There are many concepts in inventory management that can and have filled textbooks. I will try to give a simple introduction and provide a starting point for further study here. Inventory is used to fulfill demand due to the difference in timing between when a product is completed and when it is required. In most optimization models, the level of inventory that is held is dependent on the expected demand, expected lead time (time it takes for the product to arrive from the time of ordering), ordering and holding costs. The variability in demand and lead time can be hedged with the use of Safety Stock (SS). Safety stock is an extra level of inventory above the inventory required to fulfill expected demand to hedge against higher than expected demand to avoid stockouts.
There is also a management model in manufacturing where no inventory is held called Just in Time (JIT) that was pioneered and made famous by Toyota.
Below is a chart to help visualize inventory levels through time:
Note: Here Safety Stock is referred to as Buffer Stock
One well-known formula in inventory management is Economic Order Quantity (EOQ). This formula tries to minimize total costs by balancing ordering and holding costs. Ordering cost (administration, transportation costs) increases as inventory levels decrease as more ordering is required while holding cost increases as inventory increases as required space, effort in managing, and risk of loss or inventory devaluation increases. In the above example, the EOQ is the vertical line of 500 units and the Reorder Point (ROP) is 300 units meaning that once inventory reaches 300 units, the next order will be made to keep the minimum stock level above 100 units. My goal here is not to derive and go in-depth on this formula but EOQ is typically the starting point of inventory management theory.
Where:
D = demand (per year)
S = Ordering cost (per purchase order)
H = Holding costs (per unit, per year)
There are many models that attempt to optimize inventory and they can get complex. It is a good idea to have a good understanding of a few of these but you should also understand that these equations require inputs and these inputs are not necessarily fixed. In my opinion, it is as important if not more important to focus on efforts to improve input variables rather than develop increasingly sophisticated models. Inventory is about managing uncertainty. Uncertainty, ordering costs, and holding costs can all be reduced through investment in resources and communication between supply chain partners.