1. SIMULATION EXAMPLES
INVENTORY SYSTEMS

2. 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?

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

4. (s,S) Ordering Policy
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.

5. Inputs and State Variables
Demand in period i, Di
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, Xi: (On hand) – (Backorders)
Inventory position at period i, Yi: (Inventory level) + (On order)
Order quantity at period i, Qi

6. Problem Formulation
Period i

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

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