Scheduling-employees cost problem (Operations Research)

IE311 – Operations Research I – Fall 2020/21

IE311: Operations Research I Course Team Project Due on Thursday 10/12/2020, by end of the day

Instructions:

1. This is a GROUP work: Each member should contribute to it. However, collaboration between groups of the same section or other sections is PROHIBITED. Please adhere to these regulations for your own individual benefit.

2. Any member can submit the case study in the name of his group. There is no need for each member to upload the assignment.

3. Each group are expected to submit TWO files: (1) The MS EXCEL file with the solution, and (2) a report written on MS Word (in DOC or PDF format). The files should have proper formatting and labeling.

4. Use the final report requirement bellow to prepare your report. 5. Your score will be posted in BlackBoard as soon as your instructor completes the grading.

Final Report Requirements:

• Cover page: It includes course name, project title, students’ names and ID numbers.

• Table of contents: The contents and their page numbers.

• Introduction: Introduce the project’s main problem. Then, write an overview for the

remaining topics of the report.

• Project Management: Organize the tasks of the project in a timeline scale using Gantt

chart. Distribute the tasks among the group members and show that in the chart.

• Problem Formulation (Modeling):

o Define the decision variables.

o Write and explain the objective function. Identify and explain all objective function

coefficients (cj).

o Identify and explain all constraints, which includes:

▪ Identifying and explaining all right-hand side values (bi).

▪ Identifying and explaining any other supporting data, if available.

• Problem Solution: Generate an optimal solution for the problem and the sensitivity report

using a software package. Attach the software input and output in the appendix.

• Results and discussion: Analyze the output of the optimal solution. Explain the results and

the suggested decisions. Answer all the questions from the case study here.

• Conclusion: What was learned from the considered problem and the results.

• References: Give full bibliographic information on all materials cited in the report and the

sources of data used in it.

• Appendix: Contains software input and output and any material that is not directly needed

in the report’s main body.

IE311 – Operations Research I – Fall 2020/21

Case Study A famous restaurant chain decided to open three new branches in your city: one in downtown

area (DT), one in a residential area (RA), and one in a touristic area (TA). All branches will open

daily from 12pm to 10pm. According to a study done by the analyst team, the minimum number

of employees needed in each branch at each hour is shown in table 1.

Table 1

Time Branch 1

(DT)

Branch 2

(RA)

Branch 3

(TA)

12pm-1pm 12 9 5

1pm-2pm 12 9 5

2pm-3pm 11 8 6

3pm-4pm 9 8 6

4pm-5pm 7 9 8

5pm-6pm 6 10 8

6pm-7pm 6 10 10

7pm-8pm 5 11 12

8pm-9pm 5 9 12

9pm-10pm 4 7 10

The restaurant chain management offered three types of jobs to hire employees for the three new

branches: 2- hours part timers, 4-hours part timers, 8-hours full timers. The 2-hours part timers

are only available to work after 4pm.

The average cost per employee hour is different for each type and each branch (Cost includes

salaries, insurance, transportation, etc.). Table 2 shows the average cost per employee hour

($/hour) for each branch.

Table 2

Employee type Branch 1 Branch 2 Branch 3

A (2-hours) 16 10.5 12

B (4-hours) 14 9.5 11

C (8-hours) 12 8 9

The number of applicants who applied for each type of jobs is 30 for the 2-hours part time jobs,

35 for the 4-hours part time jobs, and 15 for the full-time jobs. All applicants agreed to work in

any of the new branches if hired.

The restaurant chain management has a policy that there should be at least one full time

employee available at each branch when the branch closes at the end of the day.

Your team was chosen by the restaurant chain management to consult them to find the best

action for this case. The type of analysis that they are looking for is:

IE311 – Operations Research I – Fall 2020/21

1- What would be the number of employees required from each type (i.e. 2-hour part timers,

4-hours part timers, and 8-hours full timers) in each branch that will minimize the total

daily cost? What would be the daily cost in each branch in this case?

2- How many extra employee hours will be available in each branch at each hour after the

required hours are fulfilled?

3- How much could the company saves daily if five more full-time employees were

available to hire?

4- Which branch costs the most for satisfying the policy of having one full time employee

available at the end of the day?

(Hint: You can use the sensitivity report to answer questions 3 and 4)