Hej Renze,
what you are looking for is a simple WMS (warehouse management system). I guess your needs will be fulfilled by the integrated WMS of Dolibarr. As far as i understand you, you just have products coming in and out, not for sale, but for internal use. So it’s just a simple receiving and shipping of goods.
The whole system will live or die with the people to feed it. If your goods are just taken out of the warehouse without shippment, then you will never have an overview about what still is on stock. That means, your employees will have to create a shipment if they take products out of the warehouse and to create a receiving if products are delivered. And someone has to book it, so the products are booked out. Otherwise you will never have the correct number of products in your warehouse.
But - if the employees will do this you will be happy with Dolibarr. You can just try this out and simulate some actions (purchasing, shipping, doing an inventory, loss of products and so on). And if you are happy give Dolibarr a try 
regards
Stefan
