# inventory control for vending machine like mini store

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?

• If there's no lead time and no fixed cost for replenishment, then the optimal solution is to replenish the machine every time anyone buys any item from it. It's a continuous-review base-stock policy with base-stock level = shelf space for that product. So I think you are missing something in your model that prevents this. Typically that would be either a fixed cost or a reorder interval (e.g., we can only restock once per day or once per week). Commented Feb 8, 2021 at 2:09
• If the shelf space for each item is fixed, then you just want to optimize each product individually. Carton and pack would be treated as separate items. There are models that optimize the shelf space, but those are more complicated than standard inventory models. Commented Feb 8, 2021 at 2:11
• Also: What do you mean by BOH? Beginning on-hand inventory? Commented Feb 8, 2021 at 2:11
• @LarrySnyder610 yes,at least according to fuseinventory.com/blog/inventory-planning-dictionary .@janicebaratheon if you really have no costs/restrictions at all and no lead time And want to minimize lost sales, it is intuitively and mathematically the best option to restock the moment your inventory drops below S. I also think you are missing something in your problem formulation. Commented Feb 8, 2021 at 9:40