Problem
The German Retailer GreatFoods has a broad customer base and a market penetration of 18%. It sells 500 packages of its GreatCheese per day in Berlin, normally distributed with a standard deviation of 300 packages. Demand is independent from day to day. Each package weighs 500g. The packages are produced in Spain, and GreartFoods buys them at a price of 7 Euro each from its supplier. The payment is made when the products arrive at FunFoods. FunCheese has a selling price in the stores of 15 Euro each. Once the supplier receives the order from FunFoods, the shipment will be ready for delivery and leave the supplier exactly 4 days later. The supplier offers two different means of transportation to the retailer's distribution center just outside Madrid: by truck or by train. The shipment to Spain will take 3 days by truck and 7 days by train. A shipment of cheese by truck costs 1200 Euro, while a shipment by train sums up to 950 Euro. Each time an order is placed at the supplier firm, additional fixed costs of 100 Euros incur. To reduce road transportation, the state charges a truck transportation tax that equals 17 % of the truck transportation costs. FunFoods is targeting a cycle service level of at least 97,98% and the best possible fill rate as it wants to grow its revenue. FunFoods faces costs for storage of 9% per year based on the purchase price and of additionally 14% per year for cost of capital. Value added tax on basic food items is 7% in Germany. For all calculations assume every day to be a working day (i.e., do not treat Saturdays and Sundays differently than other days of the week). Whenever you are looking for a z-value or the value for the density function, use one of the three tables provided to you.
A. How many packages does the company sell per day
B. What is the fixed order cost S for truck transportation
C. What is the standard deviation of demand during the lead time?
D. Calculate the optimal order quantity for truck transpiration
E. Calculate the optimal order quantity for train transportation
F. Calculate for truck transportation what the minimum safety inventory is for the target service level.