Modelling and Stochastic Simulation of Supply Chains

Supply chains are coordinated flows of materials from the suppliers to the locations where they are consumed [1]. Their dynamics can be very complex due for instance to the increasing complexity of today's industry. Severe disruptions of supply chains is another reason that makes the modelling and simulation of supply chains very challenging. For instance, during Covid-19 pandemic, supply chains were severely disrupted, and the production were negatively affected [2]. For these reasons, accurate modelling and simulation of complex supply chains are of paramount practical interest to avoid severe disruptions and to enhance supply chain's resilience. <br /> <br /> The aim of the project is to use stochastic reactions networks (SRNs) to model supply chains dynamics [1]. SRNs are pure jump Markov processes that have been extensively used in the modelling of chemical reactions [3]. A preliminary plan of the project is <br /> - Understand the notion of SRNs and how they are used to model chemical reactions. Moreover, get familiar with exact and approximate schemes used to simulate SRNs. <br /> - Build the analogy between chemical reactions and supply chains modelling. Moreover, introduce the notion of delayed processes to count for delays in the supply chains processes (for instance, delays that are due to disruptions). <br /> - Using the previous two steps, implement the algorithms to simulate the dynamics of supply chains. <br /> <br /> The student may work on other research directions such as<br /> <br /> - Use the concept of Monte Carlo methods to compute several statistical quantities (for instance, the expected number of a given part in the supply chain at a given future time). <br /> - Another possible idea is to perform several simulations to motivate the importance of optimal inventory management. Moreover, suggest various strategies for optimal inventory management.<br /> - Incorporate weather and climate information into the simulation process, to investigate how supply chains could be disrupted under future climate change.

<p><strong>References:</strong></p> <p><br /> [1] Nai-Yuan Chiang, Yiqing Lin, and Quan Long. Efficient propagation of uncertainties in manufacturing supply chains: Time buckets, L-leap, and multilevel monte carlo methods. Operations Research Perspectives, 7:100144, 2020.</p> <p>[2] Christopher W. Craighead, David J. Ketchen Jr., and Jessica L. Darby. Pandemics and supply chain management research: Toward a theoretical toolbox*. Decision Sciences, 51(4):838–866, 2020.</p> <p>[3] David F Anderson. A modified next reaction method for simulating chemical systems with time dependent propensities and delays. The Journal of chemical physics, 127(21):214107, 2007</p>

<p>Formal applications for research degree study should be made online through the <a href="https://www.leeds.ac.uk/research-applying/doc/applying-research-degrees">University's website</a>.Please state clearly in the Planned Course of Study section that you are applying for <em><strong>PhD Statistics FT,</strong></em> in the research information section that the research degree you wish to be considered for is <em><strong>Modelling and Stochastic Simulation of Supply Chains</strong></em> as well as <a href="https://eps.leeds.ac.uk/faculty-engineering-physical-sciences/staff/12206/dr-nadhir-ben-rached">Dr Nadhir Ben Rached</a> as your proposed supervisor and and in the finance section, please state clearly <em><strong>the funding that you are applying for, if you are self-funding or externally sponsored</strong></em>.</p> <p>If English is not your first language, you must provide evidence that you meet the University's minimum English language requirements (below).</p> <p><em>As an international research-intensive university, we welcome students from all walks of life and from across the world. We foster an inclusive environment where all can flourish and prosper, and we are proud of our strong commitment to student education. Across all Faculties we are dedicated to diversifying our community and we welcome the unique contributions that individuals can bring, and particularly encourage applications from, but not limited to Black, Asian, people who belong to a minority ethnic community, people who identify as LGBT+ and people with disabilities. Applicants will always be selected based on merit and ability.</em></p> <p>Applications will be considered on an ongoing basis.  Potential applicants are strongly encouraged to contact the supervisors for an informal discussion before making a formal application. We also advise that you apply at the earliest opportunity as the application and selection process may close early, should we receive a sufficient number of applications or that a suitable candidate is appointed.</p> <p class="MsoNoSpacing"><strong>Please note that you must provide the following documents in support of your application by the closing date of Monday 6 January 2025 if applying for the China Scholarship Council-University of Leeds Scholarship, Monday 3 February 2025 if applying for Leeds Doctoral Scholarship or Tuesday 1 April 2025 for Leeds Opportunity Research Scholarship.</strong></p> <p><strong>If you are applying for the School of Mathematics Scholarship 2025/26, or with external sponsorship or you are funding your own study, please ensure you provide your supporting documents at the point you submit your application:</strong></p> <ul> <li>Full Transcripts of all degree study or if in final year of study, full transcripts to date</li> <li>Personal Statement outlining your interest in the project</li> <li>CV</li> </ul>

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<p style="margin-bottom:12px"><strong>Self-Funded or externally sponsored students are welcome to apply.</strong></p> <p><strong>UK</strong> – The <a href="https://phd.leeds.ac.uk/funding/138-leeds-doctoral-scholarship-2025-faculty-of-engineering-and-physical-sciences#:~:text=Key%20facts&text=One%20Leeds%20Doctoral%20Scholarship%20is,rata%20for%20part%2Dtime%20study.">Leeds Doctoral Scholarship</a> <strong>(closing date: Monday 3 February 2025)</strong>, <a href="https://phd.leeds.ac.uk/funding/234-leeds-opportunity-research-scholarship-2022">Leeds Opportunity Research Scholarship</a> (closing date: Tuesday 1 April 2025) and <a href="https://phd.leeds.ac.uk/funding/55-school-of-mathematics-scholarship-2025-26">School of Mathematics Scholarship 2025/26</a> <strong>(open from October 2024)</strong> are available to UK applicants.</p> <p><strong>Non-UK</strong> – <a href="https://phd.leeds.ac.uk/funding/55-school-of-mathematics-scholarship-2025-26">School of Mathematics Scholarship 2025/26</a> <strong>(open from October 2024)</strong> are available to all International applicants.  The <a href="https://phd.leeds.ac.uk/funding/48-china-scholarship-council-university-of-leeds-scholarships-2021">China Scholarship Council - University of Leeds Scholarship</a> <strong>(closing date: Monday 6 January 2025)</strong> is available to nationals of China. The <a href="https://phd.leeds.ac.uk/funding/73-leeds-marshall-scholarship">Leeds Marshall Scholarship</a> is available to support US citizens. <a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a> is available to graduates of the University of Leeds.</p> <p>You will be responsible for paying the overtime fee in full in your writing up/overtime year (£320 in Session 2024/25), but the scholarship maintenance allowance will continue to be paid for up to 6 months in the final year of award.</p> <p><strong>Important: </strong>Please note that that the award does <em><strong>not</strong></em> cover the costs associated with moving to the UK.  All such costs (<a href="https://www.leeds.ac.uk/international-visas-immigration/doc/applying-student-visa">visa, Immigration Health Surcharge</a>, flights etc) would have to be met by yourself, or you will need to find an alternative funding source. </p> <p>Please refer to the <a href="https://www.ukcisa.org.uk/">UKCISA</a> website for information regarding Fee Status for Non-UK Nationals.</p>

<p>For general enquiries about your application, please contact PGR Admissions by email to <a href="mailto:maps.pgr.admissions@leeds.ac.uk">maps.pgr.admissions@leeds.ac.uk</a></p> <p>For questions about this research project, please contact Dr Nadhir Ben Rached by email to <a href="mailto:n.benrached@leeds.ac.uk">n.benrached@leeds.ac.uk</a></p>