I assume your goal is to compare the shops in terms of whether one seems to be more profitable than others? If so, doing each comparison for the times when both shops being compared may make sense. I say may, because if some shops cannot ever be open during some time periods (e.g. if shops at railway stations are allowed to be open on bank holidays, but other shops not, then this is simply an inherent advantage of being at a railway station - which presumably also comes with higher costs in terms of renting the space for the shop), then this may not answer the question. If it's rather that some shops did not exist / were being renovated, then it makes more sense to exclude those times from a comparison.
If you don't want to do pairwise comparisons like that, there's also the option of splitting the time periods into some intervals and then fitting, say, a linear mixed effects model for profit that has a fixed effect for shop, a random effect for each time interval (let's say week is a sensible unit) and perhaps some other factors (depends, see below, also time trends, seasonality etc.). E.g. in
R this could look like
lmer(profit ~ (1|week) + shop) (using the
lmer function from the
lme4 package, this assumes a data structure with one record per shop per week giving the
profit for that week in that shop). This is a bit too simplistic, e.g. it ignores that adjacent weeks are presumably correlated, but may give you a reasonable way to get some kind of impression of what's going on once one adjusts for what times shops were open in.
If it's really about comparing shops, then presumably there's also other considerations: rent for the shop (some locations are presumably more expensive than others), salaries for staff, what product ranges are offered (you need to figure out whether you truly want to compare shops that only sell, say, bread, pastries and coffee to go with full supermarkets or not), other costs (electricity, water, insurance...) and so on. What you wish to do about these things will really depend on exactly what your question is.