SOLVING CPM PROBLEMS USING COMPUTER - Quantitative Techniques for management

Cpm Problems With Solution

Go to MAIN MENU and select PROJECT PLANNING and CPM – CRITICAL PATH METHOD . Enter the values of the network problem as shown in the above figure.

Solving Network Problem on Computer Using TORA (Input Screen)

Now select SOLVE MENU and GO TO OUTPUT SCREEN. There are two options for output, select CPM calculations. For step-by-step calculation of earliest time and latest time using forward pass and backward pass procedure click NEXT STEP button. To get all the values instantly, then press ALL STEPS button. The screen gives all the required values to analyze the problem. You may note that at the bottom of the table, the critical activities are highlighted in red colour. The output screen is shown in the below figure, below:

Solving Network Problem on Computer Using TORA (Output Screen)

Example: The following table gives the activities in construction project and time duration.

Project Schedule with Time Duration

a. Draw the activity network of the project.
b. Find the total float and free float for each activity.

Solution:

a. From the activity relationship given, the activity network is shown in figure below:

Activity Network Diagram

b. The total and free floats for each activity are calculated as shown in table

Calculation of Total and Free Floats

Example: Draw the network for the following project given in the table.

Project Schedules

Number the events by Fulkerson’s rule and find the critical path. Also find the time for completing the project.

Solution: The network is drawn as shown in the following figure using the data provided. Number the events using Fulkerson’s rule and find the Earliest and Latest time and total float is computed for each activity to find out the critical path as given the following table.

TL, TL and TFij Calculated

Activity Network Diagram

The critical path is a – c – f – h– j and the minimum time for the completion of the project is 42 weeks.