INVENTORY SYSTEMS

Assume periodic review, i.i.d. random demands, constant (possibly non-zero) lead times and full backlogging. When to order? How much to order? Inventory Systems

Inventory Costs Ordering Cost setup cost for placing an order, K per-unit ordering cost, c order amount, Q i Holding (Storage) Cost per-period per-unit of inventory, h inventory level, X i Shortage (Unsatisfied Demand) Cost per-period per-unit of inventory, p (s, S) inventory control policy is optimal for this cost structure IGLEHART, 1963

When the inventory position (inventory level + quantity on order) falls to or below the level s, place an order to bring the inventory position up to S. (s,S) Ordering Policy

Demand in period i, D i Constant lead time, L Cost Information (K, c, h, p) Inventory control policy parameters (s, S) – decision variables Before ordering Inventory level at period i, X i : (On hand) – (Backorders) Inventory position at period i, Y i : (Inventory level) + (On order) Order quantity at period i, Q i Inputs and State Variables

Problem Formulation Period i

Inventory Simulation in Excel Lead time: 1 period Demand: Uniform over {0,1,2,3,….,10} (Integer valued)

( s, S ) Policy – Total Cost Structure S s