Inventory systems

• orders arrive (Poisson?)
• can we fulfill? If yes: Process order and deliver.
• if not: "stockout"
  • lost customer (leaves)?
  • queued customer (stays in backorder queue)
  • costs of losing/queueing orders?
• inventory review: do we need to replish?
  • continuous (check all the time)
  • periodic (check only every $k$ timeunits)
• replenish: we add to our inventory (how much?)
• lead time: time until replenishment arrives

• customer satisfaction:
  • fill rate: prob. of satisfying a demand (order can be fulfilled at first try)
  • stockout probability: 1-fillrate
• inventory-related costs
  • inventory (facilities)
  • ordering
  • backordering
  • not having stock (stockout)

• costs
  • total cost = ordering cost + inventory cost + backorder cost
  • ordering cost = per-order cost * number of orders
  • inventory cost = holding cost (per unit per time) * average inventory
  • backorder cost = per backorder cost * number of backorders
• state variables
  • $I$: inventory (this is what we have "in stock" now)
  • $IO$: inventory on order (ordered, but not arrived)
  • $BO$: backorder (queued incoming orders)
  • $IP=I+IO-BO$: the "inventory point"
• inventory control policies
  • EOQ model: reorder Q every R timeunits (see more here)
  • (r,Q) continuous review, reorder Q if IP below r
    (rQinv.doe)
  • (s,S) continuous review, reorder S-IP when IP below s.
  • (R,S) as (s,S) but check only every R timeunit (periodic),