Inventoryn

Inventoryn is a term used in inventory management and operations research to denote the quantity of stock on hand at the end of period n in a discrete-time framework. It is typically written as inventory_n in mathematical notation and functions as a state variable describing the stock level across periods.

In a simple planning model without backorders or losses, inventoryn is updated from the previous period by inventoryn = inventory_{n-1} + receipts_n - demand_n, where receipts_n are items received during period n and demand_n is customer demand within period n. If the calculation yields a negative value, the model either records a stockout or allows backorders depending on the assumptions.

In practice, inventoryn forms the basis for policies such as periodic review or continuous replenishment, and is used to compute performance metrics like service level and fill rate. More complex versions of the model may include spoilage, shrinkage, returns, or capacity constraints.

Example: with inventory0 = 100, receipts1 = 20, demand1 = 35, inventory1 = 100 + 20 - 35 = 85.

Notes: Notation varies; some sources write inventory_n or i_n. Inventoryn is a conceptual variable regardless of capitalization. It is distinct from related terms such as safety stock, reorder point, and order quantity, which describe triggers and targets rather than the current stock level.