Reference no: EM132245146

Inventory Management II The Earthlings opened three settlements on planet Mars so far: Mars Head Quarter (MHQ), Psi (Ψ), and Omega (Ω). 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 trans- porter 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 Ψ and Ω receive their oxygen from MHQ. The lead times from MHQ to Ψ and Ω are two weeks and three weeks, respectively. Each cubic meter (m3) oxygen costs 10 space dollars (currency symbol: ??) 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. Ψ’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 setup cost is only (a) What is Ψ’s optimal order quantity? (b) How often per year (= 52 weeks) does Ψ order oxygen from MHQ, and what is the average time between two orders (in weeks)? (c) What is the annual ordering cost for Ψ? (d) What is the annual inventory holding cost for Ψ? MHQ’s own weekly demand is 1000m3 with a standard deviation of 49m3. (h) Only considering its own demand, (i.e., MHQ is not holding safety stock for Ψ and Ω) how much safety stock does MHQ hold?