In the Christmas bakery, the elves are busy preparing different goods including yummy Christmas cookies. The production is sectioned into different work areas and in the baking and oven area the elves are tasked with baking the cookies being delivered from the dough preparation and cookie cutting area.
The arrival of the trays is random and cannot be controlled by the elves in the oven and baking area. Whenever a new tray arrives and an elf is currently idle, the elf picks up the tray and walks to the ovens. When an oven is free/idle, the elf puts the tray into the oven and returns to idle mode, otherwise the elf waits in front of the ovens holding the tray and waits for an oven to become idle. While waiting, elves cannot put down the tray or do other tasks.
In the oven, the cookies take some time to bake and when finished baking, they can be removed from the oven in order to be packed under the condition that an elf is currently idle for pick-up. The packing is done in the following work area for packing and shipping. Every oven only has space for one tray at a time and as soon as a tray is removed once the cookies are baked, the oven is idle again, ready to bake another tray.
This sounds like a very well thought through system, so what could possibly go wrong?! Which measures should be taken to ensure the smooth operation of the work area where all trays can be baked and subsequently being packed and shipped? (Luckily, the time it takes to bake all cookies is not relevant.)
a. 🎅✅🎉 This is a perfect system, no additional measures needed!
b. 🧝♂️➕🔥 As long as there are more elves than ovens, the system will run smoothly.
c. 🔥➕🧝♀️ As long as there are more ovens than elves, the system will run smoothly.
d. 📊⏱️🏭 As long as the average number of trays arriving in the time span required for baking a tray is less than or equal to the number of ovens, the system will run smoothly.
e. ⚠️🔥📦 Whenever a tray is ready baked and some new trays have arrived and are waiting to be baked, removing the tray from the oven must be treated with higher priority. Then, the system will be running smoothly.
f. ❌🤯🎄 None of the measures or conditions listed above will ensure smooth operation of the oven and baking area.
Related control theory topic: discrete event systems