NETWORK ANALYSIS QUESTION BANK

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1 NETWORK ANALYSIS QUESTION BANK 1. Explain the terms : Total elapsed time, idle time. 2. What do you mean by dummy activity and successor activity. 3. Write four advantages of network analysis. 4. Explain the following concepts (i) Dummy Activity (ii) Successor Activity (iii) Predecessor Activity. 5. Explain the applications of PERT. 6. Differentiate CPM and PERT. 7. Write down the advantages and disadvantages of CPM. 8. Write down the advantages and disadvantages of PERT. 9. Write a short note on CPM. 10. Write an algorithm of PERT. 11. Distinguish Events and Activities. 12. Explain the following terms corresponding to CPM/PERT (i) Earliest time (ii) Latest time (iii) total activity time (iv) Event Slack (v) Critical path 13. What is float? What are the different types of floats? 14. Discuss in brief free float and total float and explain their uses in network. 15. Explain in brief, Activity and Event of a Network Project. 16. State rules of network construction. 17. Briefly mention the areas of application of network techniques. 18. Define Optimistic time, Pessimistic time and most likely time for PERT. 19. Explain reasons for incorporating dummy activities in a network diagram. In what way do these differs from the normal activities?

2 Network Diagram 1. Draw network diagrams from the following list of activities: Activity Predecessor Activity Set 1 Set 2 Set 3 A B C D A A A E B A, B A, B F B, C A, B, C B, C G D, E, F D, E, F C H E, F F D, E, F 2. Following is the list of activities associated with the assembly of a space module for an upcoming mission. Draw the network diagram for the project. Activity Description Predecessor Act. A Construct shell of module --- B Order life support system and scientific experiment. --- C Order components of control and navigation system --- D Wire module A E Assemble control and navigational system C F Preliminary test of life support system B G Install life support system in module D, F H Install scientific experimentation package in module D, F I Preliminary test of control and navigational system E, F J Install control and navigational system in module H, I K Final testing and debugging G, J 3. A new type of water pump is to be designed for an automobile. Major specifications are given in the table. Draw the network diagram for the project. Activity Description Predecessor Act. A Drawing prepared and approved --- B Cost analysis A C Tool feasibility A D Tool manufactured C E Favorable cost B, C F Raw materials procured D, E G Sub assemblies ordered E H Sub assemblies received G I Parts manufactured D, F J Final assembly I, H K Testing and shipment K

3 4. Listed in the table are the activities and sequencing required in the computerization of a bank branch. Activity Description Predecessor Act. A Preparation/ Deliberations in the department --- B Dialogue with the union A C Discussion/Approval/Sanction of local management. A D Customer education B E Preparing specifications for the system C F Selection of staff B G Order/ Acquisition of system D, E H Alternations in the branch premises C I Training of staff F J Wiring/Power-supply set-up of the branch H K Transition G,,I, J L Parallel run K Draw the arrow diagram of activities of the above project. 5. The medical faculty of a university is considering holding a faculty development programmed. It has planned the following activities. Prepare a network diagram showing the inter-relationships of the various activities. Activity Description Predecessor Act. A Design conference meetings and theme --- B Design front cover of the conference proceedings A C Prepare brochure and send request for papers A D Compile list of distinguished speakers/guests A E Finalize brochure and print it C, D F Make travel arrangements for distinguished D G Dispatch brochures E H Receive papers for conference G I Edit papers and assemble proceedings F, H J Print proceedings B, I 6. A project schedule has the following characteristics: Activity Time Activity Time Construct a network diagram.

4 7. Develop a network based on the following information: Activity Immediate Predecessors A --- B --- C A D B E C, D F D G E H F 8. Draw an arrow diagram showing the following relationships: Activity Predecessor Activity Predecessors A None H D, E, F B None I D C None J G D A K G E B, C L H, J F A M K G C N I, L 9. Adjoining is a list and description of activities for a project XYZ building a boat. Draw the network: Activity Description Predecessor Act. A Design hull None B Prepare boot shed None C Design Mmst and mast mount A D Obtain hull A E Design sails A F Obtain mast mount C G Obtain mast C H Design rigging C J Prepare hull B, D K Fit mast mount to hull F, J L Step Mast E, H, G, K M Obtain Sails and Rigging E, H N Fit sails and rigging L, M

5 10. The activities involved in the computer installation process are detailed below. You are required to draw the network: Activity Description Predecessor Act. A Physical preparation None B Organizational planning None C Personnel selection B D Equipment installation A E Personnel training C F Detailed systems design C G File conversion F H Establish standards and controls F I Programmed preparation H J Programmed testing I K Parallel operations D, E, G, J L Finalize system documentation I M Follow up K, L 11. Draw an arrow diagram showing the adjoining relationship: Activity Predecessor Activity Predecessors A --- A None B --- B A C A C A D A D B, C E B E C F C F D G D, E G E H F, G 12. An assembly is to be made from two parts X and Y. Both parts must be turned on a lathe and Y must be polished whereas X need not be polished. The sequence of activities together with their predecessors is given below. Activity Description Predecessor Act. A Open work order --- B Get material for X A C Get material for Y A D Turn X on lathe B E Turn Y on lathe B,C F Polish Y E G Assemble X and Y D,F H Pack G Draw a network diagram for the project.

6 13. Listed in the table are the activities and sequencing necessary for a maintenance job on the heat exchangers in a refinery. Activity Description Predecessor Act. A Dismantle pipe connections --- B Dismantle heater, closure and floating front A C Remove tube bundle B D Clean bolts B E Clean heater and floating head front B F Clean tube bundle C G Clean shell C H Replace tube bundle F,G I Prepare shell pressure test D,E,H J Prepare tube pressure test and reassemble I Draw a network diagram for the project. 14. Listed in the table are the activities and sequencing necessary for the completion of a recruitment procedure for management trainees (MT) in a firm. Activity Predecessor Act. A --- B A C A D C E B F C G D,E H G I H J F K I,J L K M L N J O M,N

7 15. Activities and their description associated with the Haryali Watershed Project are listed below: Activity Predecessor Activity A ---- B A C B D C E C F C G D,E,F H G I G J H K H L I,J M I,J N I,J O I, J P M Q L, P R K S R 16. The following table gives the activities for buying a new car. Construct the project network. Activity Description Predecessor(s) A Conduct feasibility study B Find potential buyer for present car A C List possible models A D Research all possible models C E Conduct interview with mechanic C F Collect dealer propaganda C G Compile pertinent data D,E,F H Choose top three models G I Test drive all three choices H J Gather warranty and financing data H K Choose one car I,J L Choose dealer K M Search for desired color and options L N Test-drive chosen model once again L O Purchase new car B,M,N

8 CRITICAL PATH METHOD 1. A small assembly plant assembles PCs through 9 interlinked stages according to adjoining precedence/process: (i) (ii) (iii) (iv) Stage Duration From To (hours) Draw an arrow diagram representing above assembly work. Tabulate earliest start, earliest finish, latest start and latest finish time for all the stages. Find the critical path and the assembly duration. Tabulate total float, free float and independent float. 2. For a small project of 12 activities, the details are given below. Draw the network and find earliest occurrence time, latest occurrence time, critical activities and project completion time: Activity A B C D E F G H I J K L Dependence B, A C E E D,F,H E IJ G Duration(days) A small project consists of seven activities for which the relevant data are given below: Activity Preceding activities Activity duration(days) A B C D A, B 5 E A, C 7 F C, D, E 6 G C, D, E 5 Find the critical path and minimum time duration.

9 4. A small maintenance project consists of the following twelve jobs whose precedence relations are identified with their node numbers: Job (I, j) (1, 2) (1, 3) (1, 4) (2, 3) (2, 5) (2, 6) Duration(in Job (I, j) (3, 7) (4, 5) (5, 6) (6, 7) (6, 8) (7, 8) Duration(in (i) Draw an arrow diagram representing the project. (ii) Calculate earliest start, earliest finish, latest start and latest finish time for all the jobs. (iii) Find the critical path and project duration. (iv) Tabulate total float, free float and independent float. 5. Draw network diagram from following activities and find critical path and total slack of activities: Job A B C D E F G H I J K Time(Days) Predecessor --- A B C B E D,F E H G, I J 6. The activities involved in Alpha Garment Manufacturing Company are listed with their time estimates as in the following table. Activity Description Immediate Duration Predecessors(s) (days) A Forecast sales volume B Study competitive market C Design item and facilities A 5 D Prepare production plan C 3 E Estimate cost of production D 2 F Set sales price B,E 1 G Prepare Budget F 14 Draw the network for the given activities and carry out the critical path calculations. 7. Listed in the table are the activities and sequencing requirements necessary for the Completion of a research report. Activity Description Precedence Duration(weeks) A Literature search B Formulation of hypothesis C Preliminary feasibility study B 2 D Formal proposal C 2 E Field analysis A, D 2 F Progress report D 1 G Formal research A, D 6 H Data collection E 5 I Data analysis G, H 6

10 J Conclusions I 2 K Rough draft G 4 L Final copy J, K 3 M Preparation of oral presentation L 1 (a) Draw a network diagram for this project. (b) Find the critical path. What is its length? (c) Find the total float and the free float for each non critical activity. 8. An architect has been awarded a contract to prepare plans for an urban renewal project. The job consists of the following activities and their estimated times: Activity Description Predecessors Time(days) A Prepare preliminary sketches B Outline specifications C Prepare drawings A 3 D Write specifications A, B 2 E Run off prints C, D 1 F Have specifications B, D 3 G Assemble bid packages E, F 1 (i) Draw an arrow diagram for this project. (ii) Indicate the critical path, and calculate the total float and free float for each activity. 9. The NRB Company is planning to design, develop and market a new racing cycle. The project is composed of the following activities: Activity Description Precedence Duration(weeks) A Design frame None 4 B Design wheels None 3 C Design gears None 3 D Design handlebars C 2 E Test steering A, B, D 1 F Test gears A, B, D 2 G Performance test E, F 3 H Manufacturing layout A, B, D 3 I Manufacturing demonstrators H 5 J Prepare advertising G 2 K Prepare user s manuals G 4 L Distribute to dealers I, J, K 2 Construct the network, determine the critical path and the duration of the above project.

11 10. An air conditioning installation has been broken down into the following activities and restrictions: Activity Description Time(days) Restrictions A Order and deliver packaged air cond. unit 14 A < H, K B Order deliver piping 4 B < I C Order and deliver grilles, dampers, louvers 11 C < F D Order and deliver dust 8 D < F E Determine layout of dust 3 E < D,G F Install dust work, dampers and louvers 18 F < G G Install grills 1 G < M H Install air conditioning unit 1 H < L,J I Rough in piping 10 I < J J Connect piping to unit 1 J < M K Electronic wiring mainline, and thermostat 4 K < L L Controls and final wiring 2 L < M M Testing 2 M < N N Installation and clean up 4 Draw network and analyze it for the critical path and activity floats. 12. The details of a project involving 14 activities Activity Immediate Predecessor(s) Duration (months) A B C D B 3 E A 6 F A 8 G B 3 H C,D 7 I C,D 2 J E 5 K F,G,H 4 L F,G,H 3 M I 13 N J,K 7 (a) Construct the CPM network. (b) Determine the critical path and project completion time. (c) Compute total floats and free floats for non-critical activities.

12 13. An established company has decided to add a new product to its line. It will buy the product from a manufacturing concern, package it and sell it to a number of distributors selected on a geographical basis. Market research has indicated the volume expected and the size of sales force required. The steps shown in the following table are to be planned. Activity Description Predecessors Duration(days) A Organizes sales office B Hire salesmen A 4 C Train salesmen B 7 D Select advertising agency A 2 E Plan advertising campaign D 4 F Conduct advertising campaign E 10 G Design package H Set-up packaging facilities G 10 I Package initial stocks J,H 6 J Order stock from manufacturer K Select distributors A 9 L Sell to distributors C,K 3 M Ship stocks to distributors I,L 5 (A) Draw an arrow diagram for this project (B) Indicate the critical path. (C) For each non-critical activity, find the total and free float. 14. Activity Description(weeks) Immediate Predecessors A B 4 A C 2 B D 1 C E 2 A F 3 E G 2 E H 4 E I 3 H,L J 12 K K 4 D,F,G L 2 J M 2 H,L

13 (A) Draw an arrow diagram for this project. (B) Indicate the critical path and also find total float and free float for non-critical activities. 14. A project has the following characteristics: Activity Preceding Duration activity (in weeks) A None 5 B A 2 C A 6 D B 12 E D 10 F D 9 G D 5 H B 9 I C,E 1 J G 2 K F,I,J 3 L K 9 M H,G 7 N M 8 (A) Draw the network for this project. (B) Find the critical path and total project duration. 15. XYZ Ltd. Planning a project to introduce a new product, has listed the following necessary activities: Activity Preceding activity Expected time(weeks) A B C A 5 D A 4 E A 3 F C 3 G D 5 H B,D,E 5 I H 2 J I,G,F 3 Draw the critical path network for the project and determine the critical path and its duration.

14 16. The details of an activity of a project is given below: Activity Immediate predecessor Duration A B C A 20 D B 12 E B 11 F C 5 G C,D,E 4 H E 30 I G 8 J G 10 K F,I 7 L H,J,K 6 M H,J,K 4 N L 10 P M,N 3 PROGRAM EVALUATION AND REVIEW TECHNIQUE (PERT) 1. A project is represented by the network shown below and has the following data: Task A B C D E F G H I Optimistic time Pessimistic time Most likely time Determine the following: (i) Expected task times and their variance. (ii) The earliest and latest expected times to reach each event. (iii) The critical path. (iv) The probability of an event occurring at the proposed completion date if the original contract time of completing the project is 27 days. 2. The following information is given: Activity (1 2) (2 3) (2 4) (3 5) (4 6) (5 6) (5 7) (6 7) Pessimistic time (in weeks) Most likely time (in weeks) Optimistic time (in weeks) Draw the network diagram for the above. Calculate: (i) Variance to each activity.

15 (ii) (iii) Critical path and expected project length. The probability that the project will be completed in 23 weeks. 3. A construction company is preparing a PERT network for laying the foundation of a new art Museum. Given the following set of activities, their predecessor requirements and three time estimates of completion time: (i) (ii) (iii) Activity Predecessors Time estimates (weeks) Optimistic Pessimistic Most likely A None B None C A D B E C F C G C, D H F, G I E J I K H Draw the PERT network. Compute the slack for each activity and determine the critical path. The contract specifies a Rs. 5,000 per week penalty for each week the completion of the project extends beyond 37 weeks. What is the probability that this company will have to pay a maximum penalty of Rs. 15,000? 4. A project consists of eight activities with the following relevant information: (i) (ii) Activity Predecessors Estimated duration(days) Optimistic Most likely Pessimistic A B C D A E B F C G D, E H F, G Draw the PERT network and find out the expected project completion time. What duration will have 95% confidence for project completion? 5. A project consists of activities A, B, C, D,, H, I. The notation X < Y means that the activity X must be completed before Y can start and X, Y < W means that W will start only after completion of the activities X and Y. With this notation: (i) Construct the network diagram for the following constraints:

16 A < D; A < E; B < F; C < G; D < H; E, F < I. The project has the following time schedules of the above activities. Task A B C D E F G H I Optimistic time Pessimistic time Most likely time Determine the following: (i) Expected task times and their variance. (ii) The earliest and latest expected times to reach each event. (iii) The critical path. (iv) The probability of an event occurring at the proposed completion date if the original contract time of completing the project is 41.5 weeks. 6. Consider the following table summarizing the details of a project: Activity Predecessor(s) Duration(weeks) To tm tp A B C D A E A F A G B, C H C I D J E, G K F, H L F, H M I, J, K N L Construct the project network. Find the expected duration and variance of each activity. Find the critical path and the expected project completion time. What is the probability of completing the project on or before 35 weeks?

Project Planning. Identifying the Work to Be Done. Gantt Chart. A Gantt Chart. Given: Activity Sequencing Network Diagrams

Project Planning. Identifying the Work to Be Done. Gantt Chart. A Gantt Chart. Given: Activity Sequencing Network Diagrams Project Planning Identifying the Work to Be Done Activity Sequencing Network Diagrams Given: Statement of work written description of goals work & time frame of project Work Breakdown Structure Be able