Inventory Management: Finding Good Inventory Policies through Simulation and EOQ Models, Slides of Production and Operations Management

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Inventory Management

A&E Noise example Methods for finding good inventory policies:

1. simulation
2. EOQ + LTD models Using EOQ for the Distribution Game: Multi-Echelon Systems

Coordination

• Suppose each retailer uses Q (^) Lower = 20. If all retailers order at once, the total is 60.
• Active learning: you are the warehouse manager. Knowing the retailer order sizes, how would you pick the warehouse order size?

Data

• Supplier to warehouse transit time: 15 days
• Warehouse to retailer transit time: 5 days
• Demand per retailer: 730 per year
• Selling price: $100/unit
• Purchase price: $70/unit
• Supplier to warehouse order cost: $
• Warehouse to retailer order cost: $2.
• Warehouse holding cost: $14.70/unit/year
• Retailer holding cost: $17.50/unit/year

Assume open 250 days / year

… To Excel

BigBluePills, Inc.

• Expensive drug treatments
• Perishable – last only 3 months
• Order once every 3 months
• Regular cost: $400 per treatment
• If demand > order size, place rush order
• Rush cost: $1,000 per treatment
• Price to patient: $
• How much should they order?

Pg. 161

Five Years of Demand Data

Average 18. Stdev 6. min 5. max 34.

Category bin Frequency <=5 5 1 6 - 10 10 3 11 - 15 15 3 16 - 20 20 5 21 - 25 25 6 26 - 30 30 1

30 1

0

1

2

3 4 5

6 7

<=5 6 - 10 11 - 1516 - 2021 - 2526 - 30> 30 Quarterly demand

Frequency

Solution 1

• Average demand = 18, so …
  • … let’s order 18 each quarter
  • Profit = 18 × (650 – 400) = $4,
  • Right?
• Q < D  lose? / unit
• Q > D  lose? / unit
• Do these cancel out on average?

The F law of Averages

When input is uncertain... output given average input may not equal the average output

Huh?

• Average BigBluePill demand = 18
• Profit for Q = 18 , given D = 18: $4,
• Average profit with Q = 18: $1,
  • Less than half
• Optimal Q = 20 , with avg. profit: $1,
• Using avg. demand (ignoring variability)
  • Seriously overestimates profit
  • Results in a suboptimal decision

In general

Profit(AVERAGE(Demand 1 , Demand 2 , …, Demand (^) n))

AVERAGE(Profit(Demand 1 ), Profit(Demand 2 ), …, Profit(Demand (^) n ))

Simple example of the flaw of

averages:

• A drunk on a highway
• Random walk