Background of the problem for people non familiar with transfusion:

Every day, hospital transfusion services must guarantee they have enough blood to meet patient transfusion demand. This is very like managing a food stock in a refrigerator but even easier (just one product, one expiration date).

Assumptions:

- RBC (red blood cell) units are kept on a refrigerator with enough capacity

- Maximum expiration date for RBC is 42 days.

- We make a routine order to the blood bank provider (our grocery store) every day from Monday to Friday. We can make additional orders if we run out of stock.

- We practice first in first out.

The model should satisfy the following targets:

- Minimize the expiration rate (the number of RBC units expiring every certain time)

- The less time on the refrigerator the better (eat fresh)

- Avoid extraordinary orders as much as possible (some extraordinary order might be considered to cope with transfusion peaks of demand)

- Note: I have purposely simplified the problem (no considerations of ABO group distribution, crossmatched reserved units, or reduced expiration date of the irradiated blood…).

Non controlled external factors:

- Transfusion rate

- Average remaining time to expiration of the received blood.

What we are looking for is the optimal number of RBC units we must order on a routine basis (M-F) which is the only factor we can adjust to optimize the equation. Resulting figure must be recalculated when transfusion rate or average expiration date of the received units change.

Intuitively, I see how the number of extraordinary orders and RBC freshness are at opposite sides of a balance, because if a higher number of extraordinary orders is tolerated, then it should result in a smaller but fresher RBC inventory. On the other hand, in order to avoid extraordinary orders, you need a greater inventory thus increasing the average age of your products and the risk of expiration.

Any idea or suggestion? Any available script on Excel/SPSS/Stata/R/SQL? Any related bibliography?

I can provide raw data for simulations on demand if someone want to make a collaboration.