2. Inventory Management II (24 points) The Earthlings opened three settlements on planet Mars so far: Mars Head Quarter (MHQ), Psi (), and Omega (). Arnold Schwarzenegger is too busy doing politics and cannot recall how to activate the alien machine that creates a breathable atmosphere on Mars. Therefore, the United Nations Space Agency (UNSA) is sending out a space transporter every 4 weeks from Earth to Mars. Before each space transporter leaves Earth, MHQ has to decide how much oxygen (and other things) to order. The travel time from Earth to Mars is 6 months (= 26 weeks). Assume 52 weeks in a year. MHQ places each order for all three settlements on Mars together. MHQ also serves as a distribution center on Mars, and and receive their oxygen from MHQ. The lead times from MHQ to and are two weeks and three weeks, respectively. Each cubic meter (m3 ) of oxygen costs 10 space dollars (currency symbol: v ) and carrying costs are 26% per year. At all extraterrestrial settlements of Earthlings, the required service probability of oxygen is 99.99%, so z = 3.72. 's weekly demand is 100m3 with a standard deviation of 30m3. A computer-based system is managing the inventory, and orders to MHQ are placed automatically. Therefore, the order set up cost is only v 10. (a) (2 points) What is 's optimal order quantity? (b) (2 points) How often per year (= 52 weeks) does order oxygen from MHQ, and what is the average time between two orders (in weeks)? (c) (1 point) What is the annual ordering cost for (d) (3 points) What is the annual inventory holding cost for ? 's weekly demand is 300m3 with a standard deviation of 40m3. 's cost for placing an order is v 120. (e) (2 points) What is 's optimal order quantity? f) (2 points) How often per year (= 52 weeks) does order oxygen from MHQ, and what is the average time between two orders (in weeks)? (g) (2 points) What is the reorder point (ROP) for ? MHQ's own weekly demand is 1000m3 with a standard deviation of 49m3. (h) (2 points) Only considering its own demand, (i.e., MHQ is not holding safety stock for and ) how much safety stock does MHQ hold? (i) (2 points) On average how much m3 oxygen are in all transporters together that are on their way from Earth to Mars? (Hint: MHQ also needs to satisfy the demand of and .) Marc, the Martian, Manager of "Made on Mars", suggests building pipelines from MHQ to the settlements and . Assume that lead time from MHQ to the settlements will be zero now, and furthermore, ignore any volume of oxygen in these pipelines. So, MHQ will store all inventory necessary to meet the combined demand of all settlements on Mars. (j) (2 points) Marc explains to the Earthlings that this operations management concept is called Furthermore, the European Space Agency (ESA) developed a new hyper-speed spacecraft, which allows shortening the travel time between Earth and Mars to 3 months (= 13 weeks). (k) (4 points) How much safety stock will MHQ hold when using ESA's spacecraft and Marc's pipelines?