SmartOffice Construction company is building a new eco-friendly office building in southern California. The following table outlines the activities of the project. Times are expressed in days. Activity Immediate Predecessors Optimistic Time Most Likely Times Pessimistic Time A. Conduct a focus group - 15 18 27 B. Determine key features/options - 8 10 15 C. Set out design specifications A,B 5 7 12 D. Draw up blueprints C 5 8 25 E. Determine heating requirements C,D 5 6 10 F. Select appointments C 6 9 12 G. Arrange financing D 7 10 19 H. Plan marketing campaign C 6 8 10 I. Develop manufacturing specifications E 6 7 16 J. Obtain material for prototype E, F 25 40 45 K. Train workers I 15 20 29 L. Build prototype J, K 12 14 18 M. Determine selling prices E, F 3 5 8 N. Hold dealer meetings L, M 5 6 9 O. Prepare advertising literature H, L, M 7 15 20 P. Solicit initial orders O 15 20 25 Q. Determine order quantities H 4 4 6 R. Obtain materials N, Q 19 27 33 S. Schedule production G 10 12 20 a) For each activity calculate the expected completion time, and its variance. (You can use Excel to speed up the calculation and minimize error). Show calculation steps for activities "D" and "Q" only. b) Draw the project network (in the same style as in slide 4 of the lecture notes on Feb. 13). Fill in all the expected activity times, earliest start (ES), earliest finish (EF), latest start (LS), and latest finish (LF) times. Show your work on how you calculated these 4 numbers for projects Mgmt 101 - Management Science - Winter 2018 "O" and "R" only. (You are allowed to do the drawing by hand, but it should be clean and legible, on a standard printer paper). c) Determine the critical path for this project, as well as the expected completion time and its standard deviation. d) Assuming all other activities finish exactly in their expected time, how long can activity "R" be delayed in expectation before it affects the overall project completion time? e) Assuming all other activities finish exactly in their expected time, does it delay the whole project in expectation if the expected completion times of activity "F" and "M" are increased at the same time by 4 and 43 days, respectively? If so, how many days in expectation is the project delayed? f) Because of production considerations, SmartOffice will lose $15,000 if this project is not completed within 19 weeks (133 days). What is the probability that the project will be completed within this timeframe? g) Suppose SmartOffice were to hire an outside designer that could determine our design specifications (Activity C) faster than the inside team. This would guarantee that the activity is finished in exactly 4 days (with no variation). What will be the new completion time of the project if we hire the designer? What will be the new probability of finishing the project within 19 weeks (133 days)? Hint: This change could potentially change your critical path, so please check that before you calculate the new project completion time. h) What is the most SmartOffice should be willing to pay the outside designer who could finish Activity C in exactly four days? Hint: You need to compare "expected loss" with vs. without the designer. Note that you will only incur the $15,000 loss if you don't complete the project in 133 days. (You may want to review the meaning of "expected value" from Chapter 2).