When planning a new shopping mall, where should you place the most popular stores? Getting the layout right is crucial so friends can easily shop together across their favorite spots. I helped mathematically optimize this for a client using an integer programming approach.
The problem has some key details. There are 4 sought-after stores that each need to be assigned to one of 4 vacant mall locations. The distance between each spot is known. And based on market research, we have data on the estimated number of shoppers going from store 1 to store 2, from 1 to 3, 2 to 3, etc.
The goal is to minimize total walking distance weighted by customer traffic flows between the stores. So if 5,000 people may go from store 1 to store 3, we want those stores as close as possible to reduce aggregate foot travel.
I formulated this as a 0-1 quadratic programming model. The decision variables are simple: 1 if store A locates at spot #1, 0 otherwise. Additional constraints ensure only one store in any spot and each store gets just one spot.
The objective function captures the weighted distances nicely. It has terms like: (Dist_Spot1,Spot4) * (Store1,Spot1) * (Store2,Spot4)
So if Store 1 is placed at Spot 1 and Store 2 at Spot 4, this distance contributes to the total cost to minimize.
Using MATLAB, I optimized over all feasible store-to-location assignments to identify the best options delivering equal minimum cost. The client can now strategically placeanchor stores knowing quantified tradeoffs!
To see more details, check out the paper.
Disclaimer: This project was completed as part of my BSc in Mathematics at Manchester Metropolitan University. The project was supervised by Dr. Keith Yates and Dr. Philip Sinclair.
This blog post is an LLM generated text, based upon the hand written report.