The Bike & Ski Co. has two stores in Western Mass: one in E. Longmeadow and one in Easthampton. The two stores stock identical items that are delivered directly to their location from various suppliers. The stores are considering leasing a warehouse facility in Holyoke to consolidate their inventory and place joint orders from suppliers. Let’s help them understand whether a common warehouse location would be cost effective by analyzing the cost associated with two products:

Product 1: Best-Selling Junior Bike

o E. Longmeadow store weekly demand is ~ N(µ=20, s=4)

o Easthampton store weekly demand is ~ N(µ=20, s=3).

o Consider demand at the two stores is independent.

The following parameters are seen by both stores:

o Replenishment lead time in weeks: L=2 weeks

o Fixed shipping cost of replenishment: $300 (trucking cost)

o Cost per bike: $100 o Price bike is sold at: $150

o Holding cost per bike is 20% of its value per year

Product 2: Specialty Skis Imported from Sweden

o E. Longmeadow store weekly demand is ~ Poisson(l=0.4)

o Easthampton store weekly demand is ~ Poisson(l=0.6).

o Consider demand at the two stores is independent.

The following parameters are seen by both stores:

o Replenishment lead time in weeks: L=5 weeks (ocean shipping)

o Fixed cost of replenishment: $100 o Cost per ski set: $1000

o Price skis are sold at: $1800 o Holding cost per ski set is 30% of its value per year § This is higher than the holding cost rate for bikes because of the risk of obsolescence for this fashion, high-end product

Question 1: How many of each item should each location order at a time and when should they reorder if they want a 99% cycle (Type I) service level? What is the resulting fill rate for each of the products and locations? Use the Type II service level approximation to calculate the fill rate in the case of normal demand, and the actual fill rate for the Poisson demand case.

Question 2: What would these decisions change if the two locations consolidate the inventory into the new warehouse?

Question 3: What are the annual savings in fixed ordering costs and inventory costs associated with the consolidation?

Question 4: How would the decisions change if a 95% service level is deemed sufficient? What if 90%? What are the resulting fill rates?

Question 5: What service level would you recommend? Assume that customers are not willing to wait.

Question 6: Assume now that the replenishment lead time for junior bikes in weeks is a random variable L~ N(µ=2, s=0.1). What should be the ordering decisions then?

Question 7: How would your decisions change if the Swedish supplier stops charging fixed costs for ordering and shipping? That is, the only cost is $1000 per unit ordered.