Statement of the Problem The 3 questions our group tried to answer were: How long will the development project at Systems take? How to crash it to meet the 35- week deadline? What impact would there be if the estimated duration of some tasks changes? Background We referred to the lecture notes on network diagram and probabilistic time estimates. We also reviewed materials on project crashing. Additionally, before actually solving the problem, we transferred the information presented in Exhibit 1 and Exhibit 2 of the case to an Excel spreadsheet so that we could carry out calculations easily.
Methodology First, since all the data came from the case and was already on an Excel spreadsheet, we began by calculating the expected time, variance, expedition available and slope for each task using the formulas below. Expected time=(optimistic+4*(most likely)+pessimistic)/6 Expedition available=Crash time-Expected time Slope= Expedition available/(Crash cost-Norma’ cost) Calculation results can be found in Table 1 in the Appendix. Second, with the expected time for each task available, we plotted the network diagram for the project (as shown in the next page).
Third, we found out all the paths based on the diagram and calculated the expected time, variance, standard deviation, Z value, possibility of completion by deadline and beyond deadline using these formulas: Expected time-sum of Expected time of all the relevant tasks Variance= sum of Variance of all the relevant tasks SST dive=square root of Variance Z value=(Adenine- Expected time)/(SST dive) INNERMOST(Z value) Calculation results can be found in Table 2 in the Appendix. Fourth, project crashing was conducted. We identified the critical path(s) each time we tried to crash it.
We also crashed the task(s) that would influence the critical path(s) and with those having lowest slopes first. Table 3 in Appendix shows the detailed steps of the whole crashing process. Finally, we generated a graph of the crashing cost function by plotting raising cost against crashing time to help better understand the tradeoffs of crashing, as shown in Table 4 of Appendix. Rest Its 1 . Based on Table 2 in the Appendix, the estimated completion time for this project is 39. 9 weeks. The estimated project budget is 205,000, which is the sum of the normal costs for all the tasks.
The probability that the project can be completed in 35 weeks is 1% according to the calculated Z value. 2. The minimum expected time in which this project can be completed is 33 weeks, based on the crashing results. The probability of completing the project in his time is 50% because now the required completion time equals the expected time. 3. The additional cost for reducing the project time to the required 35 weeks would be 40,756. 41. In order to achieve this milestone, task F would need to be crashed by 1 week, H by 0. 2 week, D by 2. Weeks, K by 1 week and C by 0. 6 week. Details can be found in Table 3 in Appendix. 4. The expected time for task B is increased from seven to nine weeks will have no impact on the crashing solution because the 2 paths that involve task B will still not be critical paths and thus will not be crashed. 5. The impact on the raising if the expected time for task D is decreased to seven weeks is that it makes task D and J the last choices in terms of crashing. D is still on the critical path(s), but its slope is so high that we only crash it when we have no other choices. . Looking at Table 4 of Appendix, it’s clear that the crash cost curve is non-linear. This is due to the fact that the unit cost of crash each task varies. We crash the most cost- efficient task first, making the first curve segment the steepest. Then we continue to crash those less cost-efficient ones, makes the following segments more and more even. Conclusions and Recommendations In this case, B&W Systems cannot meet the deadline using with normal development cycle and should instead do some project crashing.