Question

You manage the inventory of bed frames that are sold through retail stores. The most popular model sells at wholesale for $400 per bed frame. It costs $300 to make each unit. Historical data shows that it fits a normal distribution with an average monthly demand of 1,000 bed frames and a standard deviation of 200. Your company uses an annual interest rate of 20% to estimate inventory holding cost.
1) Suppose the backorder cost is $20 per unit.
a. What optimal base stock level should you use?
b. What base stock level should you use if you want the fill rate to be at least 90%? What is the average number of backorders, B(r)?
2) Suppose any order that cannot be fulfilled through stock is, instead, fulfilled by purchasing from a competitor at $350 per unit.
a. What optimal base stock level should be used?
b. What base stock level should be used in order for the fill rate to be at least 95%? What is the average number of backorders, B(r)?
3) Explain the difference between the answers in part 1a and 2a.

Answer 1