At a local Costco, there are exactly 4 types of ink-jet printers. The weekly demand for printers is estimated to be normally distributed with mean 360. The 4 brands have equal market share on average at that Costco, and the standard deviation of demand for each type is 30 units/week.
Assume that printer demand is independent across brands (suspend your belief in substitution for a while...). Two of the competing brands operate a warehouse each in Central Valley and take 4 and 5 days to replenish an order, respectively, while the third and fourth competing brands operate warehouses each in the NoCal region and takes 6 and 7 days, respectively, to deliver a replenishment order. Costco sets a stringent target of 99% fill rate, which means customers should not face stock-outs under any normal circumstances.
1. What is Costco's safety stock for each brand of printer?
2. What is Costco's reorder point for each brand of printer?
The store manager for Costco is a person who hates inventory. She observes that
Costco's shelves are overflowing with printer pallets, so she comes up with the brilliant
idea to ask the suppliers to reduce the price in exchange for footing the bill for holding all that inventory.
3. Suppose printer holding costs are $5/unit/week (which also accounts for the obsolescence costs), what is the price discount in absolute $, she should ask for from each supplier to offset the holding costs?
4. What is your inference regarding the price savings Costco can pass on to its customers for every day it saves in supplier lead times for replenishment?