Complete Exercises 13.1, 13.3, and 13.11

Complete Exercises 13.1, 13.3, and 13.11 on pages 354–359      

Excel template for Exercises 13.1, 13.3, and 13.11   

Use these Excel automated templates for your calculations (do not submit these files, but transfer information from them to the Excel file you are submitting):     

CPM Deterministic for 13.3    

PERT Probabilistic for 13.11     

Note on using the Excel templates: For a brief description of the Excel automated templates, refer to pages 338 and 345 in Quantitative Methods. Save the templates to your desktop before using. Make sure macros are enabled.

Any existing numbers in green cells in the automated tables are for examples, and show where you should enter the data. You must delete or overwrite these numbers to perform the calculations. The yellow cells of the automated templates are protected to prevent users from accidentally deleting or overwriting the formulas. There is no need to unprotect the templates.      

Exercise 13.1: Given the diagram shown in Figure EX 13.1, with activities A through G and duration times,      

a. Identify the paths and path duration times.  

b. Determine the critical path.        

Please look at the E-Book - Quantitative Methods in Health Care Management – Techniques and Applications by Yasar A. Ozcan (2009) Pg. 354 for diagram (FIGURE EX 13.1).      

Exercise 13.3: Calculate ES, LS, EF, LF, and slack time for the activities in Exercise 13.1

Exercise 13.11: A hospital is planning to add a $60 million patient tower. In order to support both the existing hospital facility and the new patient tower, an existing energy plant will be expanded and upgraded. Equipment upgrades include a new generator, liquid oxygen tanks, cooling towers, boilers, and a chiller system to ensure adequate electricity, heating, air conditioning, hot water, and oxygen delivery systems. Existing fuel tanks will be relocated. The activities, their immediate predecessors, and the optimistic, most likely,and pessimistic times in weeks for this project are listed in Table EX 13.11.      

TABLE EX 13.11           

Activity Activity Name Predecessor Optimistic Most Likely Pessimistic

A Design - 14 15 17     

B Budget estimate A 2 3 4    

C Permits B 14 16 19     

D Bid process C 7 8 9     

E Subcontractor buyout D 4 5 7    

F Startup E 3 4 5     

G New additional construction F 18 22 24   

H Cooling tower procurement - 20 22 24   

I Cooling tower installation G,H 9 11 12   

J LOX/fuel tank I 1 1 3    

K Boiler procurement - 29 30 31    

L Boiler installation J,K 19 31 34    

M Abate old boiler L 1 1 3    

N Chiller procurement - 28 30 32   

O Chiller installation M,N 25 29 34   

P Generator procurement - 28 30 31   

Q Generator installation P 12 16 20   

R Final inspection/testing O,Q 1 1 2         

a. Calculate the mean duration time for each activity.  

b. Calculate the variance for each activity time.  

c. Identify the mean and the standard deviation for each path.

d. Calculate project completion probability for 147, 150. And 152 weeks.

Week 7 Exercises Assistance          

Exercise 13.1 a: Refer to description on pp. 334-335.        

Critical Path Method (CPM)    

One of the main features of a network diagram is that it shows the sequence in which activities must be performed. On AON networks, it is customary to add a start node preceding the activities to mark the start of the project, and an end node to mark its conclusion.

A path is a sequence of activities that leads from the start node to the end node. The radiation project has eight paths as follows:


1. A-C-D-F-H     

2. A-C-D-G-H     

3. A-C-E-F-H     

4. A-C-E-G-H     

5. B-C-D-F-H     

6. B-C-D-G-H     

7. B-C-E-F-H     

8. B-C-E-G-H     

The length of time for any path is found by summing the times of the activities on that path. The time lengths for these eight paths, using times from Exhibit 13.1, are calculated and shown in Table 13.2

The critical path or the path with the longest time is the most important: it defines the expected project duration. Paths that are shorter than the critical path could encounter some delays without affecting the overall project completion time, as long as the highest possible path time is defined by the length of the critical path. In this example, path 8 (B-C-E-G-H) is the critical path, with a total project completion time of sixty-four weeks. All activities on the critical path are known as critical activities.      

Exercise 13.3: Refer to description and formulas on pp. 336-338.      

ES: the earliest time an activity can start, if all preceding activities started as early as possible.

LS: the latest time the activity can start and not delay the project

EF: the earliest time the activity can finish.   

LF: the latest time the activity can finish and not delay the project

By computing the ES, LS, EF, and LF, one can determine the expected project duration, critical path activities, and slack time.  

Computing ES and EF Times. Two simple rules compute the earliest start and finish times:
1. The earliest finish time (EF) for any activity is equal to its earliest start time plus its ex.
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