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The Role of Mathematical Optimization in Designing Resilient Supply Chain and Logistics Networks

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Although today’s global supply chains are productive and efficient in normal conditions, they are so vulnerable to disruption and operational risks, such as demand fluctuation, natural and human-made disasters, that disrupt the flow of materials in supply chains. Such risks can disrupt different components of a supply chain and logistics network such as manufacturers, distribution centers, suppliers, and transportation links, which results in a wide range of consequences like the loss of goodwill as well as revenue and productivity reduction. 

The latest example of a global disruptive event is the COVID-19 pandemic which caused long-term supply and demand disruptions. This pandemic disrupted the supply chain of 94% of Fortune 1000 companies. In addition, many companies, which had geographically concentrated their facilities to save costs, were dramatically disrupted due to long-term lockdowns in their area. For example, at least 51,000 and five million companies have Tier 1 and Tier 2 suppliers, respectively, in Wuhan where the COVID-19 was reported for the first time. 

The COVID-19 pandemic significantly affected the supply chain of many important products. Take the NdFeB magnet as an example of such essential products. This permanent magnet is considered critical due to its increasing importance in more than 20 industrial sectors, including clean energy and healthcare. The temporary production loss and facility shutdown in China during the COVID-19 pandemic caused severe supply disruption risks for the NdFeB magnet because China has about 80% of the global market share of this magnet. 

In addition to the COVID-19 pandemic, international trade wars and geopolitical conflicts have made negative unpredictable impacts on the NdFeB magnet supply chains. Therefore, the United States has been encouraging American companies to develop alternative sources of producing NdFeB magnets such as NdFeB magnet-to-magnet recycling because the development of upstream and downstream processing capabilities for producing new NdFeB magnets is time-consuming and expensive. 

Recently, researchers and decision-makers have taken the benefit of mathematical optimization to design a resilient NdFeB magnet recycling supply chain in the United States. Indeed, they have used optimization models and algorithms to answer the following questions in the process of designing a reverse supply chain and logistics network that is resilient to the disruptions caused by the COVID-19 pandemic:

  • How should facilities be strategically located to maximize the resiliency and the profit of the network? The facilities of such as reverse network are 1. collection centers that collect end-of-life products (e.g., electric vehicle motors), which include used NdFeB magnets, 2. Dismantling centers that disassemble end-of-life products to obtain the used NdFeB magnets, 3. Recycling centers that recycle used magnets to produce new ones.
  • What are the optimal processing capacities, inventory levels, and transportation flows of the facilities of the reverse supply chain and logistic network that maximize the profit and resiliency of the network against disruptions caused by disruptive events like the COVID-19 pandemic?

Mathematical Optimization enables decision-makers to instantly identify the best decision out of a large number of alternatives (e.g., millions of possible decisions) that leads to the best possible result according to prespecified criteria such as profitability, service level, resource utilization, etc. Mathematical optimization models capture the key features of a complex business problem including business rules, objectives, and decisions. Then, they are solved by optimization solvers which are powerful computational engines that read optimization models and then deliver the best decision. Mathematical Optimization has many advantages including but not limited to considering interdependencies of complex systems, supporting what-if scenario analysis, avoiding personal bias, and significant flexibility in constantly changing business environments.

Recently, optimization researchers have used mathematical optimization techniques such as stochastic programming, chance-constrained programming, and decomposition algorithms to design a resilient supply chain and logistics network for recycling NdFeB magnets. To that end, they have included multiple risk management strategies, including backup facilities, minimum service level enforcement, geographical diversification of facilities, buffer inventories, and dynamic material flow adjustment, in the mathematical model of the supply chain and logistics network. Moreover, they have designed disruption scenarios that mimic the impacts of the COVID-19 pandemic and then inserted those scenarios in their chance-constrained stochastic programming optimization model to maximize the total profit while keeping the supply chain resilient enough to COVID-19 disruptive events. More specifically, the developed optimization model is capable of considering many details, including disruption and recovery durations, supply and demand disruptions with different timings, the non-linear post-disruption recovery process, and the rebound effect, that leads to the most efficient recycling supply chain and logistics network with highest possible revenue and resiliency. 

The developed mathematical optimization model recommends the optimal facility locations, inventory levels, material flows, and processing capacities for NdFeB magnet recycling in the United States that could meet 99.7% of total demand in this country. Moreover, the total profit generated by the reverse supply chain and logistics network recommended by the optimization model is projected to be $165 million. The optimal recycling production plans obtained by the optimization model showed that investing about 1% of the total cost in buffer inventory could satisfy over 99% of the total demand. Therefore, the suggested network configuration by the optimization model will save costs and improve business resiliency over the long term. Additionally, the what-if-scenario analysis conducted by the developed optimization models revealed that there is a trade-off between profit and resiliency where locating more dismantling centers will result in more resilient but less profitable supply chain and logistics networks for recycling NdFeB magnets.

In brief, disruptive events such as the COVID-19 pandemic which cause many operational and disruption risks can dramatically decrease the productivity and efficiency of the supply chain and logistics networks of many essential products such as NdFeB magnets. Mathematical Optimization, which is a powerful prescriptive analytics technology, can be utilized to design resilient and profitable supply chain and logistics networks that are very complex due to their multi-echelon, multi-period, and multiproduct nature. The optimization models are so flexible that decision-makers can integrate many details such as different risk management strategies such as facility diversification, buffer inventories, penalization of unsatisfied demand, enforcement of minimum service level, and dynamic material and inventory adjustments in their models to ensure the network resilience against potential operational and disruption risks. Moreover, decision-makers can insert multiple scenarios that mimic the real-world conditions into their optimization models to consider the uncertainty in their decisions as much as possible.   

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