# Operations Research in Practice — Interesting Case Studies

Operations Research (OR) is hard to define clearly in a short sentence. It is definitely optimization, yet a term too general. Some coin the phrase “Prescriptive Analytics” which, in my opinion, is equally cryptic. It is one of those things you cannot properly define but certainly recognize. Thus, in this post, we will see examples of OR use in real life problems which save lots of time and money.

I will examine three case studies in this post which I find out of the ordinary applications. So, no straightforward supply chain, production planning or scheduling problems. We are aiming for diversity. *Currently I could only finish examining Gurobi case studies. So, this post will be solely on Gurobi examples.*

Here we go. Any misunderstanding is my fault, therefore I added source links at the end of each case.

# Birchbox — Optimizing Assortments

- Birchbox sends its 1M+ subscribers who get a “surprise” box of beauty products periodically from 800+ brand partners.
- Their Mixed Integer Programming model (with Gurobi solver) started failing to handle “who gets what” problem based on subscriber profiles, box assortments and many different parameters, in a reasonable amount of time.
- Their consultants devised an MILP model called “Reciprocating Integer Programming (RIP)” and improved performance by 99% 😱.

The interesting thing is that **a subscription box service uses an OR model to determine contents to send surprise boxes to their customers**. Details were scarce but I assume objective function is a variation of utility (“happiness?”) maximization, with capacity constraints (limited products of each kind) and diversification (“do not send similar products to a customer each month”) constraints.

Read the box subscription case study here.

# Tata Steel — Optimal Coal Blending Strategy

- Quality steel production requires special attention to coal blending. Blending combinations are endless.
- Coal blending is originally conducted by specialists. On the other hand, many coal products are subject to availability and price volatility. Getting the best output with minimal cost is hard.
- It is possible to create entirely new blends working better than those generated with standard formulas. Long term savings are in terms of millions of pounds.

The amazing thing here is that **they discovered new coal blends with optimization which are both cheaper and better than known formulations**. This certainly makes production and coal inventory management more flexible.

Read the coal blending optimization case study here.

# Portland — Public School Districting Optimization

- Problem is to determine which kids to go which schools, which school buildings to serve as what grades (e.g. elementary, middle school, K-8) and which closed buildings to reopen in order to maximize “convenience” (i.e. reduce travel times, minimize disruption, optimize class sizes etc.)
- They have real life data of kids’ grades and locations, school info (capacity, location etc.) and geographical info
- They used a multi-phase model to get what the best outcome

The incredible thing here is that **OR makes life and education significantly more convenient for tens of thousands of kids **thanks to brilliant and kind analytical people.

Read more about school district optimization here.

**Bonus**

I’m making a list of case studies by searching through OR resources starting with solvers like Gurobi, CPLEX etc. Here is the table of case studies full with real life OR applications. I’m updating the list with the resources I can find. Feel free to add more resources in the comments.