IV. Alpha-Med Hospital Group (35 points) Alpha-Med Hospital Group operates three hospitals in the RDU area:...

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IV. Alpha-Med Hospital Group (35 points) Alpha-Med Hospital Group operates three hospitals in the RDU area: one each in Durham, Chapel Hill, and in Raleigh, respectively. One of Alpha-Med's staple medical- surgical safety kits, PPE-Sure, is sourced from a distributor in Virginia with an order lead-time of 2 weeks and is delivered directly to each hospital's inventory stores. Alpha- Med's had previously aimed for reduced logistics cost footprint and hence the distributor delivered PPE-Sure directly to each hospital at no additional cost, but with the condition that the PPE-Sure kits will only be delivered in pallets of 400 kits. Weekly demand (assume 52 weeks to a year) for PPE-Sure at each of the hospitals is independent but identically distributed with a mean of 150 kits and a standard deviation of 35 kits per hospital. Each hospital holds inventory of PPE-Sure to maintain 95% local service level. The annual cost of holding inventory for PPE-Sure is 25% of the product cost, which is $200 per kit. There is no fixed cost to Alpha-Med associated with placing orders for PPE- Sure. a) (10 points) What is the average inventory that should be held for PPE-Sure at each hospital in order to meet its own 95% service level requirement? Average inventory held by each hospital: Average inventory for the region (held across the three hospitals): kits kits IV. Alpha-Med Hospital Group (35 points) Alpha-Med Hospital Group operates three hospitals in the RDU area: one each in Durham, Chapel Hill, and in Raleigh, respectively. One of Alpha-Med's staple medical- surgical safety kits, PPE-Sure, is sourced from a distributor in Virginia with an order lead-time of 2 weeks and is delivered directly to each hospital's inventory stores. Alpha- Med's had previously aimed for reduced logistics cost footprint and hence the distributor delivered PPE-Sure directly to each hospital at no additional cost, but with the condition that the PPE-Sure kits will only be delivered in pallets of 400 kits. Weekly demand (assume 52 weeks to a year) for PPE-Sure at each of the hospitals is independent but identically distributed with a mean of 150 kits and a standard deviation of 35 kits per hospital. Each hospital holds inventory of PPE-Sure to maintain 95% local service level. The annual cost of holding inventory for PPE-Sure is 25% of the product cost, which is $200 per kit. There is no fixed cost to Alpha-Med associated with placing orders for PPE- Sure. a) (10 points) What is the average inventory that should be held for PPE-Sure at each hospital in order to meet its own 95% service level requirement? Average inventory held by each hospital: Average inventory for the region (held across the three hospitals): kits kits