Consider the following two-echelon spare part inventory system of the Saudi Railway Company. We have an installed base of locomotives with a wheel set as Line Replaceable Unit (LRU) that is repaired by replacement upon failure (we ignore the other parts here). The installed base is allocated to two local service centers (LSC), one in Eastern Province and one in Western Province. Upon failure, a part is replaced by a spare from the service center and the failed part is repaired. A fraction of the spare parts can be repaired at these service centers and the rest should be repaired at the central depot in Riyadh. If a failed part is sent to the central depot for repair, a part from stock is sent from the depot to the local service center is soon as one is available. The relevant data are given in the table below. Value (in 1000 SR) Fraction local repair (West and East) Repair shop throughput time (years) Demand per year Order-and-ship time (year) Current stock levels Central Depot LSC West and East LSC West LSC Est LSC West LSC East Central Depot LSC West LSC East Wheel set 10 R RTC RTW 15 9 0.20 0.25 S0 SW SE

a) Find the mean pipeline at the depot.

b) Find the expected backorders at the depot.

c) Find the mean pipeline of wheel sets at the locations in the Western province.

d) Find the fill rate of the demand of wheel sets at the locations in the Western province.

e) Find the expected number of backorders for wheel sets at each location Western province