Consider a local post$-$disaster relief center where the volunteers accept and organize different in$-$kind

donations. After a disaster, they accept three kinds of donations to be sent to the disaster area. The donors

can bring boxes that contain canned food, perishable food, or clothes. The interarrival times for canned

food donations are distributed with EXPO$(15)$ minutes, and the perishable food boxes have an interarrival

time with distribution EXPO$(25)$ minutes. Since clothes are easier to collect and store, boxes of cloth

donations are more frequent with an interarrival time distribution of EXPO$(10)$ minutes.

There are two processes at this center: accepting and sorting donations. Currently, there is one volunteer

working on accepting the donations and three more volunteers working on sorting the accepted donation

boxes. Accepting a donation lasts for UNIF$(3,10)$ minutes, and the accepting volunteer can work with one

donor at a time. The sorting time for boxes depends on the type of box. Canned food donations take

TRIA$(5,12,15)$ minutes to sort, and perishable food donations take UNIF$(8,10)$ minutes to sort. For cloth

donations, if the box contains only the same$-$size items, it takes TRIA$(2,5,8)$ minutes, and if there are

different sizes in the box, it takes TRIA$(8,10,15)$ minutes. $40\%$ of the cloth donations contain only samesized items.

The donations are processed according to a first$-$come$-$first$-$out $($FIFO$)$ discipline in both the acceptance

queue and sorting queue normally. However, when a perishable food donation arrives, it is prioritized in

both acceptance and sorting to ensure food safety. Volunteers start working on the perishable food donation

immediately if they are idle and after finishing the current activity if they are already working on a box $($both

in the accepting and sorting processes$).$

The management of this relief center wants to improve the operations and hired you to model the system

to conduct a simulation study and make some suggestions. Assume that the system is empty and all

resources are idle at time $0.$ Assume that the first arrival for each donation occurs at time $0,$ and donations

arrive one by one.

I. Model the system on ARENA and run the simulation for $10$ hours $($daily working time$).$ Report the

following. Make sure to include the time unit in your answers.

a$.$ Average waiting time for both queues in the system $($acceptance and sorting queues$).$

b$.$ Utilization of volunteers in both processes.

c$.$ The average and maximum type spent in the system by each type of donation $($canned

food, perishable food, clothes$).$

d$.$ If the maximum time for perishable foods is less than $40$ minutes, the relief center is

assumed to respect food safety rules. Are they ensuring food safety as the system is right

now?

e$.$ Number of donations processed per day.

II$.$ A new volunteer will start working at the relief center. The new volunteer can either help accept or

sort the donations, and will be trained accordingly. Once the volunteer receives the necessary

training, her$/$his service time will be the same as the existing volunteers. Based on the performance

metrics of interest, to which process should the new volunteer be assigned? Why? Discuss your

findings $($e$.$g$.,$ which change would improve which performance measure the most$).$

$($Hint: To solve this question, you must try adding the new volunteer to the acceptance and sorting

processes in different model versions and run each model for $10$ hours.$)$

can you make detailed arena flowchart of this model