Question 1- An elevator in a manufacturing plant carries exactly 400 kilograms of material. There are three kinds of material packaged in boxes that arrive for a ride on the elevator. These materials and their distributions of time between arrivals are as follows:
|
Material
A
B
C
|
Weight (kg)
200
|
Interarrival Time (minutes) |
|
4 ± 2 (uniform)
|
| 100 |
8 (constant) |
| 50 |
P(2) = 0.33. P(3) = 0.67
|
It takes the elevator 1 minute to go up to the second floor, 2 minutes to unload, and 1 minute to return to the first floor. The elevator does not leave the first floor unless it has a full load. Simulate 1 hour of operation of the system. What is the average transit time for a box of material A (time from its arrival until it is unloaded)? What is the average waiting time for a box of material B? How many boxes of material C made the trip in 1 hour?
Question 2- Consider a single-product (s, S) inventory system, where the inventory level is checked at the beginning of every week. An order up to level S is placed if the inventory level I is less than s, while no order is placed if I is greater than or equal to s. Demand occurs with inter-demand time following a discrete uniform distribution with probabilities given by p(b) = 1/3 with b = 2, 3, 4 days. Demand size = 5, 6, 7, 8 with respective probability 1/6, 2/6, 2/6, 1/6. If the current policy parameters s, and S equals 10, 40 respectively and the delivery lag (lead time) is fixed at 3 days, calculate the total inventory cost of 4 weeks given the following cost information;
Ordering cost is $32+ $3 × Q, where Q is the order size.
Holding cost is $0.1 per item per day.
Shortage cost is $1 per item per day