Q1. The Northshore Bank is working to develop an efficient work schedule for full-time and part-time tellers. The schedule must provide for efficient operation of the bank including adequate customer service, employee breaks, and so on. On Thursday, the bank is open from 8:00 a.m. to 8:00 p.m. The number of tellers necessary to provide adequate customer service during each hour of operation is summarized here.
|
Time
|
Number of tellers
|
Time
|
Number of tellers
|
|
8:00 am- 9:00 am
|
6
|
2:00 pm- 3:00 pm
|
8
|
|
9:00 am- 10:00 am
|
9
|
3:00 pm- 4:00 pm
|
7
|
|
10:00 am- 11:00 am
|
7
|
4:00 pm- 5:00 pm
|
9
|
|
11:00 am- 12:00 pm
|
12
|
5:00 pm- 6:00 pm
|
14
|
|
12:00 pm- 1:00 pm
|
11
|
6:00 pm- 7:00 pm
|
12
|
|
1:00 pm- 2:00 pm
|
14
|
7:00 pm- 8:00 pm
|
8
|
Each full-time employee starts on the hour and works a 4-hour shift, followed by 1 hour for lunch and then a 3-hour shift. We also have 2 types of part-time employees. First type of Part-time employees who works one 4-hour shift beginning on the hour, and second type of part time employees who works one 3-hour shift beginning on the hour. Considering salary and fringe benefits, full-time employees cost the bank $20 per hour (We do not pay for their lunch time), and part-time employees cost the bank $15 per hour. The bank manager wants to ensure that there is a staff of at least 3 full-time employees. Formulate an integer programming model that can be used to develop a schedule that will satisfy customer service needs at a minimum employee cost.
Q2. The Bayside Art Gallery is considering installing a video camera security system to reduce its insurance premiums. A diagram of the eight display rooms that Bayside uses for exhibitions is shown in following Figure, the openings between the rooms are numbered 1 through 13. A security firm proposed that two-way cameras be installed at some room openings. Each camera has the ability to monitor the two rooms between which the camera is located. For example, if a camera were located at opening number 4, rooms 1 and 4 would be covered; if a camera were located at opening 11, rooms 7 and 8 would be covered; and so on. Management decided not to locate a camera system at the entrance to the display rooms. Also, management wants room 7 to be covered by two cameras.
Formulate the model by providing security coverage for all eight rooms by minimum number of two-way camera and determine how many two-way cameras to purchase and where they should be located.
Q3. Sports of All Sorts produces, distributes, and sells high-quality skateboards. Its supply chain consists of three factories (located in Detroit, Los Angeles, and Austin) that produce skateboards. The Detroit and Los Angeles facilities can produce 350 skateboards per week, but the Austin plant is larger and can produce up to 700 skateboards per week. Skateboards must be shipped from the factories to one of four distribution centers, or DCs (located in Iowa, Maryland, Idaho, and Arkansas). Each distribution center can process (repackage, mark for sale, and ship) at most 500 skateboards per week.
Skateboards are then shipped from the distribution centers to retailers. Sports of All Sorts supplies three major U.S. retailers: Just Sports, Sports 'N Stuff, and The Sports Dude. The weekly demands are 200 skateboards at Just Sports, 500 skateboards at Sports 'N Stuff, and 650 skateboards at The Sports Dude. The following tables display the per- unit costs for shipping skateboards between the factories and DCs and for shipping be- tween the DCs and the retailers.
|
|
Shipping Cost ($ per Skateboard)
|
|
Factory/DCs
|
Iowa
|
Maryland
|
Idaho
|
Arkansas
|
|
Detroit
|
$25
|
$25
|
$35
|
$40
|
|
Los Angeles
|
$35
|
$45
|
$35
|
$42.5
|
|
Austin
|
$40
|
$40
|
$42
|
$32.5
|
|
|
Shipping Cost ($ per Skateboard)
|
|
Factory/DCs
|
Iowa
|
Maryland
|
Idaho
|
Arkansas
|
|
Just Sports
|
$30
|
$20
|
$35
|
$27.5
|
|
Sports 'N Stuff
|
$27.5
|
$32.5
|
$40
|
$25
|
|
The Sports Dude
|
$30
|
$40
|
$32.5
|
$42.5
|
a. Build a model to minimize the transportation cost of a logistics system that will deliver skateboards from the factories to the distribution centers and from the distribution centers to the retailers. What is the optimal production strategy and shipping pattern for Sports of All Sorts? What is the minimum attainable transportation cost?
b. Sports of All Sorts is considering expansion of the Iowa DC capacity to 800 units per week. The annual amortized cost of expansion is $40,000. Should the company expand the Iowa DC capacity so that it can process 800 skateboards per week? (Assume 50 operating weeks per year.)