Question 1:
Sharjah Parking Servicesmanages 12 Multi-story parking in various locations in the city, the parking buildings are open 24 hours by 7 days a week.
In each building, there are security guards, cleaners, maintenance contractor, and money collection employees. Therefore, the management would like to assign a parking supervisor for each parking facility to provide necessary support for customers and make sure that parking system runs smoothly. The management would like to determine the minimum number of supervisor needed to cover the parking buildings by help of an OR specialist.
The OR specialist is mandated to suggest the most effective supervisors' workload distribution to the management taking into consideration the followings:
a. The occupancy rates vary between the buildings.
b. SPS management has agreed to allocate a budget of 1.5 millions per year to cover the expenses of hiring new supervisors.
c. A supervisor would cost 12000 Dirhams per month to SPS.
d. A supervisor may be assigned to more than on parking building at a time. However she/he is not expected to cover more than 3 buildings during the day shifts and 5 buildings during the night shift. The management would like also to minimize the total travel distances by the supervisors while on duty. Table 2 provides the distance matrix between the different locations.
e. The total working hours for each supervisor is 8 hours per day (1 shift period); they work 5 days in a week and take 2 consecutive days off. SPS management agreed to pay a night shift premium between 90 and 110 Dirhams per supervisor on duty.
Shift 1: 06:00 - 14:00
Shift 2: 16:00 - 22:00
Shift 3: 22:00 - 06:00 (Night shift)
The management wants to know how many supervisors should be hired, and what could be the optimum workload distribution to be applied.
1. Suggest a workload distribution policy forthe supervisors based on the stated objective and constraints from the SPS management.
2. Find the optimum solution based the workload distribution you suggested in part 1.
Note: The solution approach (GP, IP, DP, or NLP) is highly dependent on your answer to question 1.You may suggest justified alterations to some of the a. to e. constraints.
Table 1: Occupancy rate per Parking Location
|
Average occupancy rate
|
|
Location
|
6:00
|
14:00
|
22:00
|
|
14:00
|
22:00
|
6:00
|
|
P1
|
60%
|
40%
|
3%
|
|
P2
|
85%
|
85%
|
4%
|
|
P3
|
100%
|
100%
|
15%
|
|
P4
|
75%
|
75%
|
10%
|
|
P5
|
85%
|
85%
|
3%
|
|
P6
|
98%
|
40%
|
5%
|
|
P7
|
98%
|
45%
|
3%
|
|
P8
|
98%
|
40%
|
7%
|
|
P9
|
70%
|
50%
|
7%
|
|
P10
|
55%
|
45%
|
8%
|
|
P11
|
70%
|
35%
|
2%
|
|
P12
|
70%
|
40%
|
4%
|
Table 2: Distance between Parking Locations in km
|
|
P1
|
P2
|
P3
|
P4
|
P5
|
P6
|
P7
|
P8
|
P9
|
P10
|
P11
|
P12
|
|
P1
|
|
25
|
19
|
36
|
12
|
24
|
7
|
14
|
15
|
33
|
25
|
19
|
|
P2
|
|
|
15
|
43
|
30
|
7
|
47
|
47
|
17
|
36
|
19
|
21
|
|
P3
|
|
|
|
27
|
15
|
10
|
12
|
63
|
6
|
21
|
54
|
26
|
|
P4
|
|
|
|
|
51
|
26
|
10
|
8
|
16
|
24
|
26
|
22
|
|
P5
|
|
|
|
|
|
45
|
28
|
7
|
19
|
6
|
33
|
29
|
|
P6
|
|
|
|
|
|
|
26
|
24
|
52
|
25
|
14
|
8
|
|
P7
|
|
|
|
|
|
|
|
12
|
12
|
30
|
48
|
36
|
|
P8
|
|
|
|
|
|
|
|
|
37
|
32
|
50
|
33
|
|
P9
|
|
|
|
|
|
|
|
|
|
26
|
53
|
18
|
|
P10
|
|
|
|
|
|
|
|
|
|
|
25
|
31
|
|
P11
|
|
|
|
|
|
|
|
|
|
|
|
18
|
|
P12
|
|
|
|
|
|
|
|
|
|
|
|
|