SIMULATION EXAMPLES INVENTORY SYSTEMS

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?

(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

(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.

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

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