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 CostsOrdering 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
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0 ii QcQK
)0,max( iXp
)0,max( iXh
(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, Di
Constant lead time, LCost 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
Inputs and State Variables
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YSsYIQ
QXY
DQXX
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Problem Formulation
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Period i
1 LiQ iD iX iY
Inventory Simulation in Excelhttp://ie.bilkent.edu.tr/~ie324/Inventory.xlsLead time: 1 periodDemand: Uniform over {0,1,2,3,….,10}
(Integer valued)
(s,S) Policy – Total Cost Structure
S s