1. Simulation An Inventory Simulation

2. Example Daily demand for refrigerators at Hotpoint City has a probability distribution Lead time is not fixed but has a probability distribution Customers who arrive and find Hotpoint out of stock will shop elsewhere and Hotpoint will lose the sale These conditions do not meet the restrictions of inventory models developed earlierThese conditions do not meet the restrictions of inventory models developed earlier

3. Simulation Approach Simulation cannot determine the best inventory policy But it can compare policies Compare the following: –Reordering 10 when supply reaches 6 or less –Reordering 12 when supply reaches 3 or less

4. Hotpoint Input Data Current inventory = 10 Holding costs: $2/refrigerator/day Order costs: $50 per order Shortage costs: $30 per occurrence (sale is lost) Demand/dayLead Time Demand/day Prob Lead Time Prob 0.080 days.05 1.371 day.55 2.332 days.30 3.173 days.10 4.05

5. RANDOM NUMBER MAPPINGS DAILY DEMAND DAILY DEMAND -- Use column 2 0 1 2 3 4 PROB.08.37.33.17.05 RN 00-07 08-44 45-77 78-94 95-99 LEAD TIME (DAYS) LEAD TIME (DAYS) -- Use column 14 0 1 2 3 PROB.05.55.30.10 RN 00-04 05-59 60-89 90-99

6. SIMULATION OF Q*= 10; r* = 6 COSTS DAY BI RN DEM EI LOST ORDER RN LT ORD HOLD SHORT 110 33 1 9 --- --- --- --- --- 18 --- 2 9 98 4 5 --- YES 24 1 50 10 --- 3 5 26 1 4 --- --- --- 0 --- 8 --- 414 91 3 11 --- --- --- --- --- 22 --- 511 96 4 7 --- --- --- --- --- 14 --- 6 7 48 2 5 --- YES 63 2 50 10 --- 7 5 82 3 2 --- --- --- 1 --- 4 --- 8 2 27 1 1 --- --- --- 0 --- 2 --- 911 96 4 7 --- --- --- --- --- 14 --- 10 7 46 2 5 --- YES 99 3 50 10 --- 150 112 0 Based on this one 10-day simulation average daily cost = $26.20.

7. SIMULATION OF Q*= 12; r* = 3 COSTS DAY BI RN DEM EI LOST ORDER RN LT ORD HOLD SHORT 110 33 1 9 --- --- --- --- --- 18 --- 2 9 98 4 5 --- --- --- --- --- 10 --- 3 5 26 1 4 --- --- --- --- --- 8 --- 4 4 91 3 1 --- YES 37 1 50 2 --- 5 1 96 4 0 3 --- --- 0 --- 0 90 612 48 2 10 --- --- --- --- --- 20 --- 710 82 3 7 --- --- --- --- --- 14 --- 8 7 27 1 6 --- --- --- --- --- 12 --- 9 6 96 4 2 --- YES 84 2 50 4 --- 10 2 46 2 0 --- --- --- --- --- 0 --- 100 88 90 Based on this one 10-day simulation average daily cost = $27.80. THE OTHER POLICY APPEARS BETTER!

8. Review Simulation of Inventory Models -- Comparing 2 Possible Policies For Each -- Estimate System Parameters Using Pseudorandom Numbers Simulate Cost Replicate Experiment or Longer Simulation for better results