1. Workforce Scheduling The transportation manager at a cross-dock for Walmart h
ID: 3144343 • Letter: 1
Question
1. Workforce Scheduling The transportation manager at a cross-dock for Walmart has a staffing problem. Demand for delivery of perishable goods varies throughout the day, but 24-hour coverage is necessary because the cross-dock handles a number of Walmart locations in a large metropolitan area. A recent study has shown how many delivery drivers are needed each hour in the course of the day, as shown below (hour 1 is from midnight to 1 am):
Hour
1
2
3
4
5
6
7
8
9
10
11
12
Drivers
4
3
2
2
3
5
6
6
9
10
10
10
Hour
13
14
15
16
17
18
19
20
21
22
23
24
Drivers
12
12
8
6
7
7
7
6
5
4
4
4
Under current labor policies, delivery drivers may be assigned to any one of six shifts, some of which overlap. The shifts and salary costs are as follows:
Shift
Daily Cost ($)
2 am – 10 am
160
6 am – 2 pm
145
10 am – 6 pm
148
2 pm – 10 pm
154
6 pm – 2 am
156
10 pm – 6 am
160
(a)Provide the transportation manager with a schedule that will deploy enough delivery drivers to meet hourly requirements at the minimum daily total cost.
(b)In the optimal schedule, how many hours are over-staffed?
Hour
1
2
3
4
5
6
7
8
9
10
11
12
Drivers
4
3
2
2
3
5
6
6
9
10
10
10
Hour
13
14
15
16
17
18
19
20
21
22
23
24
Drivers
12
12
8
6
7
7
7
6
5
4
4
4
Explanation / Answer
Solution
Starting with Hour 1, there are only two options available which have Hour 1. These options are:
Option 1: 6 pm – 2 am and Option 2: 10 pm – 6 am.
Proceeding with Option 1, the schedule would be:
7 drivers in the time slot 6 pm – 2 am at a cost of $156; 2 drivers in the time slot 2 am – 10 am at a cost of $160; 12 drivers in the time slot 10 am – 6 pm at a cost of $148.
Total cost = (7 x 156) + (10 x 160) + (12 x 148) = $4468
Proceeding with Option 2, the schedule would be:
5 drivers in the time slot 10 pm – 6 am at a cost of $160; 12 drivers in the time slot 6 am – 2 pm at a cost of $145; 8 drivers in the time slot 2 pm – 10 pm at a cost of $154.
Total cost = (5 x 160) + (12 x 145) + (8 x 154) = $3772.
Since 3772 < 4468, Option 2 is the optimum schedule, i.e.,
Time slot
10 pm – 6 am
6 am – 2 pm
2 pm – 10 pm
# drivers
5
12
8
Total cost = $3772.
Over staffed hours
Over staff #
Number of hours
1
7
2
7
3
4
6
2
7
1
8
1
9
1
Time slot
10 pm – 6 am
6 am – 2 pm
2 pm – 10 pm
# drivers
5
12
8
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