Indirect cost associated with project increases linearly with project duration. A typical line for indirect cost is shown in figure above.

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1 CPM Model The PERT model was developed for project characterized by uncertainty and the CPM model was developed for projects which are relatively risk-free. While both the approached begin with the development of the network and a focus on the critical path. The PERT approach is probabilistic and the CPM approach is deterministic. This does not howver mean that in the CPM analysis we work with single time estimates. In fact the principle focus of CPM analysis in on variations in activity times as a result of changes in resources assignment. These variations are planned and related to resource assignments and are not caused by random factor beyond the control of management as in case of PERT analysis. The main thrust of CPM analysis is on time-cost relationships and it seeks to determine the project schedule which minimize total cost. Assumption: The usual assumption of CPM model are: i. The cost associated with project can be divided into two components: direct cost and indirect cost. Direct costs are incurred on direct material and direct labour. Indirect cost consist of overhead items like indirect supplies, rent, insurance, managerial services etc. ii. Activities of the project can be expedited by crashing which involves employing more resources iii. Crashing reduces time but enhances direct costs because of factors like overtime payments, extra payments, and wastages. The relationship between time and direct activity cost can be reasonably approximated by a downward slopping straight line. A typical cost-time line is shown below: iv. Indirect cost associated with project increases linearly with project duration. A typical line for indirect cost is shown in figure above. Procedure: Given above assumption, CPM analysis seeks to examine the consequences of crashing on total cost (direct cost plus indirect cost). Since the behavior of indirect project cost is well defined, the bulk of CPM analysis is concerned with the relationship between the total direct cost and project duration. The procedure used in this respect is generally as follows:

2 i. Obtain the critical path in the network. Determine the project duration and direct cost. ii. Examine the cost-time slope of activities on the critical path obtained and crash the activity which has the least slope. iii. Construct the new critical path after crashing as per step-2. Determine the project duration and cost. iv. Repeat step-2 and step-3 till activities on the critical path (which may change every time) are crashed. Example Figure below shows the activity duration, direct activity cost of a project. The indirect cost is Rs 2000 per week Time in weeks Cost Cost to Expedite per week Activity Normal Crash Normal Rs. Crash Rs. Rs , Project network with normal duration is shown below: Figure CPM-1

3 The critical path in the all-normal network is ( ). The project duration is 30 weeks and the total direct cost is Rs. 45,200/- Examining the time-cost slope of activities on the critical path we find that the activity(2-4) has the lowest slope; in other words, the cost to expedite per week is the lowest for activity (2-4). Hence activity (2-4) is crashed. The proper network after such a crashing is shown below: Figure CPM-2 In this figure the critical path is ( ), with a length of 29 weeks, and the total direct cost is Rs. 46,700. Looking at the time-cost slope of the activities on the new critical path ( ). We find that the activity (5-6) has the lowest slope. Hence the activity is crashed. The project network after such a crashing is shown below where critical path is ( ) with a length of 27 weeks and the total direct cost is Rs

4 Figure CPM-3 Comparing the cost-time slope of the non-crashed activities on the new critical path ( ), we find that the activity which costs the least to crash is (1-2). Hence this is crashed. The project network after such a crash is shown below where the new critical path is ( ) with a length of 24 weeks and total direct cost of Rs /- Figure CPM-4 Looking at the time-cost slope of the non-crashed activities on the new critical path ( ), we find that the activity (6-7) has the lowest slope. Hence it is crashed. The project network after such a crash is shown below having two new critical path ( ) and ( ), both with a length of 21 weeks, and total direct cost of Rs /-

5 Figure CPM-5 Considering the time-cost of non-crashed activities on crtical path ( ) and ( ), we find that activity (3-5) which is common to both the critical paths is the least costly to crash. Hence, it is crashed. The new network is shown below having the new critical path ( ) with duration of 20 weeks and total direct cost is Rs Figure CPM-6 Looking at the new critical path ( ) we find that the only non-crashed activity is (4-6). Crashing this gives us the project network shown below having the critical path ( ) with duration of 19.5weeks and total cost Rs /- - Figure CPM-7

6 Since all the activities on the critical path ( ) are crashed, there is no possibility of further time reduction. Hence let us now look at the time-cost relationship from all above figures and as shown below: Figure Activity crashed Project duration in weeks Total Direct cost Total Indirect cost Total Cost CPM-1 None CPM-2 (2-4) CPM-3 (2-4) and (5-6) CPM-4 (1-2), (2-4) and (5-6) CPM-5 (1-2), (2-4), (5-6) and (6-7) CPM-6 (1-2), (2-4), (3-5), (5-6) and (6-7) CPM-7 (1-2), (2-4), (3-5) (5-6) and (6-7) Figure CPM-8 If the objective is to minimize the total cost of the project, the pattern of crashing suggested by CPM-6 is optimul. If the objective is to minimize the project durationthen the pattern of crashing suggested by fig CPM-7 is optimal. In real life situation, however, both the factors may be important. In addition, factors like strain on resources and degree of manageability are also important. The final decision would involve a careful weighing and balancing of these diverse factors, some quantitative, some qualitative. In any case, information along the lines provided in figure CPM-8 provides useful input for decision making.

INTRODUCTION PROJECT MANAGEMENT

INTRODUCTION PROJECT MANAGEMENT CHAPTER 7. 1 RESOURCE INTRODUCTION ALLOCATION TO PROJECT MANAGEMENT Prepared by: Dr. Maria Elisa Linda T. Cruz Prepared by: Dr. Maria Elisa Linda T. Cruz 1 Chapter 7. Resource Allocation 7.1 Critical Path