Tesco's Burger Relish Best Before End date number
PowerShell, 74 70 67 bytes



param($y,$m,$d)-join"$y 00$((date "$m/$d/$y"|% d*r)-1)"[2,3+-3..-1]


Try it online!

Exactly what it says on the tin (but formatted weirdly). Takes in $year, $month, $day, plucks out the last two digits of the $year, gets a .NET datetime object of the specified day, then gets the dayofyear (with |% d*r) thereof. Subtracts one to make it zero-indexed, then uses string formatting and slicing to make it three-padded (e.g., 000 instead of 0), and then -joins it all together into a single string with implicit output.

Note this is culture dependent due to the datetime formatting. This works in en-us, which is what TIO also uses.

-3 bytes thanks to mazzy