Let's say we have a kiosk inside gas station selling cigarettes and snacks outside a supermarket. There are limited space for each product. The kiosk only allows to get restocked from the supermarket, so there's no lead time to restock. The objective is to figure out what is the ideal BOH(balance on hand )value or (s,S), (r,Q) for each product to minimize the lost sales. There's no labor or any type of cost. We have the ability to monitor the BOH every day. Another question is that some people buy a carton of cigarette rather than an individual pack, and I think we need to treat them as different product. We can only restock once per day.
My thinking: since each product has fixed self space(could be changed based in the future), this space number becomes the S. The problems becomes to find the right safe stock s considering the demand(could be bootstrapped from history or forecast).
Is there any inventory model for this kind of problem? Is it too over-simplified?