A pizza restaurant that orders cheese from a global mozzarella cheese manufacturer is considering two different transportation carriers for its (in-bound) shipments of this "raw material." The pizza restaurant uses 1 lb of mozzarella cheese per pizza. Average demand for pizzas at the restaurant is 100 per day (so, average demand for cheese is 100 lbs/day). The restaurant estimates that the sD for pizza demand is 5 pizzas per day (so the sD for cheese required is 5 lbs/day). The materials cost for the cheese is $2/lb. Holding costs for inventory in the restaurant is 0.50 per year (h), and for in-transit inventory (i), 0.25. The carriers provide the following schedule to the restaurant:

Performance Carrier 1 Carrier 2
Minimum shipment, lbs 1,000 1,250
Transit time, average 2 days 1 day
Order processing time 1 day 1 day
Lead time 3 days 2 days
s.d. of lead time, sL 0.5 day 1 day
Shipment cost, $/lb 0.25 0.275

a) How much safety inventory of mozzarella cheese will the pizza restaurant need to hold under each of these two carrier options? Show how you calculated this SI value.

b) If the company orders the minimum shipment amount each time it orders, what is the intransit inventory cost if the mozzarella manufacturer uses FOB Origin, Freight Collect for shipment?

c) Which carrier should the pizza restaurant contract with if it wants to minimize the total costs associated with purchasing the cheese? Show why you make this recommendation