Announcements Quiz 3 Tomorrow If you can’t do what you’re supposed to do; DO SOMETHING CHECK you submission!

Using EOQ for the Distribution Game: Multi-Echelon Systems MGTSC 352 Lecture 21: 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 QLower = 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?

Using EOQ for a 2-echelon system: the details Upper echelon: DUpper = 3  DRetailer SUpper = SWarehouse HUpper = HWarehouse LTUpper = LTSupplier  Warehouse + LTWarehouse  Retailer ROPUpper = DUpper  LTUpper Lower echelon DLower = DRetailer SLower = SRetailer HLower = HRetailer - HWarehouse LTLower = LTWarehouse  Retailer ROPLower = DLower  LTLower Coordination: QUpper = n  SUM(QLower) Choose n (an integer) and QLower to minimize total cost for the whole system

Data Supplier to warehouse transit time: 15 days Assume open 250 days / year 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: $200 Warehouse to retailer order cost: $2.75 Warehouse holding cost: $14.70/unit/year Retailer holding cost: $17.50/unit/year … To Excel

BigBluePills, Inc. Expensive drug treatments Pg. 161 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: $650 How much should they order?

Single period models Perishable product Past demand data Must decide how much to order before knowing actual demand for the period Must live with the consequences Q > D wasted product Q < D lost profit We’ve seen this before: it’s called the “newsvendor problem”

Five Years of Demand Data

Solution 1 Average demand = 18, so … Q < D  lose ? / unit … let’s order 18 each quarter Profit = 18  (650 – 400) = $4,500 Right? Q < D  lose ? / unit Q > D  lose ? / unit Do these cancel out on average?

Solution 2: simulation Solution 1 predicted this profit with Q = 18

The Flaw 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: $4,500 Average profit with Q = 18: $1,740 Less than half Optimal Q = 20, with avg. profit: $1,786 Using avg. demand (ignoring variability) Seriously overestimates profit Results in a suboptimal decision

How bad can it get? What if rush cost is $1,800 (instead of $1,000) The “averaging analyst” will still recommend Q = 18 and estimate P = $4,500. The actual profit with Q = 18 will be -$565. Using Q = 20 generates P = $1,217 Using average inputs is a bad idea. “How bad” will depend on data.

In general  Profit(AVERAGE(Demand1, Demand2, …, Demandn)) AVERAGE(Profit(Demand1), Profit(Demand2), …, Profit(Demandn))

Simple example of the flaw of averages: A drunk on a highway Random walk

Consider the drunk’s condition The AVERAGE location of the drunk Middle of the road The outcome at the middle of the road ALIVE What do you think the average outcome for the drunk is? DEAD Average inputs do not result in average outputs.