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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.

##### Solution Summary

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

##### 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 ...

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