The Bayesian t-shirts: a taste of optimal inventory

This repo contains the homemade inventory system I use to manage the flow of promotional t-shirts I send out as gifts as part of my marketing.

Key assets:

• tshirt_inventory.xlsx (included as tshirt_inventory_redacted.xlsx): a spreadsheet to capture and organize the flow of individual shirts going out, boxes of bulk shirts coming in from the screen printing shop, and tabulations of these to track when I'm running out of certain sizes.
• inventory_to_shippo_labels.py: a script to turn the inventory spreadsheet into a CSV file understood by Shippo, which draws upon a crib sheet to turn t-shirt sizes into order weights for the postage.
• address_parser.py: a hand-rolled international mailing address parser, used by inventory_to_shippo_labels.py. It only has parsing rules for the few countries I've sent t-shirts to - definitely not comprehensive for public use.
• build_order.py: the interesting thing from a data scientist's point of view: a script that uses Bayesian inference (closed-form Dirichlet posterior, so far) and discrete optimization (brute-force refinement, so far) to build an optimal re-order for a box of shirts. In other words, it answers, "if I have this inventory on hand, and that order history, how many of each size should I buy?"

Usage

# Create a CSV suitable for import into Shippo
./inventory_to_shippo_labels.py tshirt_inventory.xlsx xxxx-yy-zz-labels.csv

# Optimal order to console using a fast heuristic
./build_order.py tshirt_inventory.xlsx
./build_order.py tshirt_inventory.xlsx -m heuristic -o console

# Optimal order with some brute-force refinement
./build_order.py tshirt_inventory.xlsx -m optimized

# Write optimal order to the "Hypothetical order" row in the "inventory" sheet
./build_order.py tshirt_inventory.xlsx -o hypothetical

# Finalize optimal order to the "incoming" sheet with today's date
./build_order.py tshirt_inventory.xlsx -o final

Note: As of writing, the openpyxl calls that write the optimal order data to the spreadsheet are fiddly. To avoid errors, one must save the workbook in Excel, then close the workbook before writing to it with this script.

Prior/industry knowledge

According to this blog post by a t-shirt wholesaler, the global t-shirt size distribution is as follows:

• XS: 1 percent
• S: 7 percent
• M: 28 percent
• L: 30 percent
• XL: 20 percent
• 2XL: 12 percent
• 3XL: 2 percent

This information can feed into an informative prior for building an optimal order.