution information (Ben-Tal, El Ghaoui, and Nemirovski 2009). By the limited uncertain data in the post-disaster environment, we can find a suitable uncertainty set with the specific properties. Besides, the computational tractability of DRO can remove the problem of optimisers, we handle the chance constraint with uncertain parameters through distributionally robust optimisation (Goh and Sim 2010; Wiesemann, Kuhn, and Sim 2014). DRO is more suitable for addressing chance constraints where the probability distribution is known to belong to an ambiguity set . Based on the set constructed from the partial distribution information (mean, variance, etc.) of the uncertain parameters, the computationally tractable safe convex approximations of the chance constraints can be derived. Liu, Li, and Zhang (2019) proposed a distributionally robust model for assigning the ambulances in emergency medical service. Zhang et al. (2019) presented distributionally robust model in a humanitarian relief network after disasters, considering resource allocation among the large distribution centres.