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    Explanation of PERT-CPM, Decision Analysis, and EOQ

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    1. PERT & CPM

    Widgetco is about to introduce a new product. One unit of this product is produced by assembling subassembly 1 and subassembly 2. Before production begins on either subassembly, raw materials must be purchased and workers must be trained. Before the subassemblies can be assembled into the final product, the finished subassembly 2 must be inspected. A list of activities, their predecessors, and their durations is given in the following Table.

    Activity Predecessors Duration(days)
    A - Train workers --------- 6
    B - Purchase raw materials --------- 9
    C - Make subassembly 1 A,B 8
    D - Make subassembly 2 A,B 7
    E - Inspect subassembly 2 D 10
    F - Assemble Subassemblies C,E 12

    Problem:

    1. Draw a project diagram (network) for this project?
    2. What is the total project time?
    3. What is the critical path?

    2. DECISION ANALYSIS

    Visual Tech is considering marketing one of two new video games for the coming holiday season: Battle Pacific or Space Pirates. Battle Pacific is a unique game and appears to have no competition. Estimated profits (in thousands of dollars) under high, medium, and low demand as follows:

    Demand
    Battle Pacific High Medium Low
    Profit $1000 $700 $300
    Probability .2 .5 .3
    Visual Tech is optimistic about its Space Pirates game. However, the concern is that profitability will be affected by competitors' introduction of a video game viewed as similar to Space Pirates. Estimated profits (in thousands of dollars) with and without competition is as follows:

    Demand
    Space Pirates
    With Competition High Medium Low
    Profit $800 $400 $200
    Probability 0.3 0.4 0.3

    Demand
    Space Pirates
    Without Competition High Medium Low
    Profit $1600 $800 $400
    Probability 0.5 0.3 0.2

    Problem:

    1. Develop a decision for Visual Tech problem?
    2. If Visual Tech believes that its competitor will launch the similar Space Pirates with probability 0.6. The director of planning recommends marketing the Battle Pacific video game. Using the expected value, what is your recommend decision?
    3. Show the risk profile for your recommend decision?

    3. FORECASTING

    Blue Grass Computer is the Company that sells CPU chip. The following data show sales for the past seven years by quarters. The group's manager wants an accurate method for forecasting future sales.

    Year Quarter 1 Quarter 2 Quarter 3 Quarter 4 Total Sales
    1 6 15 10 4 35
    2 10 18 15 7 50
    3 14 26 23 12 75
    4 19 28 25 18 90
    5 22 34 28 21 105
    6 24 36 30 20 110
    7 28 40 35 27 130

    Problem:

    (a) Show the 4 quarter moving average values for this time series. Plot both the original time series and the moving averages on the same graph (use Excel Spread Sheet).
    (b) Compute the seasonal indexes for the four quarters.
    (c) When the Blue Grass Computer experience the largest seasonal effect? Does this result seem reasonable? Explain.

    4. ECONOMIC QUANTITY ORDER

    Washington Metro Bus Inc. operates a fleet of 400 buses. The fleet includes buses used for public transit as well as school buses. Buses used in public transit average close to 400 miles per day, seven days a week. School buses also amass considerable mileage, though not nearly as much as public transit bus. Metro Bus is interested in setting up inventory policy for bus tires that minimizes the sum of annual ordering and carrying cost. All buses use the same type of tires and the annual requirement of tires are 5000. Ordering cost per order is $125, and the cost for carrying a tire annually in inventory is $20. For practically purposes, the lead time is zero, as the supplier agrees they will deliver on the day the order is placed. Note that the basic unit of measurement for a period is one year in this case.

    Problem:

    1. What is the Economic Order Quantity (EOQ)?
    2. Compute the optimal number of orders each year?
    3. What is the length of the inventory cycle ?

    5. LINEAR PROGRAMMING

    1The production manager for the Bonka Toy Manufacturing Company is scheduling hourly production levels for three of its more popular dump trucks: Bonka Junior, Mighty Bonka, and Super Bonka. Each truck is processed through three departments: Fabrication, Assembly, Packaging. The following Table A-1 indicates the time to required to process one unit in each department (in minutes per unit) the total production time available during each hour of operation and profit margin for each product.
    Management has specified minimum hourly production levels for Bonka Junior and Mighty Bonka trucks of 200 and 250 units respectively, Also no more than 225 units of the Super Bonka truck should be produced each hour.
    The production manager wishes to determine the number of trucks to schedule each hour so as to maximize total contribution to profit while:
    Using no more time in each department than available each hour.
    Satisfying minimum production levels for Bonka Junior and Mighty Bonka
    Producing no more than the maximum specified for Super Bonka

    TABLE A-1 Product Mix Data
    Processing / Time (minutes/Unit) Available Production Time (Minutes/Hour of operation)
    Department Bonka
    Junior Mighty
    Bonka Super
    Bonka
    Fabrication 1.00 1.20 1.25 1200
    Assembly 1.30 1.50 1.60 1500
    Packaging 0.80 0.75 0.90 950

    Profit/Unit $0.55 $0.70 $0.75

    Problem:
    1. Write down Mathematical Model.
    2. Use geometric method to find the optimal solution.
    3. Run data in Excel to do sensitive analysis.

    © BrainMass Inc. brainmass.com October 10, 2019, 2:37 am ad1c9bdddf
    https://brainmass.com/business/accounting/explanation-pert-cpm-decision-analysis-eoq-385662

    Attachments

    Solution Preview

    PERT & CPM

    Problem:
    a. Draw a project diagram (network) for this project?
    b. What is the total project time?
    c. What is the critical path?

    Note: I made a detailed analysis and computation for this. I have attached the answer with a filename PERT-CPM.docx

    DECISION ANALYSIS

    Visual Tech is considering marketing one of two new video games for the coming holiday season: Battle Pacific or Space Pirates.

    Note: The answer is attached with a filename of decision analysis.doc

    ECONOMIC ORDER QUANTITY PROBLEM (EOQ)

    Solutions:

    1. EOQ

    EOQ formula= Sqrt ...

    Solution Summary

    This solution gives detailed and step-by-step explanation of PERT-CPM, Decision Analysis, and Economic Order Quantity.

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