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## Question 1: Calculation of Total Labor Cost for Painting Project

Assume that the owner pays only for hours worked (wait time and idle time is not paid for) and that the prepping work costs \$50/hour and painting costs \$30/hour. Compute the total labor cost of the paint project under these conditions?

Assume that the following new conditions:

1. Workers work Monday to Friday on a standard 8 hours per day from 8 AM to 5 PM with a lunch break between noon and 1 PM.

2. The owner can choose which resource(s) to hire each day so she is not required to hire all resources every day

3. Owner pays workers per day whether they were idle or working.

4. There are two Prep Experts available: Prep Expert 1 (PE1), at the rate of \$400/day and Prep Expert 2 (PE2), at the rate of \$600/day

5. There are three painters available, i.e., Painter 1 (P1) and Painter 2 (P2), at the rate of \$250/day each and Painter 3 (P3) at the rate of \$350/day.

6. All workers are available to work up to 3 additional hours overtime from 5 PM to 8 PM at double their hourly rate. That is the overtime hourly rates are as follows: PE1 at \$100/Hour, PE2 at \$150/hour, P1 at \$62.5/ Hour, P2 at \$62.5/ Hour and P3 at \$75/ Hour. Note that (a) overtime is possible only if the same worker was hired to work during regular hours for that day; and (b) overtime is paid only for time the worker is required to stay on the job (whether idle or working) and can be a fraction of an hour.

7. If more than one resource is assigned to a task, each resource contributes equally to the task 8. A task can get started on one day and finish on a different day

Develop and present a project plan under the above conditions with the objective of minimizing the labor cost as much as possible while respecting the predecessor relationships and all assumptions and other constraints provided above.

The owner would like to crash the project under the same assumptions provided in Question 2.

Develop and present a project plan under the above conditions to crash the entire project with the objective of completing the paint job as soon as possible while respecting the predecessor relationships and without spending any more money than necessary on labor to achieve the lowest earliest completion time possible (i.e., if you can complete the project in the same earliest time with lower cost, then do it).

For questions 3 compute the crash cost/time slope for each activity and for the entire project. Note that the cost of each activity is somewhat tricky since there is potentially idle time, so you need to account for the idle time cost in your total cost. Under what circumstances would it be worth to crash the project schedule and pay the extra cost?

Question 1: Calculation of Total Labor Cost for Painting Project

For answering the question it is assumed that the payment is done by the owner only for the hours worked, the idle and the waiting time are non-paid. The cost of prepping is \$50/hr and the painting cost is \$30/hr. The given conditions are noted for the calculation of the total labour cost for the painting project. The following excel table is attached after the calculation of the cost of the project.

 Date Resource Daily Regular Cost Overtime Hrs Overtime Rate Overtime Cost Total Cost Mon 4-9-2018 PE1 \$               400.00 \$     100.00 \$                                 - \$          400.00 Mon 4-9-2018 P1 \$               250.00 1.00 \$       62.50 \$                          62.50 \$          312.50 Tue 4-10-2018 PE1 \$               400.00 \$     100.00 \$                                 - \$          400.00 Tue 4-10-2018 P1 \$               250.00 1.00 \$       62.50 \$                          62.50 \$          312.50 Wed 4-11-2018 PE1 \$               400.00 \$     100.00 \$                                 - \$          400.00 Wed 4-11-2018 P2 \$               250.00 1.00 \$       62.50 \$                          62.50 \$          312.50 Thu 4-12-2018 PE2 \$               600.00 \$     150.00 \$                                 - \$          600.00 Thu 4-12-2018 P3 \$               300.00 1.00 \$       75.00 \$                          75.00 \$          375.00 Fri 4-13-2018 PE2 \$               600.00 \$     150.00 \$                                 - \$          600.00 Fri 4-13-2018 P2 \$               250.00 1.00 \$       62.50 \$                          62.50 \$          312.50 Sat 4-14-2018 PE2 \$               600.00 \$     150.00 \$                                 - \$          600.00 Sat 4-14-2018 P1 \$               250.00 1.00 \$       62.50 \$                          62.50 \$          312.50 TOTAL \$            4,550.00 6.00 \$                        387.50 \$       4,937.50

The project plan is created maintaining the constraints including the lunch breaks and the following the standard 8 hours per day from 8 A.M to 5 P.M. The resources are selected each day such that all the resources are not hired for the day and cost of the project is kept minimum. The rate of the Prep Experts and the Painters are considered for the calculation of the cost of the project. It is assumed that if more than one of the resource is allocated for the completion of the task each of the member would have an equal contribution for the completion of the activity.

 ID Room Activity Effort Wait Time Predecessor(s) Resource(s) Abbr. (e.g., PE1, P1,P2) Duration (Hrs) Start Time End Time Resource Overtime Hours Calculated at End of Day 1 Bathroom 1 Prepping 3 PE1 3.00 Mon 4-9-2018 8:00 AM Mon 4-9-2018 11:00 AM 2 Bathroom 1 Paint coat 1 2 1 P1 4.00 Mon 4-9-2018 11:00 AM Mon 4-9-2018 3:00 PM 3 Bathroom 1 Coat 1 Dry Time 1 2 1.00 Mon 4-9-2018 3:00 PM Mon 4-9-2018 4:00 PM 4 Bathroom 1 Paint Coat 2 2 3 P1 4.00 Mon 4-9-2018 4:00 PM Mon 4-9-2018 8:00 PM 1.00 5 Bathroom 2 Prepping 3 PE1 3.00 Tue 4-10-2018 8:00 AM Tue 4-10-2018 11:00 AM 6 Bathroom 2 Paint coat 1 2 5 P1 4.00 Tue 4-10-2018 11:00 AM Tue 4-10-2018 3:00 PM 7 Bathroom 2 Coat 1 Dry Time 1 6 1.00 Tue 4-10-2018 3:00 PM Tue 4-10-2018 4:00 PM 8 Bathroom 2 Paint Coat 2 2 7 P1 4.00 Tue 4-10-2018 4:00 PM Tue 4-10-2018 8:00 PM 1.00 9 Master Bedroom Prepping 6 4, 8 PE1 3.00 Wed 4-11-2018 8:00 AM Wed 4-11-2018 11:00 AM 10 Master Bedroom Paint coat 1 4 9 P2 4.00 Wed 4-11-2018 11:00 AM Wed 4-11-2018 3:00 PM 11 Master Bedroom Coat 1 Dry Time 1 10 1.00 Wed 4-11-2018 3:00 PM Wed 4-11-2018 4:00 PM 12 Master Bedroom Paint Coat 2 4 11 P2 4.00 Wed 4-11-2018 4:00 PM Wed 4-11-2018 8:00 PM 1.00 13 Bedroom 2 Prepping 3.5 4, 8 PE2 3.00 Thu 4-12-2018 8:00 AM Thu 4-12-2018 11:00 AM 14 Bedroom 2 Paint coat 1 3 13 P3 4.00 Thu 4-12-2018 11:00 AM Thu 4-12-2018 3:00 PM 15 Bedroom 2 Coat 1 Dry Time 1 14 1.00 Thu 4-12-2018 3:00 PM Thu 4-12-2018 4:00 PM 16 Bedroom 2 Paint Coat 2 3 15 P3 4.00 Thu 4-12-2018 4:00 PM Thu 4-12-2018 8:00 PM 1.00 17 Hallway Prepping 4 12,16 PE2 3.00 Fri 4-13-2018 8:00 AM Fri 4-13-2018 11:00 AM 18 Hallway Paint coat 1 3 17 P2 4.00 Fri 4-13-2018 11:00 AM Fri 4-13-2018 3:00 PM 19 Hallway Coat 1 Dry Time 1 18 1.00 Fri 4-13-2018 3:00 PM Fri 4-13-2018 4:00 PM 20 Hallway Paint Coat 2 3 19 P2 4.00 Fri 4-13-2018 4:00 PM Fri 4-13-2018 8:00 PM 1.00 21 Foyer Prepping 3 20 PE2 3.00 Sat 4-14-2018 8:00 AM Sat 4-14-2018 11:00 AM 22 Foyer Paint coat 1 2 21 P1 4.00 Sat 4-14-2018 11:00 AM Sat 4-14-2018 3:00 PM 23 Foyer Coat 1 Dry Time 1 22 1.00 Sat 4-14-2018 3:00 PM Sat 4-14-2018 4:00 PM 24 Foyer Paint Coat 2 2 23 P1 4.00 Sat 4-14-2018 4:00 PM Sat 4-14-2018 8:00 PM 1.00 Total Schedule Days 5.50

In the question 3 the project is crashed for the solution of question 2 and a project presentation plan is created for the management of the relationship between the resource and the activity. The crashing is applied for completing the project before time and adding more resources for completing the critical activities earlier. It can help the project manager for faster tracking the project and getting the project back to the track. With the crashing of project the need of providing overtime to the workers are eliminated and thus the effort of the employee can be divided for increasing the efficiency of the project.

 ID Room Activity Effort Wait Time Predecessor(s) Resource(s) Abbr. (e.g., PE1, P1,P2) Duration (Hrs) Start Time End Time 1 Bathroom 1 Prepping 3 PE1, PE2 1.50 Mon 4-9-2018 8:00 AM Mon 4-9-2018 9:30 AM 2 Bathroom 1 Paint coat 1 2 1 P1, P2 2.00 Mon 4-9-2018 9:30 AM Mon 4-9-2018 11:30 AM 3 Bathroom 1 Coat 1 Dry Time 1 2 1.00 Mon 4-9-2018 11:30 AM Mon 4-9-2018 12:30 PM 4 Bathroom 1 Paint Coat 2 2 3 P1, P2 2.00 Mon 4-9-2018 12:30 PM Mon 4-9-2018 2:30 PM 5 Bathroom 2 Prepping 3 PE2, PE1 1.50 Tue 4-10-2018 8:00 AM Tue 4-10-2018 9:30 AM 6 Bathroom 2 Paint coat 1 2 5 P2, P3 2.00 Tue 4-10-2018 9:30 AM Tue 4-10-2018 11:30 AM 7 Bathroom 2 Coat 1 Dry Time 1 6 1.00 Tue 4-10-2018 11:30 AM Tue 4-10-2018 12:30 PM 8 Bathroom 2 Paint Coat 2 2 7 P2, P3 2.00 Tue 4-10-2018 12:30 PM Tue 4-10-2018 2:30 PM 9 Master Bedroom Prepping 6 4, 8 PE2, PE1 1.50 Wed 4-11-2018 8:00 AM Wed 4-11-2018 9:30 AM 10 Master Bedroom Paint coat 1 4 9 2.00 Wed 4-11-2018 9:30 AM Wed 4-11-2018 11:30 AM 11 Master Bedroom Coat 1 Dry Time 1 10 P3, P1 1.00 Wed 4-11-2018 11:30 AM Wed 4-11-2018 12:30 PM 12 Master Bedroom Paint Coat 2 4 11 P3, P1 2.00 Wed 4-11-2018 12:30 PM Wed 4-11-2018 2:30 PM 13 Bedroom 2 Prepping 3.5 4, 8 PE1, PE2 1.50 Thu 4-12-2018 8:00 AM Thu 4-12-2018 9:30 AM 14 Bedroom 2 Paint coat 1 3 13 P1, P3 2.00 Thu 4-12-2018 9:30 AM Thu 4-12-2018 11:30 AM 15 Bedroom 2 Coat 1 Dry Time 1 14 1.00 Thu 4-12-2018 11:30 AM Thu 4-12-2018 12:30 PM 16 Bedroom 2 Paint Coat 2 3 15 P1, P3 2.00 Thu 4-12-2018 12:30 PM Thu 4-12-2018 2:30 PM 17 Hallway Prepping 4 12,16 PE1, PE2 1.50 Fri 4-13-2018 8:00 AM Fri 4-13-2018 9:30 AM 18 Hallway Paint coat 1 3 17 P2, P3 2.00 Fri 4-13-2018 9:30 AM Fri 4-13-2018 11:30 AM 19 Hallway Coat 1 Dry Time 1 18 1.00 Fri 4-13-2018 11:30 AM Fri 4-13-2018 12:30 PM 20 Hallway Paint Coat 2 3 19 P2, P3 2.00 Fri 4-13-2018 12:30 PM Fri 4-13-2018 2:30 PM 21 Foyer Prepping 3 20 PE1, PE2 1.50 Sat 4-14-2018 8:00 AM Sat 4-14-2018 9:30 AM 22 Foyer Paint coat 1 2 21 P2, P3 2.00 Sat 4-14-2018 9:30 AM Sat 4-14-2018 11:30 AM 23 Foyer Coat 1 Dry Time 1 22 1.00 Sat 4-14-2018 11:30 AM Sat 4-14-2018 12:30 PM 24 Foyer Paint Coat 2 2 23 P2, P3 2.00 Sat 4-14-2018 12:30 PM Sat 4-14-2018 2:30 PM Total Schedule Days 5.27

The cost of the project after crashing is calculated and given in the following table. The crashing of the project is applied when the there is a need to complete the project at a faster rate than it is progressing currently. If the deadline for the completion of the project is fixed and the current project needs some changes the project crashing is applied. For the crashing the relationship between the sponsors and the team members of the project should be identified and the project should be flexible such that it can adopt the new changes. The crashing is also applied if there is a delay in the progress of the project due to unavailability of the team members and some complexity in the project. During the progress of the project some of the resources may become suddenly unavailable and who was contributing to the project and thus at the end of the project more resource are added and the project is crashed for completing the project within the scheduled deadline.

 Date Resource Daily Regular Cost Overtime Hrs Overtime Rate Overtime Cost Total Cost Mon 4-9-2018 PE1 \$               400.00 \$     100.00 \$                      - \$          400.00 Mon 4-9-2018 PE2 \$               600.00 \$     150.00 \$                      - \$          600.00 Mon 4-9-2018 P1 \$               250.00 \$       62.50 \$                      - \$          250.00 Mon 4-9-2018 P2 \$               250.00 \$       62.50 \$                      - \$          250.00 Tue 4-10-2018 PE1 \$               400.00 \$     100.00 \$                      - \$          400.00 Tue 4-10-2018 PE2 \$               600.00 \$     150.00 \$                      - \$          600.00 Tue 4-10-2018 P2 \$               250.00 \$       62.50 \$                      - \$          250.00 Tue 4-10-2018 P3 \$               300.00 \$       75.00 \$                      - \$          300.00 Wed 4-11-2018 PE2 \$               600.00 \$     150.00 \$                      - \$          600.00 Wed 4-11-2018 PE1 \$               400.00 \$     100.00 \$                      - \$          400.00 Wed 4-11-2018 P3 \$               300.00 \$       75.00 \$                      - \$          300.00 Wed 4-11-2018 P1 \$               250.00 \$       62.50 \$                      - \$          250.00 Thu 4-12-2018 PE1 \$               400.00 \$     100.00 \$                      - \$          400.00 Thu 4-12-2018 PE2 \$               600.00 \$     150.00 \$                      - \$          600.00 Thu 4-12-2018 P1 \$               250.00 \$       62.50 \$                      - \$          250.00 Thu 4-12-2018 P3 \$               300.00 \$       75.00 \$                      - \$          300.00 Fri 4-13-2018 PE1 \$               400.00 \$     100.00 \$                      - \$          400.00 Fri 4-13-2018 PE2 \$               600.00 \$     150.00 \$                      - \$          600.00 Fri 4-13-2018 P2 \$               250.00 0.00 \$       62.50 \$                      - \$          250.00 Fri 4-13-2018 P3 \$               300.00 \$       75.00 \$                      - \$          300.00 Sat 4-14-2018 PE1 \$               400.00 0.00 \$     100.00 \$                      - \$          400.00 Sat 4-14-2018 PE2 \$               600.00 0.00 \$     150.00 \$                      - \$          600.00 Sat 4-14-2018 P2 \$               250.00 0.00 \$       62.50 \$                      - \$          250.00 Sat 4-14-2018 P3 \$               300.00 0.00 \$       75.00 \$                      - \$          300.00 TOTAL \$            9,250.00 0.00 \$                      - \$       9,250.00

Revised Project plan after crashing the project with the updates such as actual start date, end date, hours and the new tasks that are needed to be performed for the completion of the project.

 ID Room Activity Effort Wait Time Predecessor(s) Resource(s) Abbr. (e.g., PE1, P1,P2) Duration (Hrs) Start Time End Time 1 Bathroom 1 Prepping 3 PE1, PE2 1.50 Mon 4-9-2018 8:00 AM Mon 4-9-2018 9:30 AM 2 Bathroom 1 Paint coat 1 2 1 P1, P2 2.00 Mon 4-9-2018 9:30 AM Mon 4-9-2018 11:30 AM 3 Bathroom 1 Coat 1 Dry Time 1 2 1.00 Mon 4-9-2018 11:30 AM Mon 4-9-2018 12:30 PM 4 Bathroom 1 Paint Coat 2 2 3 P1, P2 2.00 Mon 4-9-2018 12:30 PM Mon 4-9-2018 2:30 PM 5 Bathroom 2 Prepping 3 PE2, PE1 1.50 Tue 4-10-2018 8:00 AM Tue 4-10-2018 9:30 AM 6 Bathroom 2 Paint coat 1 2 5 P2, P3 2.00 Tue 4-10-2018 9:30 AM Tue 4-10-2018 11:30 AM 7 Bathroom 2 Coat 1 Dry Time 1 6 1.00 Tue 4-10-2018 11:30 AM Tue 4-10-2018 12:30 PM 8 Bathroom 2 Paint Coat 2 2 7 P2, P3 2.00 Tue 4-10-2018 12:30 PM Tue 4-10-2018 2:30 PM 9 Master Bedroom Prepping 6 4, 8 PE2, PE1 1.50 Wed 4-11-2018 8:00 AM Wed 4-11-2018 9:30 AM 10 Master Bedroom Paint coat 1 4 9 2.00 Wed 4-11-2018 9:30 AM Wed 4-11-2018 11:30 AM 11 Master Bedroom Coat 1 Dry Time 1 10 P3, P1 1.00 Wed 4-11-2018 11:30 AM Wed 4-11-2018 12:30 PM 12 Master Bedroom Paint Coat 2 4 11 P3, P1 2.00 Wed 4-11-2018 12:30 PM Wed 4-11-2018 2:30 PM 13 Bedroom 2 Prepping 3.5 4, 8 PE1, PE2 1.50 Thu 4-12-2018 8:00 AM Thu 4-12-2018 9:30 AM 14 Bedroom 2 Paint coat 1 3 13 P1, P3 2.00 Thu 4-12-2018 9:30 AM Thu 4-12-2018 11:30 AM 15 Bedroom 2 Coat 1 Dry Time 1 14 1.00 Thu 4-12-2018 11:30 AM Thu 4-12-2018 12:30 PM 16 Bedroom 2 Paint Coat 2 3 15 P1, P3 2.00 Thu 4-12-2018 12:30 PM Thu 4-12-2018 2:30 PM 17 Hallway Prepping 4 12,16 PE1, PE2 1.50 Fri 4-13-2018 8:00 AM Fri 4-13-2018 9:30 AM 18 Hallway Paint coat 1 3 17 P2, P3 2.00 Fri 4-13-2018 9:30 AM Fri 4-13-2018 11:30 AM 19 Hallway Coat 1 Dry Time 1 18 1.00 Fri 4-13-2018 11:30 AM Fri 4-13-2018 12:30 PM 20 Hallway Paint Coat 2 3 19 P2, P3 2.00 Fri 4-13-2018 12:30 PM Fri 4-13-2018 2:30 PM 21 Foyer Prepping 3 20 PE1, PE2 1.50 Sat 4-14-2018 8:00 AM Sat 4-14-2018 9:30 AM 22 Foyer Paint coat 1 2 21 P2, P3 2.00 Sat 4-14-2018 9:30 AM Sat 4-14-2018 11:30 AM 23 Foyer Coat 1 Dry Time 1 22 1.00 Sat 4-14-2018 11:30 AM Sat 4-14-2018 12:30 PM 24 Foyer Paint Coat 2 2 23 P2, P3 2.00 Sat 4-14-2018 12:30 PM Sat 4-14-2018 2:30 PM Total Schedule Days 5.27

Chitra, K. and Halder, P., 2017. Scheduling Project Crashing Time Using Linear Programming Approach: Case Study. International Journal of Research in Industrial Engineering, 6(4), pp.283-292.

Mortazavi Nejad, M. and Tareghian, H.R., 2017. Payment scheduling under project crashing based on project progress. Iranian Journal of Numerical Analysis and Optimization, 7(2), pp.39-56.

Rumeser, D. and Emsley, M., 2017, October. Learning Style and Learning Method Preference in Project Management Education: What Happens When Things get More Complex?. In European Conference on Games Based Learning (pp. 860-865). Academic Conferences International Limited.

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