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Supply Chain Network Design Models for a Circular Economy
Published in Anil Kumar, Jose Arturo Garza-Reyes, Syed Abdul Rehman Khan, Circular Economy for the Management of Operations, 2020
Sreejith Balasubramanian, Mahshad Gharehdash, Mahnoush Gharehdash, Vinaya Shukla, Arvind Upadhyay
The supply chain network of the countries that are faced with stochastic demand and strategic level of uncertainty could be configured with the frameworks that address uncertainty such as the model proposed by Fattahi et al. (2018). These models could be implemented to mitigate the uncertainty of demand while redesigning the supply chain network; most of these models use stochastic programming and scenario analysis to mitigate the risk while solving the production-distribution problem. Supply chain network design models such as Rahimi et al. (2019) and Goh et al. (2007) could be implemented for countries that have both demand and political uncertainty. These models address the optimal selection of distribution links and facility locations (including inventory and warehouse) with consideration of risks.
Modelling risk effect using Monte Carlo Technique
Published in Stephen O. Ogunlana, Prasanta Kumar Dey, Risk Management in Engineering and Construction, 2019
The deterministic simulation is for systems whose behaviour is completely predictable. An example of this system is the traditional planning of projects. A stochastic simulation is for a system whose behaviour cannot be completely predictable which fits well with the characteristics of innovation process information, as described above. The stochastic simulation refers to using mathematical models to study systems that are characterised by the occurrence of random events.
Modeling and Simulation in Applied Livestock Production Science
Published in Robert M. Peart, R. Bruce Curry, Agricultural Systems Modeling and Simulation, 2018
A certain type of stochastic models are called probabilistic or Markov chain models. In a probabilistic livestock herd model, the classes of animals constitute a transition matrix expressing a probability distribution of animal movement from a specific class to all other classes in the next step. Probabilistic models follow the so-called Markovian property in which the outcomes of each step depend only on the last state of the model. Examples of probabilistic livestock herd models are dairy and swine models described by Jalvingh et al. (1992a, 1993).
Solvability and optimal controls of neutral stochastic integro-differential equations driven by fractional Brownian motion
Published in Journal of Control and Decision, 2023
Ravikumar Kasinathan, Ramkumar Kasinathan, Varshini Sandrasekaran
In recent years, the topic of stochastic differential equations (SDEs) is still developing and attracting interest from theoretical and applied disciplines. In many real-world phenomena, the deterministic models fluctuate due to random influences or noise, so we have shifted from deterministic models to stochastic models. For example, stock prices, heat conduction in materials with memory, rising population, etc. fluctuate due to random influences or noise, hence randomness must be introduced into mathematical descriptions of these phenomena. The differential equations which involve randomness are said to be SDEs. Moreover, the theory of SDEs can be successfully used to solve numerous non-mathematical issues, such as those in chemistry, economics, epidemiology, mechanics, finance and a variety of engineering disciplines. For the results of recent works on mild solutions for SDEs, see Ogouyandjou et al. (2019), Lakhel and Hajji (2015), Ren et al. (2017) and Lakhel and McKibben (2018). There have been many good books and monographs that are available on this field (Chen, 2010; Chen et al., 2014; Da Prato & Zabczyk, 1992; Mane et al., 2016; Mao, 1997; Oksendal, 2013; Sakthivel & Luo, 2009; Yang & Zhu, 2014).
Mathematical modelling to inform New Zealand’s COVID-19 response
Published in Journal of the Royal Society of New Zealand, 2021
Shaun Hendy, Nicholas Steyn, Alex James, Michael J. Plank, Kate Hannah, Rachelle N. Binny, Audrey Lustig
We developed a stochastic, continuous-time branching process model for the spread of COVID-19 (Figure 3). Stochastic models are a class of mathematical model that includes a random element and are defined in terms of the probabilities of certain events occurring. Stochastic models of disease spread have several advantages over their deterministic counterparts: Deterministic models break down when the number of cases is relatively small and so cannot be used to look at questions relating to the elimination of the virus.Stochastic models intrinsically allow for random variations in the transmission process, for example superspreading events or variations in the timing of secondary infections, symptom onset, testing and isolation. This enables uncertainty in model outputs to be quantified and the probability of elimination to be estimated.Stochastic individual-based models track individual infected cases, so they are more compatible with data on the number of cases and individual attributes of those cases such as age, time of symptom onset, hospitalisation status.Stochastic individual-based models allow the structure of the transmission tree (Figure 3) to be explicitly tracked. This is essential for models of contact tracing, which require information on who infected whom.
Incorporating geological and equipment performance uncertainty while optimising short-term mine production schedules
Published in International Journal of Mining, Reclamation and Environment, 2020
Matthew Quigley, Roussos Dimitrakopoulos
There are three main areas that may be improved and should be the focus for avenues of future work. First, the complexity and size of the case study presented in this work challenges the limits that commercial solvers can handle efficiently. In order to accommodate more blocks, more mining areas, and more detailed equipment decisions, future work on short-term problems should be developed using customised heuristic solvers [33]. Second, more comprehensive cycle time distributions should be investigated. There is significant value to be gained through allowing new stochastic solvers to make well-informed decisions considering complex equipment variability factors in short-term production scheduling. More robust trucking information could be exploited to allocate more performant trucks to high-value areas in crucial periods. Lastly, to expand into different areas of mine plan optimisation, different short-term aspects could be optimised in parallel to the production schedule; such as optimal equipment maintenance scheduling, optimal temporary ramp placement, and optimal grade blending, which is undoubtedly one of the most important aspects of short-term mine planning.