We start by assuming that the antecedent of "their" is somewhere in the previous sentence. I've numbered the obvious referents for convenience:
During the last few years, there has been an enormous increase1 in the number2 of shops, stores and supermarkets4 which provide facilities for self-service5.
I'll explain the missing number 3 in a moment.
"Their" is plural. It does not refer to 1 or 2, since those two words are singular here.
The next available referent is the coordination shops, stores and supermarkets4. The final referent is facilities for self-service5. In this case, 5 is subordinate to 4. We treat "which provide facilities for self-service" as a modifier of "shops, stores and supermarkets".
I'm going to give this inclusive reference its own referent number:
During the last few years, there has been an enormous increase in the number of shops, stores and supermarkets which provide facilities for self-service3.
As I parse this, the antecedent of "their" is 3: the entire phrase "shops, stores and supermarkets which provide facilities for self-service".
Since 1 and 2 are unavailable because they disagree in grammatical number, 3 is the first available antecedent for the pronoun in question.
4 and 5 are still available. We count the whole first, and then count the available parts within the whole. We count independent elements before subordinate elements.
If later context includes something that makes 3 nonsensical, we would consider 4 (all shops, stores and supermarkets -- regardless of self-service facilities) as the next option. Only if that becomes nonsensical should we consider 5 (all self-service facilities -- regardless of location).
As posted, the only context we have is the following sentence. Given that, referent 3 is sensible:
[The] general purpose [of shops, stores and supermarkets which provide facilities for self-service] is to provide goods of every description attractively and hygienically and in perfect condition, so that the customer can serve herself and then pay for the goods with the minimum of delay.