Q 2 ( 40 po i n t s ) CC Loads Prob. of Occurrence 30 0.4 70 0.6 Sese Trucking o
ID: 1168347 • Letter: Q
Question
Q2 (40 points)
CC
Loads
Prob. of Occurrence
30
0.4
70
0.6
Sese Trucking owns two types of trucks: normal cargo (FS) and car carriers (CC). Sese has 100 drivers for FS trucks and 50 drivers for CC. Drivers are not interchangeable (i.e., a FS driver cannot drive a CC and vice versa). Each driver can deliver one load a day. The discrete demand distributions for daily loads are given below:
FS
Loads
Prob. of Occurrence
120
0.2
100
0.8
a) What are the expected number of loads handled by Sese for FS and CC respectively?
b) What are the expected utilizations for FS and CC drivers respectively?
Sese decides to lease 20 FS trucks and 10 CC trucks (and their drivers) on a daily basis in addition to its own fleet
c) What are the expected loads Sese can handle for FS and CC respectively now?
d) What are the expected lost sales (loads Sese cannot handle) for FS and CC respectively now?
e) What is the expected capacity utilization of the total fleet?
f) Sese always uses its own trucks and drivers first before using the leased fleet. What is the
expected number of unused trucks in the leased fleet?
Since the leased fleet did not meet Sese’s expectations on quality and handling, Sese decided to stop leasing. Sese decided to invest instead in making its trucks totally flexible and retraining its drivers on both types. (i.e., any truck and driver in Sese’s fleet can now handle both FS and CC)
g) What is the expected capacity utilization of Sese’s fleet now?
h) What are the expected lost sales (loads Sese cannot handle) of FS and CC now?
CC
Loads
Prob. of Occurrence
30
0.4
70
0.6
Explanation / Answer
(a)
Expected load, FS = (120 x 0.2) + (100 x 0.8) = 24 + 80 = 104
Expected load, CC = (30 x 0.4) + (70 x 0.6) = 12 + 42 = 54
(b)
Driver utilization = expected load / number of driver
For FS = 104 / 100 = 104%
For CC = 54 / 50 = 108%
(c)
Revised expected load, FS = 104 + 20 = 124
Out of which, Sese can handle only (100 + 20) = 120 loads
Revised expected load, CC = 54 + 10 = 64
Out of which, Sese can handle only (50 + 10) = 60 loads
(d)
Expected lost sales = expected load - number of drivers
For FS = 124 - 120 = 4
For CC = 64 - 60 = 4
(e)
Expected capacity utilization (overall) = Total expected load / total number of driver
= (124 + 64) / (120 + 60) = 188 / 180 = 104.44%
(f)
Total expected load = 188 which is more than the total fleet size of Sese even before leasing any trucks.
So all leased trucks will remain unutilized (total 30).
(g)
Expected capacity utilization = total expected load / total number of drivers
= (104 + 54) / (100 + 50) = 105.33%
(h)
Expected lost sales = total expected load - total number of drivers
= (104 + 54) - (100 + 50) = 158 - 150
= 8
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