Admiral George Dewey and Admiral Chester W. Nimitz Essay

Admiral George Dewey and Admiral Chester W. Nimitz - Essay Example In the Navy of the United States, the admiral is a four-star flag officer grade. At the top ranks the Admiral, then the sub-admiral and lower is the Fleet Admiral. There is no a founded ranking above the admiral. Admiral is equal to the position of general in the other uniformed services. In 1899, the Congress acknowledged George Dewey's achievements in the Spanish-American War by empowering the President to select him Admiral of the Navy. In 1944, Chester W. Nimitz was endorsed by the Congress as one of the five-star rank of Fleet Admiral. This paper analyzes the achievements of these two admirals, their leadership traits and their strengths and weaknesses. Introduction While Chester W. Nimitz was still schooling at Tivy High School, Kerrville, Texas, he sought for an appointment to West Point since he had interests on an Army profession. When he missed this chance, he sat for a cutthroat test for Annapolis and was chosen and appointed from the Twelfth Congressional District of Texa s in 1901. In 1905, he left high school to join the Naval Academy Class of that year. He essentially was conferred his high school diploma several years later, after he was a Fleet Admiral. Nimitz was an outstanding student at the Academy, particularly in mathematics and got a distinction. In addition to this, he was an excellent athlete and stroked the squad in his first year class1. After graduating with a distinction from the United States Naval Academy Class of 1905, Nimitz started his profession as a surface officer on several ships. Later, he achieved success as one of the foremost leaders of submarine development and war after being relocated to the new submarine service. These attempts concluded with several aide ranks to flag officers and later control of ships and flotillas2. On the other hand, young Dewey was posted to the steam frigate Wabash after his graduation from the Naval Academy at Annapolis. He stayed here until 1859 when he went back to Annapolis to get his fina l examination. George Dewey got his first assignment on April 18 1861. He became lieutenant, and in the period from 1861 to 1863, he operated on the Mississippi, which was a steam sloop of the West Gulf Squadron. He would not have experienced a lot of service if he had been graduated at a different time. However, that time had a lot of promise for the navy and the army3. Admiral Nimitz had a very admirable and strong character that was characterized with a lot of confidence and patience. For instance, he never wavered from his commitment to task and nation, from rivalry with General MacArthur to the political scheming in the Navy Department. Nimitz never lost concentration of his reliability or the bigger picture of what had to be done for the nation and the war struggle. He deemed himself a man of team and was contented with it. He was not a Man of strict orders but concentrated much on working with the team. He declined several rewarding positions after the Second World War and vi ewed them as not in the best concern of the Navy. Moreover, he did not want to profit on the lives lost during the warfare4. In addition, Nimitz was the pre-renowned carrier strategist of the Pacific. Due to this, Turner (U.S. Naval Academy, 1906) won Nimitz' esteem for leading amphibious associations all through the Pacific in time of the war5. The character of Admiral George is characterized by honesty, refinement, clean and eager, and being a believer in himself6. In the aspects of his command, Dewey knew how to put his foot down with a ton's strength when the situation demanded it. He was fit for leading the United States navy since he created order and discipline, which encompasses the making of a soldier7. It was the routine of Admiral Dewey to abstain from attractive words and used words with accuracy. He definitely did not seek to affirm a case in colors and curves, and yet, through his statements, letters and cables, it is clear that he was a man whose sound was high

Locke vs. Rousseau Essay Example for Free

Locke vs. Rousseau Essay ?According to Rousseau, the original condition of mankind was a peaceful and quixotic time in which people lived solitary, uncomplicated lives. This differs from Lockes concept of the state of nature in that, his natural condition of mankind was a state liberty in which one was able to conduct ones life as they saw fit. Like Rousseaus, it was a time of peace between the people, but Lockes was not necessarily a solitary life. ?The state of nature for Locke was a state wherein there were no civil authorities or governments to punish people for transgressions against laws, but was not a state without morality. It was pre-political, but was not pre-moral. In it, persons were assumed to be equal to one another, and therefore equally capable of realizing and being obliged by the law of nature. (The law of nature being one internal, which commanded that no one should harm another as concerning their life, health, liberty, or possessions [p. 4]). In Lockes pre-contract condition, one was not at absolute liberty to do whatever one chose to do; they were inherently bound by the law of nature. ?Rousseaus state of nature had no private property. Private property was something which arose from the stages leading up to the need for authority. Where Locke saw property as something which was naturally protected in the state of nature, Rousseau conceived of property ? the result of greed, competition and vanity- as humanities reason for abandoning such a time and entering into the contract. ?For Rousseau, the few needs of the people in the pre-contract condition were easily satisfied by nature. Because of the abundance of nature and the small size of the population, competition was non-existent, and persons rarely even saw one another, much less had reason for conflict or fear. ?Moreover, for Rousseau, the simple and morally pure persons in the pre-contract condition were naturally endowed with the capacity for pity, and therefore were not inclined to bring harm to one another. There were no inherent ? laws forbidding transgressions on another; it was an internal aptitude for pity. It was the division of labor (once families and communities had developed and leisure time had resulted) that led to value and property, whereas Locke saw property as something that was existent in the natural condition.

Apocalypse :: essays research papers

Apocalypse FOLLOWING IS AN IMPORTANT REVELATION BEING MADE TO THE GENERAL PUBLIC. THIS IS THE ONLY TIME YOU WILL BE CONTACTED. Disclaimer: The following information contains predictions of the future. This has been written for people who want to know what is on the horizon for humanity, and most importantly, WHAT THEY CAN DO ABOUT IT. Please understand that if you read this material, you will be doing it by your own choice. If your reaction causes you to want to report me to AOL for sending unsolicited email, it could result in my account being closed. I don't ask that anyone believe what I say just because I say it. I do ask that if you choose to read this material, please suspend your judgment of it until enough time passes for its validity to be proven or disproven. Please don't let your personal beliefs cause you to want to deprive others of receiving this. Written October 20, 1996 NOTE: This document is quite lengthy, so it might be best to either print it or copy it to your word processor so it may be read off-line. Dear Friend,   Ã‚  Ã‚  Ã‚  Ã‚  The choice of whether or not to read this message all the way through may have important consequences for you as the events of our immediate future unfold. This is being done solely for the benefit of others so that people may understand what to do about the times now approaching humanity. What I'm about to explain will strike many people as ridiculous, because this kind of thing has been predicted over and over again and people are not inclined to take things like this seriously. I am not your average tabloid psychic. In fact, I'm not a psychic at all. I am what could be called a modern day seer, but I prefer to be thought of as just a human being with an important message.   Ã‚  Ã‚  Ã‚  Ã‚  I have studied prophecy and the techniques used to produce it for many years now. Through a combination of my own findings, the prophecies of Nostradamus, the prophecies given by Jesus and the prophet Daniel, I have figured out the future of humanity. As stated above in the disclaimer, the reader's belief in what I say is not necessary at this point.   Ã‚  Ã‚  Ã‚  Ã‚  This message has been written over and over again since I first set out to do this. In previous versions, I have tried to describe what will cause the rough times to come... but everyone is pretty much aware of the world's problems and they don't really need to have it all pointed out to them. Besides, it makes the message unnecessarily long.

The Main Theme of “On Liberty”

The main theme of on liberty was the individual. Everything else, society, education,government and so forth had their basis in the individuals rights to his own liberty. Noone, no member of society, government, even God, if he appeared before an individual, could inforce his will upon him. That is not to say that you couldnt change someones mind through discussions, but instead, that noone had a right to force his views upon another. Your happiness is yours(individual) to enjoy without any infringements. Conversations between individuals or groups of individuals is essential in eveloping the notion of liberty. Mill claims that you should feel free to convey your views openly without forcing them onto others. After all, a man who learns from noone but himself has a fool for a teacher. There is however an exception to this rule. That is, if an individual in any way harms or comes onto anothers rights to liberty, or causes a social threat, hence he or she is subjected to forced inclinations by other members of society. For example, walking around nude on the streets of Cairo might be youre cup of tea, alas, in Cairo they prefer coffee. In other words, if ou offend other individuals, you are in fact infringing on their rights as free citizens who poses a sovereign mind. However if you choose to remain nude while in the comfort of your hotel room in Cairo, then there is no reason why you According to Mill, education is a fundamental requirement for being an individual as well. But once again, there should be no forceful applications towards what is being taught. Man is after all, a rational being and has the capabilities to reason things through. Education serves more as a guide then as a factual basis for each individual. No wo individuals can have the exact same experiences in life. Therefore, it is up to the individuals themselves to conclude what they perceive to be their own ideas of happiness. An individual who follows traditions and customs soleley because they are inherrent in society, is nothing more than an animal. The very fact that you can reason said mill, means that you have the option of disregarding all customs and traditions if you feel they are not beneficial towards your happiness. That is not to say that you shouldnt follow customs and traditions, merely that you ought not to, for the sake of eing just another brick in the wall. The progressive nature of humans leads to the ultimate conclusion that there is no need for a governing force outside society consisting of individuals that have their own interests at heart. There should not be a government, a monarch, a ruler that is outside society. Instead, it should be attached to the people, having their best interests at heart. Rulers are not needed to protect the people from themselves. In fact, they should be in all regards, responsible to the people and subjected to being removed by he people, beacause it is the people who ultimately have the power. This is a true democratic state, with individuals as the microscopic entities that make it up. Members of this society must not allow themselves to be surpressed by any group who claim to be their legitimate representative of the state. This will subdue individual growth and sovereignity, creating a state with tyranny at its heart. TO avoid this, individuals should freely express themselves, their beliefs, ideas and so forth. No government has the authority to silence individuals who convey their eliefs as the truth. Even if there are a thousand people with a thousand different views, it is for the benefit of society as a whole to hear them out, for there is a chance that among the various beliefs, one of them may contain the essence of truth. Noone has the right to silence another merely because they express conflicting views. Members of society must be able to keep an open mind towards other individuals â€Å"truths†. Reason and logic will see to it that they are capable of readjusting and reconstructing themselves if they find that there is truth in what another individual ays. This is exactly why individuals and society are The only way a state can progress is by allowing its members to progress. Supression of individual rights and happiness will lead to nothing more than stagnation. Governments are the watchdogs of the people, granting them liberty to expand without inteferences. Mill undoubtedly believed in laissez-fairre for the very reason that it promoted individuality with minimum government intervention. All said, Mills on liberty held the individual as the nucleus of society, with everything else revolving.

Coleman Managerial Report

R. C/ Coleman distribute a variety of food products that are sold through grocery store and supermarket outlets. The company receives orders directly from the individual outlets, with a typical order requesting the delivery of several cases of anywhere from 20 to 50 different products. Under the company’s current warehouse operation, warehouse clerks dispatch order-picking personnel to fill each order and have the goods moved to the warehouse shipping area.Because of the high labour costs and relatively low productivity of hand order-picking, management has decided to automate the warehouse operation by installing a computer-controlled order-picking system, along with a conveyor system for moving goods from storage to the warehouse shipping area. R. C. Coleman’s director for material management has been named the project manager in charge of the automated warehouse system. After consulting with members of the engineering staff and warehouse management personnel, the dir ector compiled a list of activities associated with the project.The optimistic, most probable and pessimistic times (on weeks) have also been provided for each activity. Activity A B C D E F G H I J K Description Determine equipment needs Obtain vendor proposals Select vendor Order system Design new warehouse layout Design warehouse Design computer interface Interface computer Install system Train system operators Test system Immediate Predecessor A, B C C E C D, F, G D, F H I, J Activity Optimistic Time Most Probable Pessimistic A B C 4 6 2 6 8 4 8 16 6 Page 1 D E F G H I J K 8 7 4 4 4 4 3 2 0 10 6 6 6 6 4 4 24 13 8 20 8 14 5 6 Managerial Report Develop a report that present the activity schedule and expected project completion time for the warehouse expansion project. Include a project network in the report. In addition, take into consideration the following issues: 1. R. C. Coleman’s top management established a required 40-week completion time for the project. Can this co mpletion time be achieved? Include probability information in your discussion. What recommendations do you have if the 40-week completion time is required? 2.Suppose that management requests that activity times be shored to provide an 80 percent chance of meeting the 40-week completion time. If the variance in the project completion time is the same as you found in part (1), how much should he expected project completion time be shortened to achieve the goal of an 80 percent chance of completion within 40 weeks? 3. Using of expected activity times as the normal times and the following crashing information, determine the activity crashing decisions and revised activity schedule for the warehouse expansion project.Costs ($) Activity Crashed Activity Time (weeks) A B 4 7 Normal 1,000 1,000 Crashed 1,900 1,800 Page 2 C D E F G H I J K 2 8 7 4 5 4 4 3 3 1,500 2,000 5,000 3,000 8,000 5,000 10,000 4,000 5,000 2,700 3,200 8,000 4,100 10,250 6,400 12,400 4,400 5,500 END OF QUESTIONS MANAGERI AL REPORTS 1. 2. 3. 4. 5. 6. 7. Objective Introduction Methodology Analysis & Discussion Recommendation Conclusion Reference Appendix Page 3 1. Objective Introduction This report is the analysis study of R. C. Coleman Company; a company on distribution business with varieties of food products that are sold through grocery store and supermarket outlets.The company receives orders directly from the individual outlets, with a typical orders requesting the delivery of several cases of anywhere from 20 to 50 different products. Present company’s current warehouse operation, the practise which has been utilized manually by warehouse clerks. The dispatch order-picking personnel are to fill each order and have the goods moved to the warehouse shipping area. Manual operation has been rationale as high labour cost and low productivity on the distribution system. Management has decided to change into automate the warehouse operation with the objective to improve on the operations and ut put efficiency. R. C. Coleman’s top management has established requirement of 40-weeks completion time for the project of installation of computer-controlled order-picking system, this come along with conveyor system for moving goods from storage to the warehouse shipping area. The management also has drawn up others requirement and completion percentage at any particular time. The establishment of the report will be base objectively to analyse and examine all possibilities on the predetermine activities on the project network and completion time for the warehouse distribution upgrading project of R.C. Coleman Company. Hence, the result from this report is vital Page 4 information required to the company’s top management team to make effective decision for this project meeting with business objective and goal. 2. Methodology Upon appointed as Project Manager, Mr R. C. Coleman is responsible for planning, scheduling and controlling the project that consist of numerous s eparate jobs or task performed by a variety department and individual. The project team need to establish the project network and making the analysis based on the Quantitative Approaches to Decision Making processes.In order to draw up project network, the team need information on the project activities involved and time required. As this project is rather new and they had never attempted before by the team, Mr Coleman have to establish the time by estimation. The activities are following the concept of probability distribution whereby they have to determine by estimating each activities time at a range of possible value. After a meeting with his project team, he has established a list of activities associated with the project as per below; Table 1: Project Activities and links Activity Description Immediate Predecessor A, B C A B C DDetermine equipment needs Obtain vendor proposals Select vendor Order system Page 5 E F G H I J K Design new warehouse layout Design warehouse Design c omputer interface Interface computer Install system Train system operators Test system C E C D, F, G D, F H I, J The incorporation of uncertainty activity with estimating time above is defined as; i. ii. Optimistic time (a) = the minimum activity time if everything progresses ideally. Most Probable time (m) = condition. iii. Pessimistic time (b) = the maximum activity time if significant delays are encountered Below table is the result for the uncertain activities time achieved.Table 2: Probable timing in weeks Time Optimistic Activity (a) (m) A B C 4 6 2 6 8 4 8 16 6 Most Probable (b) Pessimistic the most probable activity time under normal Page 6 D E F G H I J K 8 7 4 4 4 4 3 2 10 10 6 6 6 6 4 4 24 13 8 20 8 14 5 6 To ensure that the project is progressing as planned, Mr Coleman is advised to utilize and incorporate the analysis with the concept of probability distribution; Project Scheduling with Uncertain Activity Times. Such situation, the understanding and utilization of Progr am Evaluation and Review Technique (PERT) and Program of Critical Path Method (CPM) has proven to be extremely valuable.The PERT/CPM system will furnish to project manager on the information of project planning, scheduling and the progress of the project so that he able to coordinate and monitoring the project and be complete as expected by the management. 4. Discussion Analysis When the top management of R. C. Coleman has decided to modernize and expand the current warehouse and its distribution system, there is certain project requirement and goal has been drawn up to the project manager and the team to find out the feasibility to achieve target goal on the completion timing and possible percentage.Hence, the analysis will be representing on each part of the management requirement. There is two parts as per below: PART 1 Page 7 Apart from to find out the project completion time, the project Manager; R. C. Coleman has to find out the possibility that this expansion project could be complete within 40 weeks. Upon finding the result, he needs to come out on recommendation to supporting the result. Various parts below is to solving as per PERT/CPM steps procedures; PART 1 (a) Project Network Flow and VarianceThe identified activities and links from the table one (1) above require illustration in form of work flow chart using CPM /PERT technique to analysis further in determining critical activities and critical path for the project. Figure three (3) below is the project network depicting the activities and linkage of immediate predecessors on each individual activity from start until complete. Figure 3: R. C. Coleman Project Network. Part 1 (b) Expected Project Time, Project Network and Completion Time. Page 8To illustrate the project network with PERT/CPM procedures and finding the completion time, the three (3) estimate time above should be calculate and convert to expected time. Expected time (t) can be finding with the formula; Expected Time (t) = (a+4m+b) / 6 Upon finding the result on expected time, we could analysis to determine ‘start’ and ‘finish’ time for each activities from starting the project until completion. At the end of the flow we could establish that on the total time required to complete the project based on calculation of expected time. Below is the determine project network work flow and estimated completion time in weeks.Figure 4: Project network flow and completion time E 13 23 10 13 23 A 6 0 3 6 9 C 4 B 9 0 0 9 9 9 9 13 13 G 8 13 21 21 29 F 6 23 29 23 29 START H 6 29 35 29 35 I 7 29 36 32 39 K 4 39 43 39 43 FINISH (43 WEEKS) D 13 25 12 17 29 J 4 35 39 35 39 From the project network work flow at figure four (4) above, we have noted that the R. C. Coleman warehouse expansion project and conveyor system distribution upgrading will be completed at 43 weeks. Page 9 The team also needs to determine the slack associated with each activity. The term ‘Slack’ is the length of time of a n activity can be delayed without increasing the project completion time.The amount of slack of an activity is computed as follows; Slack = LS – ES = LF – EF Conversely, the activities which appear having zero slack is the critical activity whereby delaying in this process or steps could post an effect to total project schedule completion timing. As ruled, with uncertainty activity times, the team must aware that the differences between those three estimation time (Optimistic, most probable and pessimistic) could give great effect on the value of the variance. The term ‘variance’ is indication on the dispersion or variation in the activities time value. The value of variance could calculate with this formula; 2 = 2 Having greater value between tis value among the activities could give great reflect a high degree of uncertainty in the activity time. For easy to overview on the whole project, we have summarize the information into table manners as on Table f ive (5) below; Table 5: Project network summary information and critical path. Activity Expected Time Variance Earliest Start (ES) Latest Start (LS) 3 0 9 Earliest Finish (EF) 6 9 13 Latest Finish (LF) 9 9 13 Slack LS – ES 3 0 0 Critical path A B C 6 9 4 0. 44 2. 78 0. 44 0 0 9 YES YES Page 10 D E F G H I J K 12 10 6 8 6 7 4 4 7. 11 1 0. 44 7. 11 0. 44 2. 78 0. 11 0. 44 3 13 23 13 29 29 35 39 17 13 23 21 29 32 35 39 25 23 29 21 35 36 39 43 29 23 29 29 35 39 39 43 4 0 0 8 0 3 0 0 YES YES YES YES YES Part 1 (c) Critical Path and the Curve From the table above, we could note that the activity schedule for the warehouse expansion project which shows zero slack is the critical path for the project is; B – C – E – F – H – J – K. From the critical path shown, the expected time of the project is E (t) = tB + tC + tE + tF + tH + tJ + tK = 9 + 4 + 10 + 6 + 6 + 4 + 4 = 43 Weeks Hence, the variance in the project completion time is the sum of the variance on the critical path activities, which is; 2 = ? B + ? C + ? E + ? F + ? H + ? J + ? K = 2. 78 + 0. 44 + 1. 0 + 0. 44 + 0. 44 + 0. 11 + 0. 44 = 5. 65 ? = = 2. 38 Page 11 Figure 6: Standard Normal Distribution Curve STANDARD NORMAL DISTRIBUTION CURVE AREAS ? = 2. 38 EXPECTED COMPLETION TIME (T) 43 TIME (T) WEEKS Since the top management of R. C. Coleman allotted 40 week to complete the project, the probability distribution is; Z = = = – 1. 26 With the obtained value ‘z’ is -1. 26, we could enter the normal distribution from the table and we found out that; Project time (T) Z ? 40 weeks = -1. 26 Standard Normal distribution value = 0. 962 So, the probability that the R. C Coleman Project would complete 40 weeks or less is; Z = 0. 50 – 0. 3962 = 0. 1038 Page 12 ? 10. 38 % Figure 7: Standard Normal Distribution Curve with Target Weeks STANDARD NORMAL DISTRIBUTION CURVE AREAS When (T) = 40 z = (40 -43) / 2. 38 z = – 1. 26 ? = 2. 38 EXPECTED COM PLETION TIME 40 z = -1. 26 43 z=0 TIME (T) WEEKS With that result above, the top management of R. C Coleman is advised that the chances of completion of project on 40 weeks is doubtful and impossible to achieve as the percentage shows is very slim; approximate about 10 percent chances only.Hence, we recommend that the top management consider shortening activities time by adding more resources into it and by applying ‘crashing’ technique on the appropriate activities. PART 2 Considering that the project could complete with 80 per cent at 40th Week with a variance reference is maintained same as on part (I), Mr. Coleman need to find out on the possibility time to be shortened to achieve of 80 per cent chances of completion of project is within 40 weeks. In part one (1) of the analysis, we have found that the probability to complete the project within 40 weeks is only at 10 per cent.At this part, we need further analysis on the probability that the project will be meeting the 40-week completion time is at 80 per cent and a Normal Distribution Table with a mean of zero and a standard deviation of 1 is referred with the variance (z) is 2. 38; Based on the formula; Z = Page 13 Let say, P (T ? 40 weeks) = 0. 5 + Zn = 80% or 0. 8 0. 8 = 0. 5 + Zn Zn = 0. 8 – 0. 5 = 0. 3000 Using the new mean value or Zn = 0. 3000 and we will enter the table for normal distribution to find the closest value ‘z’. So, the closest value for Zn = 0. 300 is 0. 2995 where the closest normal probability distribution z at E (Tn) is equal to 0. 4. If the variance (z) is maintained at 2. 38, then in the project completion time is; Z = z = (T- E (Tn)) / 2. 38 = 0. 84 (T – E (Tn)) = 0. 84 x 2. 38 (40- E (Tn)) = 1. 9992 or 2. 0 E (Tn) = 40 – 2. 0 = 38 weeks. We have determine from the above calculation shows that the project completion time is shortened to 38 weeks in order to achieve the goal of an 80% chances in order to complete within 40 weeks. Fig ure 8 below showing the probability of the project to provide an 80 per cent probability chances of meeting 40-week of completion project time. Figure 8: Standard Normal Distribution Curve with Percentage Target Weeks.Page 14 STANDARD NORMAL DISTRIBUTION CURVE AREAS When (T) = 40 z = (40 -38) / 2. 38 z = 0. 84 ? = 2. 38 PLAN COMPLETION TIME @ 80% EXPECTED COMPLETION TIME 38 z=0 40 z = -1. 26 TIME (T) WEEKS 5. Conclusion Upon the completion on the calculation and analysis for both part; (1) and (2), Mr. R. C. Coleman; the appointed Project Manager on the upgrading the premises to automated warehouse system may advise to top management of the Company that on both part the result obtained on the requirement stipulated by the Management seems doubtful and is difficult to achieve.In order to pursue the objective goal, top management is advised to consider and approve to Mr. R. C. Coleman to exercise shortening activity times at part (1). This shortening in other words is known as ‘ crushing’ technique. Those activities time may require additional resources, either man power or financial in order to complete or meeting the percentage goal which has vision by the top management. Page 15 6. Reference An Introduction to Management Science; Quantitative Approaches to Decision Making. 13th Edition, Anderson, Sweeney, Williams & Martin. 7. Appendix R. C. COLEMAN PROJECT NETWORKPage 16 A Determine equipment need E Design new warehouse F Design warehouse I Install System G Design computer H Interface Computer J Train system operators START C Select vendor K Test system FINISH B Obtain vendor proposal D Order system TO FIND EXPECTED TIME (t); Time Activity Optimistic Most Probable a A B C D E F G H I J 4 6 2 8 7 4 4 4 4 3 m 6 8 4 10 10 6 6 6 6 4 b 8 16 6 24 13 8 20 8 14 5 Pessimistic Page 17 K 2 4 6 The incorporation of uncertainty activity with estimating time above is defined as; i. Optimistic time (a) = the minimum activity time if everything progresses ideall y. ii.Most Probable time (m) = the most probable activity time under normal condition. iii. Pessimistic time (b) = the maximum activity time if significant delays are encountered Expected time (t) can be finding with the formula; Expected Time (t) = (a+4m+b) / 6 1. For activity time A, the time average is; (t) = (a+4m+b) / 6 (t) = (4+6(4) +8) / 6 (t) = 6 2. For activity time B, the time average is; (t) = (a+4m+b) / 6 (t) = (6+8(4) +16) / 6 (t) = 9 3. For activity time C, the time average is; (t) = (a+4m+b) / 6 (t) = (2+4(4) +6) / 6 (t) = 4 4. For activity time D, the time average is; (t) = (a+4m+b) / 6 (t) = (8+10(4) +24) / 6 (t) = 12 5.For activity time E, the time average is ; (t) = (a+4m+b) / 6 (t) = (7+10(4) +13) / 6 (t) = 10 6. For activity time F, the time average is; (t) = (a+4m+b) / 6 (t) = (4+6(4) +8) / 6 (t) = 6 Page 18 7. For activity time G, the time average is; (t) = (a+4m+b) / 6 (t) = (4+6(4) +20) / 6 (t) = 8 8. For activity time H, the time average is; (t) = (a+4m+b) / 6 (t) = (4+6(4) +8) / 6 (t) = 6 9. For activity time I, the time average is; (t) = (a+4m+b) / 6 (t) = (4+6(4) +14) / 6 (t) = 7 10. For activity time J, the time average is; (t) = (a+4m+b) / 6 (t) = (3+4(4) +5) / 6 (t) = 4 11.For activity time K, the time average is; (t) = (a+4m+b) / 6 (t) = (2+4(4) +6) / 6 (t) = 4 With uncertainty time, we need to find the variance in order to describe the dispersion or variation in the activity time values. The variance of the activity time is given by the formula; ?2 = 2 1. The variance for activity A is; ? 2A = 2 = (8-4/6)2 = (2/3)2 = 0. 44 2. The variance for activity B is; Page 19 ?2B = 2 = (16-6/6)2 = (10/6)2 = 2. 78 3. The variance for activity C is; ? 2C = 2 = (6-2/6)2 = (2/3)2 = 0. 44 4. The variance for activity D is; ? 2D = 2 = (24-8/6)2 = (16/6)2 = 7. 11 5. The variance for activity E is; ? E = 2 = (13-7/6)2 = (6/6)2 = 1 6. The variance for activity F is; ? 2F = 2 = (8-4/6)2 = (2/3)2 = 0. 44 7. The variance for activity G is; ? 2G = ? 2H = 2 = (20-4/6)2 = (16/6)2 = 7. 11 = (8-4/6)2 = (2/3)2 = 0. 44 8. The variance for activity H is; 2 9. The variance for activity I is; ? 2I = 2 = (14-4/6)2 = (10/6)2 = 2. 78 10. The variance for activity J is; ? 2J = 2 = (5-3/6)2 = (1/3)2 = 0. 11 11. The variance for activity K is; ? 2K = 2 = (6-2/6)2 = (2/3)2 = 0. 44 Hence, the table below is the summary from the calculation of expected time and the variance of each activity; EXPECTED TIME AND VARIANCE FOR THE R.C. COLEMAN COMPANY PROJECT ACTIVITES Activity Expected time (week) A 6 0. 44 Variance Page 20 B C D E F G H I J K 9 4 12 10 6 8 6 7 4 4 2. 78 0. 44 7. 11 1 0. 44 7. 11 0. 44 2. 78 0. 11 0. 44 Activity Expected Time 6 9 4 12 10 6 8 6 7 4 4 Variance Earliest Start (ES) 0 0 9 13 13 23 13 29 29 35 39 Latest Start (LS) 3 0 9 17 13 23 21 29 32 35 39 Earliest Finish (EF) 6 9 13 25 23 29 21 35 36 39 43 Latest Finish (LF) 9 9 13 29 23 29 29 35 39 39 43 Slack LS – ES 3 0 0 4 0 0 8 0 3 0 0 Critical path A B C D E F G H I J K 0. 44 2. 78 0. 44 7. 11 1 0. 44 7. 11 0. 44 2. 78 0. 11 0. 44YES YES YES YES YES YES YES From the table above we could note that the activity schedule for the warehouse expansion project which shows zero slack is the critical path for the project; B – C – E – F – H – J – K. From the critical path shown, the expected time of the project is E (t) = tB + tC + tE + tF + tH + tJ + tK = 9 + 4 + 10 + 6 + 6 + 4 + 4 = 43 WEEKS Page 21 Project network flow and completion time E 13 23 10 13 23 A 6 0 3 6 9 C 4 B 9 0 0 9 9 9 9 13 13 G 8 13 21 21 29 F 6 23 23 29 29 START H 6 29 29 35 35 I 7 29 36 32 39 K 4 39 39 43 43 FINISH (43 WEEKS) D 13 25 12 17 29 J 4 35 39 35 39Hence, the variance in the project completion time is the sum of the variance on the critical path activities, which is ?2 = ? B + ? C + ? E + ? F + ? H + ? J + ? K = 2. 78 + 0. 44 + 1. 0 + 0. 44 + 0. 44 + 0. 11 + 0. 44 = 5. 65 ? = = 2. 38 Z = = Since the management allotted 40 week to comple te the project, the probability distribution Z = = -1. 26 Page 22 Using the table for standard distribution had shown that the value area of 1. 26 is 0. 3962. So the probability of the project will be complete at 40 weeks is P (40 weeks) = 0. 5 -0. 3962 = 0. 1038 ? 10. 38 % Standard Normal Distribution CurveSTANDARD NORMAL DISTRIBUTION CURVE AREAS ? = 2. 38 EXPECTED COMPLETION TIME (T) 43 TIME (T) WEEKS Standard Normal Distribution Curve with Target Weeks Page 23 STANDARD NORMAL DISTRIBUTION CURVE AREAS When (T) = 40 z = (40 -43) / 2. 38 z = – 1. 26 ? = 2. 38 EXPECTED COMPLETION TIME 40 z = -1. 26 43 z=0 TIME (T) WEEKS Standard Normal Distribution Curve with Percentage Target Weeks. STANDARD NORMAL DISTRIBUTION CURVE AREAS When (T) = 40 z = (40 -38) / 2. 38 z = 0. 84 ? = 2. 38 PLAN COMPLETION TIME @ 80% EXPECTED COMPLETION TIME 38 z=0 40 z = -1. 26 TIME (T) WEEKS END OF REPORT Page 24

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