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MM305 UNIT 9 Project: Project Analysis and Forecasting: Application of Decision Models, Statistical Methods, and Optimization Techniques

Application of decision models and statistical methods in project forecasting.

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    MM305 UNIT 9 PROJECT 1 MM305 UNIT 9 Project : Project Analysis and Forecasting: Application of Decision Models, Statistical Methods, and Optimization Techniques Name: Directions: • In this project you will be using the States Data file that is found in Doc Sharing under the Instructor - Graded Projects: • Steps for accessing the States Data file: 1. Open your Excel with PhStat2 2. Click File — Open 3. Select the States Data file • Not all questions require the use of technology or the States Date file. • You may insert your answers, including any charts, graphs, or output, on this document. • Be sure to put your name on this document and save it to your computer. 1 . Allen Machines specializes in developing weed - harvesting equipment that is used to clear small lakes of weeds. Allen Machines is contemplating the construction of a machine that would harvest weeds on narrow rivers and waterways. The activities and time in weeks necessary to build one of these experimental machines are shown in the table below. Activity Immediate Predecessors Time in Weeks A none 6 B none 5 C A 3 D A 2 E B 4 F B 6 G C,E 10 H D,F 7 1. What is the minimum possible time required for completing the project? 19 weeks. This is the minimum time needed for completing the longest path in project - ACG or BEG, i.e. 6+3+10 or 5+4+10 . Kindly refer to the chart included here:

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    MM305 UNIT 9 PROJECT 2 2. What is the latest possible time that Activity D may be started without delaying the completion of the project? 10 weeks ; Since D is a predecessor for the activity H which takes a 7 weeks and since D takes 2 weeks. If D starts at the most after 10 weeks, then it will be completed after 12 weeks after which F will start lasting for 7 weeks and will be completed after 19 weeks which will e nsure that the project is still completed within the minimum duration 3. What is the latest finish time for Activity F ? 12 weeks; Since F is the predecessor for H which takes 7 weeks, F can finish at the most by 19 - 7=12 weeks. This will ensure the project completes within the minimum duration 4. What is /are the critical path (s) ? A - C - G and B - E - G are the paths that take the maximum amount of time, these are the critical paths.

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    MM305 UNIT 9 PROJECT 3 2 . The following is the activity and associated costs for the renovation of the local high school football stadium. The times are in weeks. Activity Immediate Predecessor Time Cost ($) A - 4 25 , 000 B - 5 30 , 000 C A 3 15 , 000 D B 8 50 , 000 E B 2 12 , 000 F C, D 3 15 , 000 G C, D 7 46 , 000 H E, F 2 20 , 000 1. What is the critical path for this project? B - D - G , since this path is the one which takes the maximum amount of time and hence determines the fate of the project. Kindly refer to the figure below. 2. How much of the total budget would be spent in Week 8 (Period 8) with the earliest start budget? In the 8 th week, only the activities D and E can run. The activities F,G, and H need predecessors which are yet to complete during the 8 th week. The activity E has a budget of 12,000$ and is spread over 2 weeks. Thus the budget spent during the 8 th week would be 12,000$/2=6,000$. Similarly, the activity D has a budget of 50,000$ and is spread over 8 weeks. Thus the budget spent during the 8 th week would be 50,000$/8= 6,250$. Thus the budget spent during 8 th week is 6,000$ + 6,250 $ =12,250 $. 3 . Precision Manufacturing has a government contract to produce stainless steel rods for use in military aircraft. Each rod is required to be 20 millimeters in diameter. Each hour, random samples of size n = 4 rods are measured to check process control. Five hours of observations yielded the following:

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    MM305 UNIT 9 PROJECT 4 Diameter Time Rod 1 Rod 2 Rod 3 Rod 4 9 A.M. 19.8 20.4 19.9 20.3 10 A.M. 20.1 20.2 19.9 19.8 11 A.M. 19.9 20.5 20.3 20.1 Noon 19.7 19.8 20.3 20.2 1 P.M. 19.7 20.1 19.9 19.9 1. Construct the xbar - chart and the R - chart . Time Rod 1 Rod 2 Rod 3 Rod 4 Sample Means Sample Range 9:00 AM 19.8 20.4 19.9 20.3 20.1 0.6 10:00 AM 20.1 20.2 19.9 19.8 20 0.4 11:00 AM 19.9 20.5 20.3 20.1 20.2 0.6 Noon 19.7 19.8 20.3 20.2 20 0.6 1:00 PM 19.7 20.1 19.9 19.9 19.9 0.4 Control chart formula: X - bar n is the number of observations k is the number of subgroups Upper control limit: Lower control limit: Range k is the number of subgroups. Upper control limit: Lower control limit:

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