Question

A manufacturer of personal computers has recently identified time estimates, activities and predecessors to design, manufacture and market a new laptop computer. Their estimates are listed below Immediate Activity Description Estimated completion time (days) 90 15 Predecessors Prototype design Purchase of materials Manufacture of prototype Revision of design Initial production run Staff training Staff input on prototype Sales training Preproduction advertising campaign Post production advertising campaign 20 21 25 14 28 30 C,F D,I Management has also provided you with cost estimates for each activity showing normal costs and crash costs as well as normal time to complete each activity and crash times Activity time Normal Cost Crash (days) Crash Cost Normal Time (days) ($,000) ($,000) 90 $2,250 85 $2,520 15 $180 13 $210 $90 4 $120 20 16 $300 $340 21 17 $231 $315 25 $375 $250 14 $70 $112 28 $392 25 $448 30 28 $570 $510 45 $1,350 41 $1,530 Task You are tasked with preparing a report detailing a project network for the senior management of this company and addressing specific questions that the management of the company has requested (see below), The method to employ will be critical path analysis (CPM) You are to present a report of no more than 500 wards in length to the management board of the company detailing your network. Alternatively, you may present your results as a PowerPoint presentation with no more than 8-12 slides in total. The senior management of the company have questions which must be addressed in the report These are listed below and must be incorporated into your report/presentation Points that must be incorporated into your report a) Management have requested you to prepare an apprapriate AON (Activity on Node) network diagram for this project. You should draw the node for each activity as per the examples in your readings e.g. Acivity Name or Symbol Larbest Start Activity Duration b) Management would like to know from your project network the critical path, the length of the critical path, the earliest start, earliest finish, latest start and latest finish of each activity of the project network. Yau can identify these on the network diagram or sunmarise this information in a table if you so wish. c) Management have an incentive to bring the new computer to market as quickly as possible as they also believe that a competitor will be bringing a similar product to market at approx. the same time. As such, they would like to know what activities to crash and at what cost to bring their computer to market eight (8) days earlier than scheduled i.e. they wish to evaluate the option of crashing days from the project schedule. Provide a brief summary of the information that management requires so that they can make an informed decision d) Finally, remember that your report should not be read as a purely technical document although you can certainly present the more detailed and technical analysis in your appendices (which do not count as part of your word/PowerPoint limits). Rather, your report to the management of this company should be presented in a clear, concise and logical manner with well-argued points/diagrams/tables in answer to the questions raised.

Answer 1

Pre-requisite Formulas

ES = EF of Preceding activity (0 for source task), highest to be selected

EF = ES + Activity Time of the tasks

LF = LS of succeeding activity (Critical path time for Sink Task), lowest to be selected

LS = LF - Activity Time of the tasks

Answer-

The Network flow diagram along with the Early Start (ES), Early Finish (EF), Late Start (LS) and Late Finish (LF) is as shown in the diagram-

129149 149170 115 129 90 115 173 21 94 14 129129 20 149 90 25 115 149 H 177 105 C 110 90 105 0 A 90 166 28 194 110 5 115 9095 15 110 0 90 149 194 149 45 194 90 120 119 30 149

To identify the critical path, we will first identify those tasks which has ES=LS and EF=LF. The tasks A,F,G.D & J are the tasks adhering to this criteria and hence, constitute the critical path. Therefore the critical path is A-F-G-D-J.

The scheduled project duration is = Sum of tasks in critical path = 90+25+14+20+45 = 194 days

Time taken by Non Critical paths-

A-F-G-D-E = 90+25+14+20+21 = 170 days

A-F-G-D-H = 90+25+14+20+28 = 177 days

A-B-C-G-D-E = 90+15+5+14+20+21 = 165 days

A-B-C-G-D-H = 90+15+5+14+20+28 = 172 days

A-B-C-G-D-J = 90+15+5+14+20+45 = 189 days

A-I-J = 90+30+45 = 165 days

B) The management wants to bring the project 8 days before the scheduled period. Therefore, the critical activities needs to be crashed by 8 days.

Calculating Improvement factor for all activity using formula - Improvement factor = (Crash Cost - Normal Cost)/(Normal Time - Crash Time)

Activity	Normal Time	Normal Cost	Crash Time	Crash Cost	Improvement Factor
A	90	2250	85	2520	54
B	15	180	13	210	15
C	5	90	4	120	30
D	20	300	16	340	10
E	21	231	17	315	21
F	25	250	22	375	41.66666667
G	14	70	12	112	21
H	28	392	25	448	18.66666667
I	30	510	28	570	30
J	45	1350	41	1530	45

Highlighted are the critical activities.

From the above table we see that, out of the critical activities, the Improvement factor of Activity D is least and should be crashed first. On crashing Activity D, we shall get a reduction in project duration of 4 days.

Now, we see that the Improvement factor of Activity G is the next lowest figure and should be crashed second. On crashing Activity G, we shall get a reduction in project duration of 2 days. Thus resulting in the total project duration reduction to 6 days.

Now, we see that the Improvement factor of Activity F is the next lowest figure and should be crashed third. On crashing Activity F, we shall get a reduction in project duration of 3 days. Thus resulting in the total project duration reduction to 9 days.

Therefore, the critical path duration after crashing will now be = 90+22+12+16+45 = 185 days

Time taken by Non Critical paths-

A-F-G-D-E = 90+22+12+16+21 = 161 days

A-F-G-D-H = 90+22+12+16+28 = 168 days

A-B-C-G-D-E = 90+15+5+12+16+21 = 159 days

A-B-C-G-D-H = 90+15+5+12+16+28 = 166 days

A-B-C-G-D-J = 90+15+5+12+16+45 = 183 days

A-I-J = 90+30+45 = 165 days

As the non-critical paths still have time duration less than the critical path, the critical path doesn't change on crashing.

C) To achieve the desired time of project completion, the management has to undergo the above stated crashing steps. This crashing would subsequently also increase the investment required for project completion. Based on the investment capabilities, the management should decide how much early they should target to release the product as compared to the normal scheduled time. Nevertheless, evaluating the steep increase of Improvement factor in the third crashing step, the management should stop crashing at the second step itself. The monetary investment required to undertake the third crashing doesn't justify the extent to which it bring reduction in project duration. Therefore, the product should be launched at 188th day rather than on 186th, if monetary investment is given highest precedence.

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