Mathematical Programming is a marvelous field with a huge potential to improve everyday systems and processes.  The name “mathematical programming” is somewhat misleading, as it usually has more to do with problem formulation and mathematical modeling than it does with actual computer programming.  The field is technically demanding, but the results it yields can provide substantial improvements to existing practices.

Resource allocation problems are a special class of optimization problems that are of particular interest to L1 Scientific.  These problems involve assigning resources to distinct activities, such as vehicles to routes, jobs to machines, components to products, and personnel to labour.  The problems are always tied to constraints, such as limited availability or cash-flow,  and objectives, such as minimizing cost or maximizing profits.  In most cases, even a small number of variables and a handful of constraints leads to a staggering number of candidate solutions to consider.  With a mix of continuous and discrete variables, finding the optimal solution makes finding a needle in a haystack look easy.

Key areas where L1 excels are in linear programming (LP), integer programming (IP), and mixed integer-linear programming (MILP).  These branches of optimization can be used in an incredibly diverse range of problems, from solving Sudoku puzzles to minimizing drag on a wing, to selecting warehouse sites for optimal distribution of goods.  At L1 we’re using mathematical programming in some of our Data Science projects and mechanical designs, but we are also working on custom software systems that we will discuss in more detail in the future.