These are 2 questions (2nd being a follow-up).

And, both must be answered using Little's law formula: Inventory = Throughput x Flowrate

FIRST QUESTION:

Container ships from Asia arrive at the Port of Los Angeles (PLA) constantly. When the ship is docked, the unloading process starts immediately. Based on PLA's current system, all unloading cranes can unload 2800 TEU (Twenty-ft Equivalent Unit) containers per hour. This2800 TEUis thetheoretical maximum capacity of PLA, but it does not mean PLA always operates at its maximum capacity. PLA currently works 12 hours per day to handle all containership calls at the port. After unloading at PLA, all containerswill be sent to UP (Union Pacific, US class I railroad that handles Intermodal containers for PLA)'s railyard near PLA,The traffic time from PLA to UP's railyard is7.6hours in average (including all handlings for all railcars & containers, also an ideal traffic time, in reality it takes slightly longer). UP rail tracks and railyards operate 24/7. After containers arrive at the railyard, containers will wait for volume aggregations such that there are enough containers to be shipped out by rail locomotives to their destinations. Assume the current container volume is 30,000 TEUs per day. On average, from the ship is docked till the container is loaded to the railcar, it takes 10 hours. UP's IT system shows that their track systems (from PLA to UP Railyard) have an average of 9,500 TEUs. Once containers arrive at UP's railyard, it takes an average of 32.5 hours to be shipped out.Please run all numbers to its nearest tenth.Please use the " PLA + Transship to UP Railyard+ UP Railyard" as your system's scope for analysis, and answer the following questions.

USING LITTLE'S LAW: Inventory = Throughput x Inventory

(1). What is the expected total time from when a container's ship arrives at PLA tothe container is leaving UP's railyard to the destinations?

(2). What is the total number of TEU inventory that exist in the wholesystem?

(3). What is the capacity utilization for the crane system at PLA?[Hint: please use day/hour carefully, since all entities operate at different hours. I recommend using 'hour' as your analysis time unit]

SECOND question:

After the pandemic, the demand for rebuilding the economy in the US is strong. The container volume coming through PLA is estimated to increase at least by 15%. PLA has followed the Biden government's request to operate 24/7. However, due to lack of space at PLA for transloading space and other constraintsat the UP side, the throughput time for a TEU to pass through PLA is now increased to 26 hours, while its TEU inventory at PLA reaches 40,000 TEUs, which is the maximum (no more room to store) at PLA.Please run all numbers to its nearest tenth.

USING LITTLE'S LAW: THROUGHPUT x Inventory

(1) What is the new throughput rate at PLA? and what is the capacity utilization at PLA?

BNSF, which is another class I railroad, was asked to handle the excess volume and works 24/7 to take care of the excess volume. BNSF's railyard is farther away, which takes 21 hours to load TEUs from PLA to BNSF's railyard. BNSF's IT systems shows its inventory on the track (from PLA to BNSF's railyard) is 16280TEUs, and 18820 TEUs at BNSF. At the same time, UP's system shows that a TEU will stay on UP's track (from PLA to UP's railyard)for 11.2 hours, and at UP's railyard for 50.7 hours.

(2) What is the new TEU throughput rate at UP after BNSF took some of the transloading responsibility?

(3) What is the total average length of time for a TEU container passing through PLA and railroad's railyards (from Arrival PLA till it leaves UP's or BNSF's railyards)?Does adding BNSF really improve the throughput time (from Arrival PLA till it leaves UP's or BNSF's railyards)?

(4) What is the total number of TEU inventory that exists in thewhole newsystem (From PLA to UP's and BNSF's railyards)?