Mathematics Saves Lives and Avoids Conflicts

Written By: Sanjay Jagdale
  • 5/26/2022
  • Read Time : 5 min

Military standards, known as Mil-Spec, are the highest, with no room for compromise. The unified focus on accomplishing a mission requires “readiness” across the entire team, including warfighters, support systems, and leadership. To achieve the mission, personnel must make the best decisions quickly and move forward without hesitation. It’s no surprise the military deploys the highest standard for mathematics and service parts supply chain optimization to save lives and avoid conflicts.

Ensuring weapon systems and asset readiness requires Mil-Spec service parts optimization capabilities. Sophisticated software can crunch the numbers and analyze immense data sets to ensure fully optimized operations that support maximum readiness. What undermines military readiness? Disruption.

We’ve all witnessed the major disruptions caused by COVID-19. Supply shutdowns left raw materials in short supply, and many vital components have been unavailable due to reduced supplier capacity. Transportation delays have dramatically changed everyone's shipping and receiving timelines, causing unreliability to grow for procurement lead time and repair turnaround times, etc. Despite these and other disruptions, military readiness remains a priority and imperative. When disruptions compound, the military must capitalize on cutting-edge technology capabilities.

What if we could model supply chain disruptions and translate them quantitatively to understand the impact on readiness?

Mathematical models, sophisticated algorithms, and emerging technology can represent service supply chains with laser-point accuracy. Fuel for this high-tech decision-support engine includes system configuration data, multi-indenture bills of materials, multi-echelon supply chain configuration, asset deployment location information, a mapping of the service supply chain network, and an overlay of mission profiles and operational hours. Don’t forget that not all parts are equally critical in driving readiness. This complexity demands high order math, advanced service supply chain logic, and a well-trained team to execute and accomplish its mission.

With this infrastructure, we can understand parts demand above and beyond what we have planned and factor in the reality of changing deployments from location to location, changing flying hours and profiles. Reliability characteristic data with operational hours help understand what is driving the demand.

Is the military ready for whatever demand comes its way? Is your organization ready?

The military requiring readiness and other organizations requiring asset uptime and availability will similarly find that advanced technology delivers the capabilities needed to model stocking levels and mitigate the impact on service levels. How does it work, though?

This sophisticated analysis gets us to a part-level service metric for issue effectiveness (some call it fill rate). It helps compute the expected backorders based on available parameters. However, the military must focus on system-level metrics to achieve readiness goals. Even if we target to achieve a 90% issue effectiveness or a 90% fill rate for every single part, that alone will not be sufficient to guarantee a 90% readiness level. Part-level, individual metrics do not necessarily translate to system-level metrics. Put another way, just ensuring 10% stock outs is not sufficient to ensure that only 10% of the time we’ll have downtime on a weapon system.

What is essential is the number of backorders and the duration of the backorders. The duration of the backorders determines the duration of the downtime. A key realization here is that it’s actually the combined number and duration of expected backorders that drives the fleet's readiness. This gives us the flexibility to decide that if we cannot perform to an optimal level on certain parts because of supply chain constraints, maybe we have the flexibility to keep the overall total backorders under the same threshold.

Lower performance on one part can be made up for by getting higher performance on other parts. It seems counterintuitive, if your demand is for part A, how is more of part B going to help? With readiness as the target, you can understand what causes unreadiness, which is usually a mix of various parts. It’s the combination of improving the mix and better forecasting. With mathematics and modeling, we can do trade-offs. The supply chain disruptions are represented in parameters such as higher variability in lead times, longer order and ship times or delays, or capacity constraints. If a supplier is capacity constrained, they can no longer meet the same lead times. This can be modeled very accurately statistically to illustrate a combined impact of disruption.

Based on these observations, we can think of strategies for mitigating when we know circumstances have changed. The first thing to do, given new longer lead times, new variability, new demands, etc., is to re-compute stocking levels to be optimal again. Intuitively, you can imagine that if the lead time on a part has gone up, the stocking level that's going to be recommended will be higher on that point as well. That may be mathematically true, but the reality is that the supplier is already struggling to give us the current stocking level.

Therefore, we need to make up for any performance loss on this part somewhere else. This can be represented in the mathematical model by constraining the aggregate total stocking level for a part to be within whatever you currently have in the system plus whatever limited supply they can promise to you over the planning horizon. Constraining your optimization to that level allows optimization software to calculate better trade-offs and identify if other parts can take up the slack.

Another idea is to look for other suppliers who may have different lead times so you can split the supply of the demand you put on your suppliers and model that within your mathematical formulation. Since we know readiness is so strongly dependent on backorders, another idea is if we cannot increase our supply, we can try to reduce our demand.

How can we reduce the demand, especially during significant disruptions? You can readjust your scheduled maintenance events. Since each event has its work scope and probabilistic bill of materials, you can juggle around your schedules so that some demand for those critically constrained parts is reduced. With a lower forecast, even with the current stocking levels, you can reduce the backorders and thereby improve your readiness levels. These techniques and quantitative analysis deliver tangible improvement in readiness.

Another mathematical tool we can call upon is Monte Carlo simulation. The mathematical models we discussed are put into software systems, including those from PTC like Servigistics, which are based on probability distributions that assume static or quasi-static processes. Monte Carlo simulations are designed to model service supply chains to get a good sense of the impact of long-term steady state improvements on stocking level changes. These simulations will tell you how long it will take to feel the impact of stocking and demand changes.

An illustrative example in the commercial sector is Thermo Fisher Scientific. As they adapted to Covid delays from suppliers we helped them model the impact for quite a few suppliers and parts, which would have caused tremendous disruption. We analyzed the model to understand the disruption and impact on service and downtime. The analysis showed a disruption over two to three months, which helped to understand and better mitigate the impact on service levels. Prioritized mitigation strategies for specific parts helped get through the constraint. Suppliers were notified of the top 12 parts (out of hundreds impacted) that were the highest priority to ensure Thermo Fisher Scientific could maintain service levels with critical customers.


As supply disruptions have become more common, mathematical spending models and advanced simulations help quantify the impact of the disruption on service levels. This analysis informs mitigation strategies that maintain service levels even during prolific disruptions. It’s beautiful to see the mathematics and advanced software helping to save lives and avoid conflicts.

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About the Author

Sanjay Jagdale

Dr. Sanjay Jagdale is a Principal Architect with PTC and a well-respected service supply chain expert. Dr. Jagdale consults with the global leaders in DoD, aerospace, commercial aviation, and high tech offering his two decades of experience developing and deploying leading-edge service supply chain solutions. Dr. Jagdale’s vision and experience are in high demand, particularly around improving demand planning and military readiness. Dr. Jagdale spent seven years as a professor of systems and industrial engineering at the University of Arizona. Additionally, Dr. Jagdale has developed and deployed service supply chain solutions for i2, MCA, Servigistics, and PTC. Dr. Jagdale holds a Ph.D. in Operations Research from Cornell University.