Practical Management Science
Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
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### Epsilon Airlines Call-Center Staffing Model

**Introduction:**
Epsilon Airlines services predominantly the eastern and southeastern United States. Most of Epsilon's customers make reservations online, but some use phone reservations. Call-center personnel handle these reservations and support for booking changes. Efficient staffing is crucial to avoid excessive costs or poor service.

**Staffing Requirements:**
Epsilon analysts estimate the minimum number of employees needed for each day during the vacation season (June, July, and the first two weeks of August) as follows:

| Day       | Minimum Number of Employees Needed |
|-----------|------------------------------------|
| Monday    | 60                                 |
| Tuesday   | 45                                 |
| Wednesday | 40                                 |
| Thursday  | 45                                 |
| Friday    | 80                                 |
| Saturday  | 75                                 |
| Sunday    | 35                                 |

**Work Schedule:**
- Employees work five consecutive days followed by two days off.
- Employees can start on any day of the week.
- All employees receive equal pay.
- Schedules are cyclic and independent of start/stop transitions.

**Objective:**
Develop a model to minimize the total number of call-center employees while meeting daily staffing needs. Use the following notation:
- Let \( x_i \) be the number of employees starting work on day \( i \) (where \( i = 1 \) for Monday, \( i = 2 \) for Tuesday, etc.).

**Optimization Model:**
- Objective: Minimize the total employees \( (x_1 + x_2 + x_3 + x_4 + x_5 + x_6 + x_7) \)
- Subject to constraints:
  - Monday: \( \begin{array}{c|c}
      & \\
      & \\
      & \\
    \end{array} \)
  - Tuesday: \( \begin{array}{c|c}
      & \\
      & \\
      & \\
    \end{array} \)
  - Wednesday: \( \begin{array}{c|c}
      & \\
      & \\
      & \\
    \end{array} \)
  - Thursday: \( \begin{array}{c|c}
      & \\
      & \\
      & \\
    \end{array} \)
  - Friday: \( \begin{array}{c|c}
      & \\
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Transcribed Image Text:### Epsilon Airlines Call-Center Staffing Model **Introduction:** Epsilon Airlines services predominantly the eastern and southeastern United States. Most of Epsilon's customers make reservations online, but some use phone reservations. Call-center personnel handle these reservations and support for booking changes. Efficient staffing is crucial to avoid excessive costs or poor service. **Staffing Requirements:** Epsilon analysts estimate the minimum number of employees needed for each day during the vacation season (June, July, and the first two weeks of August) as follows: | Day | Minimum Number of Employees Needed | |-----------|------------------------------------| | Monday | 60 | | Tuesday | 45 | | Wednesday | 40 | | Thursday | 45 | | Friday | 80 | | Saturday | 75 | | Sunday | 35 | **Work Schedule:** - Employees work five consecutive days followed by two days off. - Employees can start on any day of the week. - All employees receive equal pay. - Schedules are cyclic and independent of start/stop transitions. **Objective:** Develop a model to minimize the total number of call-center employees while meeting daily staffing needs. Use the following notation: - Let \( x_i \) be the number of employees starting work on day \( i \) (where \( i = 1 \) for Monday, \( i = 2 \) for Tuesday, etc.). **Optimization Model:** - Objective: Minimize the total employees \( (x_1 + x_2 + x_3 + x_4 + x_5 + x_6 + x_7) \) - Subject to constraints: - Monday: \( \begin{array}{c|c} & \\ & \\ & \\ \end{array} \) - Tuesday: \( \begin{array}{c|c} & \\ & \\ & \\ \end{array} \) - Wednesday: \( \begin{array}{c|c} & \\ & \\ & \\ \end{array} \) - Thursday: \( \begin{array}{c|c} & \\ & \\ & \\ \end{array} \) - Friday: \( \begin{array}{c|c} & \\
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