Question: Reconsider the scheduling problem we discussed in class. American Airline is expanding its operations by adding more flights to and from its hub airport. To
Reconsider the scheduling problem we discussed in class. American Airline is expanding its operations by adding more flights to and from its hub airport. To handle the increased workload, they need to hire additional customer service agents. The required number of agents for each time period is shown in the last column of the table below. The table also reflects one of the provisions in the company's contract with the union representing the customer service agents. According to this provision, each agent works an eight-hour shift. The authorized shifts and their corresponding times are:
- Shift 1: 7:00 AM to 3:00 PM.
- Shift 2: 9:00 AM to 5:00 PM.
- Shift 3: 1:00 PM to 9:00 PM.
- Shift 4: 5:00 PM to 1:00 AM.
- Shift 5: 11:00 PM to 7:00 AM.
Table: Data for the Union Airways Personnel Scheduling Problem
| Time Period | Required Agents |
|---|---|
| 7:00 AM - 9:00 AM | ?1=15 |
| 9:00 AM - 1:00 PM | ?2=20 |
| 1:00 PM - 5:00 PM | ?3=25 |
| 5:00 PM - 9:00 PM | ?4=18 |
| 9:00 PM - 11:00 PM | ?5=12 |
| 11:00 PM - 7:00 AM | ?6=10 |
Daily Compensation for Each Shift
| Shift | Daily Compensation per Agent |
|---|---|
| Shift 1 | $200 |
| Shift 2 | $220 |
| Shift 3 | $250 |
| Shift 4 | $240 |
| Shift 5 | $230 |
The tables show the time periods covered by the respective shifts and the wages specified in the contract differ by shift. The problem is to determine how many agents should be assigned to the respective shifts each day to minimize the total personnel cost for agents, to meeting (or surpassing) the service requirements.
a. Formulate algebraic form for this problem. (Please clearly define all the decision variables, clearly write down the objective function and each constraint)
b. Formulate and solve this model on a spreadsheet.
Union_Airways_Personnel_Scheduling [Protected View] - Excel Search Sign in X File Home Insert Page Layout Formulas Data Review View Help Share PROTECTED VIEW Be careful-files from the Internet can contain viruses. Unless you need to edit, it's safer to stay in Protected View. Enable Editing X A1 X Shift S T U A A B C D E F G H K L M N O P Q R Shift pensation per Agent Shift 1 200 3 Shift 2 220 4 Shift 3 250 5 Shift 4 240 6 Shift 5 230 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 Shifts & Compensation Time Periods & Agents + + 100% Ready Scroll Lock W CA X A Z () ENG 7:11 am H Type here to search 10/10/2024Union_Airways_Personnel_Scheduling [Protected View] - Excel Search Sign in X File Home Insert Page Layout Formulas Data Review View Help Share Enable Editing X 1PROTECTED VIEW Be careful-files from the Internet can contain viruses. Unless you need to edit, it's safer to stay in Protected View. A1 X Time Period H K L M N O P Q R S T U A A B C D E F G ime Periojuired Agents 2 7:00 AM - 15 3 9:00 AM - 20 4 1:00 PM - 25 5 5:00 PM - : 18 6 9:00 PM - 12 7 11:00 PM - 10 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 Shifts & Compensation Time Periods & Agents + + 100% Ready Scroll Lock 7:11 am Type here to search W CA O X A Z () ENG 10/10/2024
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