Numerical problems

a. A construction company has been awarded a contract to construct a flyover in a city with a completion period of 18 months. The major activities in the project and the relationships among them, the normal and crash durations, and the corresponding normal and crash costs are given in Table Q7.1.1.

(i) If the project attracts a penalty of ` 10,000 per month for project completion beyond 18 months, find out the total project cost including penalty if the company does not ‘crash’ any activity.
(ii) Which of the activities should be crashed first in order to reduce the penalty payable and reduce the total cost?

b. The precedence requirements, normal and crash activity times, and normal and crash costs for a construction project are given in Table Q7.2.1. The overhead costs are ` 4 lakh per week.
(i) Find the critical path and time for completion under normal working conditions.
(ii) Find the optimum duration for the project to minimize the total project cost. What is the total project cost for the optimum duration?

c. Construction of a school building is scheduled to start from May 1, 2008. The details of different activities of the project are given in Table Q7.3.1. The budgeted costs shown in the table for different activities are to be spent uniformly over their duration. The activities start on the first day of the start month and finishes on the last day of the finish month. Draw a Gantt chart for project schedule and work out the monthly and cumulative cash flows for the project.

d. The details of activities for a small project are given in Table Q7.4.1. If the indirect cost for the project is ` 11.5 lakh per week,

(a) what is the minimum time in which the project can be completed considering maximum possible crashing, and

(b) what would be the total project cost if the schedule is crashed to the maximum?

e. A critical activity in a project is estimated to need 15 days to complete at a cost of ` 15,000. The activity can be expedited to complete in 12 days by spending a total amount of ` 27,000. If the indirect costs of the project are ` 3,000 per day, is it economically advisable to complete the activity early by crashing?

f. In a small project there are nine activities. The duration for each of these activities and the labour required to do them are given in Table Q7.6.1. The project must be completed within 27 days.

Nevertheless, the contractor wishes to carry out some resource levelling/smoothing in order that there are no excessive peaks or troughs in his labour schedule. Prepare labour schedule based on early start and late start of activities, and by visual inspection indicate the adjustment you would make in activities in order to perform resource scheduling.
g. For the data given in Table Q7.7.1, perform resource levelling within the minimum project duration for the smallest number of workers if activities cannot be split.