Project Management Methods

PMM – Semminary 1


  1. Solve the following planning problems:


  • Two resources Z1 and Z2 are assigned to the task X. Normalized work of a resource Z1 unit is 96 hours and the number of assigned units equals to 4, normalized work of a resource Z2 unit is 48 hours and the number of assigned units equals to 3. The project, which includes the activities X, and both resources are scheduled by the calendar with 8 hours of working time a day.
  1. What will be the total duration of task X?
  2. What will be the elapsed duration of the task X?
  3. Which resource is critical for the task X?
  4. What is the usage of uncritical resources and what this implies?
  5. Assume that X is a task of the “Fixed units” type. What happens if the work for Z2 increases to 96h?
  6. Assume that X is a task of the “Fixed duration” type. What happens if the work for Z2 increases to 96h?
  7. Assume that X is a task of the “Fixed duration” type and is not “effort driven”. What happens if Z2 is not available?
  8. Assume that X is a task of the “Fixed duration” type and is “effort driven”. What happens if Z2 is not available?

2) Draw following situations, define the relationship type and give an example.

  1. Task B starts at 25% of previous task A.
  2. Task B starts 5 days after completion of task A, but not less than June 1st. .
  3. The task B ends one day before the end of task A, but not later than August 6th..
  4. Task B starts at any time between August 1st and 1August 15th.
  5. Task B starts after August 1st and must finish before August 15th.
  6. Task B must be in progress January 1st.


  1. Let’s have a graph G :
    1. Describe the graph G.
    2. Find the highest node degree and calculate it.
    3. Determine at least one sequence of vertices that is not a path.
    4. Identify at least one path.
    5. Determine at least one closed sequence, which is not a circuit.
    6. Identify at least one circuit.
    7. Identify at least one Hamiltonian circuit.
    8. Find the minimum spanning tree of G (arc weights represent a cost).


  1. Let’s have a graph Q :
  1. Describe the graph Q.
  2. Identify at least one way.
  3. Identify the Hamiltonian path.
  4. Identify the cycles
  5. What is the number of circuits in the graph?.


PMM – Semminary 2


  • Formulate the projectbelow using AOA graph. For this purpose,supposeall thelinks are of FS type, exclude summary tasks!
  • Formulate the project below using AONFor this purpose, exclude summary tasks!
  • Draw the Gantt Chart of the project below, find graphically the critical path.


Task Code  Task Name Task Duration (in days) Predecessors Name
A Site Plan 3
B Building Plans 90
C Construction Permit and Contract 2 Site Plan, Building Plans
D Groundwork 30 Construction Permit and Contract
E Garage Construction 60 Construction Permit and Contract
F Walls 90 Groundwork
G Frame and Roof 30 Walls
H Garden 10 Frame and Roof, Garage Construction (SS+80%)


  • Provide the CPM analysis (critical path, task time parameters, slacks)


PMM – Seminary 3


  • InExcelassembleincidencematrixto perform the calculationandimplementation of thetime parametersof nodes.Determine thecritical path.


  • Adjust thedeterministicmodel intostochasticPERTand perform its time analysis (use file PERT_blank.xls)


PMM – Seminary 4


  • Perform the GERT probabilistic analysis
  • Find the expected critical path


  • Find the critical path using MPM method

                A   5                                       E   5
                                                                 10          G   4
                                                                         1                    -12
                B   10                                     C   6                                                                            8        H   10
                 15                                                                          -2           
                                                                                F   6                          14
                                                                D   8                       1

PMM – Seminary 5

1) Make the following stochastic simulation model

1 Preparation works for reforestation 30 d 3 d
2 Renewals 25 d 2d
3 Preparation for treatment 4 d 0 d
4 Fencing cultures 50 d 1d
5 Treatment of cultures 30 d 4d
6 Summer protection of cultures 80 d 7 d
7 Pruning 80 d 4 d
8 Collection of prunings 80 d 10 d

AON graph of the project
Find out using simulations in Excel:
a) Most likely CP

  1. a) Max. duration of the project
    b) Min. duration of the project
    c) Average duration of the project

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