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C RITICAL P ATH A NALYSIS : C OOKING B OLOGNESE

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T ASK When you leave home, you will need to start being able to cook your own meals. You would like to cook a spaghetti bolognese for tea tonight but your friends would also like to go to the cinema with you. It is your task to find out the quickest time it takes to cook spaghetti bolognese, so that you can tell your friends what the earliest film showing you can go and see is.

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U SEFUL I NFORMATION You start cooking at exactly 7pm. The possible film times available are: 7.30pm, 7.45pm, 8.00pm, 8.15pm, 9.00pm or 9.30pm It will take you a total of 1 hour to eat your tea and wash up after. It will take you 15 minutes to walk to the cinema.

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Y OUR T ASKS You have managed to find a very simple recipe online outlining the different tasks you need to complete to cook your spaghetti bolognese. Here are the tasks and their durations: Tasks Duration (minutes) A - Boil water5 B - Add pasta to water and cook10 C - Chop up onion, carrot and bacon7 D - Cook minced/quorn meat30 E - Add onion, carrot, bacon and tomato puree to minced/quorn meat and stir3 F - Drain pasta2 G - Mix Bolognese and pasta together and serve2

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P RECEDENCE T ABLE Your precedence chart should like this: ActivityDepends on A - Boil water - B - Add pasta to water and cook A C - Chop up onion, carrot and bacon - D - Cook minced/quorn meat - E - Add onion, carrot, bacon and tomato puree to minced/quorn meat and stir C,D F - Drain pasta B G - Mix Bolognese and pasta together and serve E,F

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A CTIVITY N ETWORK Using this precedence chart, it is possible to create an activity network for the information. A(5) C(7) D(30) B(10) E(3) F(2) G(2) Earliest Start Time (EST) Latest Finish Time (LFT) Task/Activity and Duration (minutes) Dummy Activity

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C RITICAL P ATH A NALYSIS Critical Path Analysis and their derivatives had acquired a high reputation following their use in American defence programme management and procurement. In Britain, Concorde was one of the first projects which these techniques were used. Quote from Government and British civil aerospace by Keith Hayward Critical Path Analysis was used to build the Leven viaduct on the Cumbrian Coast: a vital rail link between the north and south. Case study : http://businesscasestudies.co.uk/network- rail/critical-path-analysis-at-network- rail/introduction.html#axzz2XmaJo6nu http://businesscasestudies.co.uk/network- rail/critical-path-analysis-at-network- rail/introduction.html#axzz2XmaJo6nu

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W ORKING O UT THE E ARLIEST S TART T IME (EST) For EST, we start from the start node and end at the end node (i.e. we work forwards ). EST = Earliest Start Time of the previous activity + Duration of the previous activity If there are two or more previous activities, choose the highest EST. E.g. A(4) B(2) C(5) 0 4 6 9 12 D(6) E(1) The EST of the start node is always 0 0 + 4 = 4 4 + 2 = 6 4 + 5 = 9 6 + 6 = 12 9 + 1 = 10 12 is therefore the highest EST so choose 12

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W ORKING O UT THE L ATEST F INISH T IME (LFT) For LFT we start from the end node and end at the start node (i.e. we work backwards ). LFT = Latest Finish Time at the end of the following activity – Duration of the following activity If there are two or more activities which follow on from the same node, choose the smallest LFT. E.g. (using the previous example) A(4) B(2) C(5) 0 4 6 9 12 D(6) E(1) 0 12 6 11 4 The LFT of the start node is always 0 The LFT of the end node is always equal to its Earliest Start Time 12 – 1 = 11 12 – 6 = 6 6 – 2 = 4 11 – 5 = 6 4 is therefore the smallest LFT so choose 4 This is the shortest time the project can be completed in.

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W HO W ANTS T O B E A M ILLIONAIRE ?

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1. What is the formula to work out the Earliest Start Time (EST)? A. EST = Earliest start time of the following activity – Earliest start time of the previous activity B. EST = Earliest start time of the previous activity + Duration of the previous activity C. EST = Latest finish time of the previous activity + Duration of the previous activity

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£250,000!

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2. What is the formula to work out the Latest Finish Time (LFT)? A. LFT = Duration of the previous activity – Latest finish time of the following activity B. LFT = Earliest start time of the following activity + Duration of the following activity C. LFT = Latest finish time of the following activity – Duration of the following activity

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£500,000!

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3. When we calculate the Earliest Start Time (EST), which node do we start from? A. The first (i.e. the start node) B. The last (i.e. the end node) C. A random node

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£750,000!

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4. How do we work out the value of the Latest Finish Time (LFT) of the end node? A. We guess a number B. It is always equal to its Earliest Start Time (EST) C. We add one to its Earliest Start Time (EST)

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Congratulations! You have won £1,000,000!!!

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Sorry, thats the wrong answer. Better luck next time though!

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Y OUR T URN ! Using your knowledge of Earliest Start Times and Latest Finish Times, use the activity network for cooking your spaghetti bolognese to calculate the quickest possible time that it takes to cook this dish. Using this information, conclude which film showing you should see with your friends. Recall: You start cooking at exactly 7pm. The possible film times available are: 7.30pm, 7.45pm, 8.00pm, 8.15pm, 9.00pm or 9.30pm It will take you a total of 1 hour to eat your tea and wash up after. It will take you 15 minutes to walk to the cinema

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Y OUR A NSWER Your completed activity network should look like the following: A(5) C(7) D(30) B(10) E(3) F(2) G(2) 0 0 5 7 30 15 33 35 33 30 31 21 30 We can see here that the critical time to complete the project is 35 minutes. If we then add 60 minutes (i.e. the time it takes to eat the meal and wash up afterwards, plus 15 minutes walking time to the cinema, we get a total of 110 minutes. Starting at 7pm, this means that one could get to the cinema for 8.50pm. The earliest possible film showing which one could see would therefore be at 9.00pm.

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E VALUATION 1) What is good about Critical Path Analysis? 2) What is a disadvantage of Critical Path Analysis? 3) What have you found interesting about todays lesson? 4) Do you think you will use Critical Path Analysis again? If yes, how? If no, why not?

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