This article uses the phrase "linear programming". Keep in mind that a lot of supply chain problems will involve integer valued variables (unit quantities, on-off decisions, etc.). Thus, you will probably see terms like Mixed Integer Linear Programming (MILP) or Mixed Integer Programming (MIP) used more often than just Linear Programming (LP).

When tackling real-world supply chain challenges, start by understanding the problem and stakeholder priorities to ensure the solution development process aligns with business needs, rather than prematurely selecting specific methods like linear programming (LP) or mixed-integer programming (MIP). Assess current operations and openness to change, focusing on practical solutions over optimal ones, and choose the appropriate methodology based on complexity and data availability. Manage the expectation from the beginning so the solution doesn't come as a surprise and is unimplementable.

I would start by defining the key variables: costs, demand, supply, and constraints like capacity or delivery times. I then set up an objective function, usually to minimize costs or maximize service levels, while ensuring that supply meets demand across the network. Linear programming allows us to create a model that includes all these factors, enabling us to test different scenarios and identify the most efficient distribution strategy. We need to analyze the results, so as to make data-driven decisions that strike the best balance between cost savings and maintaining high service levels, ensuring we meet customer needs without overspending.

Objectives usually include minimizing cost- transportation and processing, minimizing late delivery, minimize unmet demand and maximize service level. That’s is done by insuring the availability of the material, sending them through the channels and sites that can handle that type of material, respecting capacities in shipping means and processing sites