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 25 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: ____________________ kits

Average inventory for the region (held across the three hospitals): ______________ kits

b)(5 points)What is the total annual inventory holding cost for the RDU region for PPE-Sure under the direct-to-hospital delivery scheme as described above? Show the steps in your calculations.

Total annual inventory holding cost for the region (all hospitals):$_________________

Alpha-Med's newly hired procurement officer has introduced a new regional and rapid depot concept by converting the Chapel Hill hospital storeroom to a regional depot for certain high demand items.

1.Under this system, Alpha-Med will maintain inventory for PPE-Sure kits only at one location in the region -- the Chapel Hill regional depot -- and will supply the daily demand for each hospital (including Chapel Hill) from this depot through daily van deliveries.

2.This would increase the cost of shipment from Chapel Hill depot to Raleigh and to Durham hospitals, respectively, by $1 per kit delivered (we can ignore the fixed cost of deliveries and the cost of supplying the Chapel Hill hospital).

3.The depot would maintain the same 95% service level to each hospital, as before. Orders to the distributor would now be placed only from the Chapel Hill depot.

4.These orders will continue to be delivered from the distributor to this Chapel Hill depot in a pallet of 400 PPE-Sure units. The distributor would still absorb the shipment cost to the Chapel-Hill depot, and the pricing would remain unchanged.

c)(10 points) What would be the safety stock for PPE-Sure at the new Chapel Hill depot serving the three hospitals from its central location?

Safety Stock for the new CH-Depot: ____________________ kits

d)(10 points) What would be the total cost to Alpha-Med of maintaining this new centralized CH-depot system for PPE-Sure, excluding the product cost itself (inventory holding cost and cost to transport from CH warehouse to Raleigh and Durham hospitals)?

Total Cost of centralized CH-depot inventory system: ____________________ $'s / year