Inventory Management

Inventory Management

1. News Vendor Model

   • Balancing Cost of Overage & Underage
     • Ordering 1 more unit increases chances of overage (Co x Prob (D < Q)
     • Ordering 1 less unit increases changes of underage (Cu x 1-Prob (D < Q)
     • Profit is maximise when expected loss on Qth unit equals to expected gain on Qth unit
       • P (D<=Q)= Cu / (Cu + Co)
         • Q = Mean Demand x Z Stats based on P(D<=Q) x Standard Deviation)
   • Performance Measurement
     • 1) Expected Lost Sales = SD x L(Z) <--Calculate Z First then find L(Z) value
       • 2) Expected Sales = Expected Demand (Mew) - Expected Lost Sales
         • 3) Expected Left over Inventory= Q- Expected Sales
           • 4) Expected Profit = Cu x Expected Sales - Co x Expected Left over Inventory
             • 5) Expected Fill Rate = Expected Sales/Expected Demand
     • Instock Probability = 1) Find Z and 2) Find Prob
       • Stockout probability = 1 - Instock Probability
   • Applies to: 1) "too much" or "too little", 2) Single Order (Order LT > Demand Period), 3) Uncertain Demand

2. Continuous Review Model (Multiple Periods Inventory Model)

   • EOQ (Assumes Demand & Lead time is deterministic)
     • EOQ (How Much to Order) = SQRT ( (2 X D x Ordering Cost)/ Holding Cost)
     • ROP (When to order) = Demand over Lead time
       • Under uncertain demand, ROP = Demand over Lead time + Safety Stock
         • Safety Stock = Standard Deviation of Demand x Z value (Attained using Critical Ratio or Instock Probability Level/Cycle Service Level
           • 3 Factors affecting Safety Stock: Lead TIme, Service Level & Standard Deviation
         • What if Demand is uncertain but daily/weekly follows normal distribution ?
           • Demand during leadtime and standard deviation of demand during lead time is uncertain
   • Order is triggered once ROP is reached
   • Performance Measures
     • Average on hand inventory = Cycle Stock + Safety Stock
       • Cycle Stock = Q/2
     • Expected Back Order = SD x Sqrt (LT) x L(Z)

3. Periodic Review Model (Order Up to model)

   • Order Up To Level: S= U(T+L) + Z*SD*SQTRT(T+L)
     • Optimal Z (Instock Probability) = Cost of Shortage/Cost of Excess + Cost of Shortage
   • Expected Backorder = SD * SQRT(T+L)* standard normal Loss function (LZ)
   • Expected Fill Rate = 1 - Expected Bsckorders/UT( Demand during Review period)
   • Advantages: Easy to Implement, Inventory level needs to be known only when time to order.