You're facing supply chain disruptions. How can you adapt your linear programming model effectively?

There is a difference between a Linear Programming model and a Mixed Integer Linear Programming model. The difference is so huge that one can prove there exist uncountable numbers between 0 and 1. Most of the real case scenarios fall under the second umbrella. Also, there are thousands of reasons for supply chain disruptions. Say, raw materials are not coming in time due to the supplier issue. Maybe, some common sense or descriptive analytics can solve the issue. The problem is that, the method will come later. Firstly, we need to understand the reason behind the supply chain disruptions. If it requires analytical prescriptive model to solve the issue, do the modelling properly and use the output to minimize the pain points of the planner.

As others have mentioned MIP models are usually better models than LP models for supply chain management. After finding the issue, you need to adjust the model. If the problem is related to a supplier and the raw material is not available or not enough, you need to adjust the constraints considering the maximum capacity of that supplier to reflect the problem. If there are problems with the transportation, you need to adjust the routing section of the model accordingly. Generally, generating actionable and realistic output that can help the company requires constant updates on the model.

To adapt your linear programming model during supply chain disruptions, you need to look at how external shocks affect your constraints and objective functions. Variability in transportation lead times, fluctuating supplier reliability, and capacity issues often shift optimal solutions. It’s essential to review constraint robustness and adjust parameters for real-time decision-making. You might have to relax or tighten constraints like capacity or cost limits, depending on how the disruption impacts your supply chain's efficiency. Small adjustments can shift the feasible region, leading to a more resilient solution that balances operational flexibility and long-term strategic goals.

You need to ensure your model reflects real-time changes in key variables. If you’re seeing supplier delays, inventory shortages, or unexpected demand spikes, your linear programming model must adapt. Adjust parameters such as lead times, production capacities, and supply availability dynamically. Instead of a one-time update, set up your system for continuous recalibration. For instance, integrating real-time data feeds can ensure your decisions remain aligned with the disruptions you're facing. This will enable more resilient allocation strategies and resource optimisation.

It is really important to update models in supply chain management. Depending on the current circumstances, the company's priorities might change. In regular situations, usually, the top priority is cost minimization and profit maximization, while in specific situations, such as when a material shortage happens or when there is a problem with transportation, the top priority might change to meeting the demands on time, avoiding delays and etc. Knowing the priorities at the moment is the key to successfully managing the supply chain system especially in unusual circumstances. Multi-objective optimization techniques can help to generate actionable outputs when we have more than one objective which need to be optimized simultaneously.

When disruptions hit, adapt your linear programming model by refining constraints and goals to reflect the current supply chain dynamics. Instead of solely focusing on cost, incorporate factors like lead times and resource availability. Practical scenario: you're dealing with variable supplier reliability, and it's essential to adjust your model to account for those fluctuations. Consider adding penalties for delays or shortages, which help align your model with operational realities. Keep service levels stable while balancing inventory and delivery costs, optimizing the mix based on what's feasible under evolving constraints.

Depending on the type of disruption, the relevant constraints can be adjusted to accommodate the scenario. For instance, if there’s a capacity shortage, you could relax the associated constraint to determine the extent of the shortfall and respond appropriately. In the event of a machine breakdown, constraints related to that specific machine can be temporarily disabled to assess the impact on the overall plan. However, to achieve this functionality, the original LP/MIP model must be formulated with the necessary flexibility.

It's important to first understand the reason for supply chain disruption. For instance, demand forecasts might be incorrect due to some uncertainties, delayed lead times etc. Covid was a completely unforeseen situation which led to supply chain disruptions. These disruptions can happen anytime and hence it is necessary to build adaptive models. When it comes to linear programming, the constraints have to be revised accordingly with the new forecasts. Stochastic linear programming can help in mitigating disruptions to some extent.

Stochastic optimization can be integrated into Linear programming by introducing probability scores for different scenarios and integrating them in the same Linear model.

This is a fascinating topic. One can simulate and run varying runs to observe the random variable characteristics of optimal solutions and how the problem changes under uncertainty (constraints and objective function). Some methods even include importance sampling to determine which scenarios to consider. Then, a MILP is typically applied to solve representative scenarios rather than low-level and extraneous scenarios.