# Project management; problems,formulas and calculations

Project management; problems,formulas and calculations

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All formulas and calculations must be shown

Problem 1.
Arsenal Electronics is going to construct a new \$1.2 billion semiconductor plant and has selected four towns in the Midwest as potential sites. The important location factors and ratings for each town are as follows:
Scores (0 to 100)
Location Factor Weight Abbeton Bayside Cane Creek Dunnville
Work ethics 0.18 80 90 70 75
Quality of life 0.16 75 85 95 90
Labor laws/unionization 0.12 90 60 60 70
Infrastructure 0.10 60 50 60 70
Education 0.08 80 90 85 95
Labor skill and education 0.07 75 65 70 80
Cost of living 0.06 70 80 85 75
Taxes 0.05 65 70 55 60
Incentive package 0.05 90 95 70 80
Government regulations 0.03 40 50 65 55
Environmental regulations 0.03 65 60 70 80
Transportation 0.03 90 80 95 80
Space for expansion 0.02 90 95 90 90
Urban proximity 0.02 60 90 70 80

Recommend a site based on these location factors and ratings.

Problem 2.
Sawyer Furniture is one of the few remaining domestic manufacturers of wood furniture. In the current competitive environment, cost containment is the key to its continued survival. Demand for furniture follows a seasonal demand pattern with increased sales in the summer and fall months, culminating with peak demand in November.
The cost of production is \$16 per unit for regular production, \$24 for overtime, and \$33 for subcontracting. Hiring and firing costs are \$500 per worker. Inventory holding costs are \$20 per unit per month. There is no beginning inventory. Ten workers are currently employed. Each worker can produce 50 pieces of furniture per month. Overtime cannot exceed regular production. Given the following demand data, use Excel Solver to design an aggregate production plan for Sawyer Furniture that will meet demand at the lowest possible cost.
Input: Beg. Wkrs 10 Regular \$16 Hiring \$500
Units/wkr 50 Overtime \$24 Firing \$500
Beg. Inv. 0 Subk \$33 Inventory \$20
Month Demand Reg OT Subk Inv #Wkrs #Hired #Fired
Jan 500 500 0 0 0 10 0 0
Feb 500 500 0 0 0 10 0 0
Mar 1000 1,000 0 0 0 20 10 0
Apr 1200 1,000 200 0 0 20 0 0
May 2000 1,000 1,000 0 0 20 0 0
Jun 400 400 0 0 0 8 0 12
Jul 400 400 0 0 0 8 0 0
Aug 1000 1,000 0 0 0 20 12 0
Sep 1000 1,000 0 0 0 20 0 0
Oct 1500 1,500 0 0 0 30 10 0
Nov 7000 3,500 3,500 0 0 70 40 0
Dec 500 500 0 0 0 10 0 60
Total 17,000 12,300 4,700 0 0 246 72 72

Problem 3.
Complete the following MRP matrix for Item X. Determine when orders should be released and the size of those orders.
Item: X LLC: 0 Period
Lot Size: Min 50 LT: 2 1 2 3 4 5 6 7 8
Gross Requirements 25 30 56 25 100 40 30 20
Scheduled Receipts 50
Projected on Hand 30
Net Requirements
Planned Order Receipts
Planned Order Releases
Release orders in periods 1 through 5 for quantities of 50, 50, 56, 50, and 50 respectively.

Problem 4.
Fibrous Incorporated makes products from rough tree fibers. Its product line consists of five items processed through one of five machines. The machines are not identical, and some products are better suited to some machines. Given the following production time in minutes per unit, determine an optimal assignment of product to machine:
Machine
Product A B C D E
1 17 10 15 16 20
2 12 ?9 16 ?9 14
3 11 16 14 15 12
4 14 10 10 18 17
5 13 12 ?9 15 11

Problem 5.
The following probabilistic activity time estimates are for a CPM/PERT network.
Time Estimates (days) Time Estimates (days)
Activity a m b Activity a m b
1 1 2 ?6 ?7 1 1.5 2
2 1 3 ?5 ?8 1 3 5
3 3 5 10 ?9 1 1 5
4 3 6 14 10 2 4 9
5 2 4 ?9 11 1 2 3
6 2 3 ?7 12 1 1 1
Determine the following:
a. Expected activity times
b. Earliest start and finish times
c. Latest start and finish times
d. Activity Slack
e. Critical Path
Expected Project duration and standard deviation.

To determine appropriate location

Based of the above calculations the appropriate site location is Bayside

Release orders in periods 1 through 5 for quantities of 50, 50, 56, 50, and 50 respectively.

A table showing time taken to produce the products by each machine

 Product Machine Totals A B C D E 1 17 10 15 16 20 78 2 12 9 16 9 14 60 3 11 16 14 15 12 68 4 14 10 10 18 17 69 5 13 12 9 15 11 60 Totals 67 57 64 70 74 335

To get the optimal assignment of product for machine the percentage of total time taken by each machine to produce the five products with regards to the total time to produce all products by all machines is calculated as follows:

Machine B is the most optimal since it utilizes the least percentage of time (i.e. 17%) to produce all the products.

The formulas:

Where;

 Activity t ES EF LS LF S 1 8 0.44 0 8 1 9 1 2 6 1.00 0 6 0 6 0 3 3 0.44 0 3 2 5 2 4 5 2.78 8 13 16 21 8 5 3 0.11 6 9 6 9 0 6 4 0.11 3 7 5 9 2 7 2 0.00 3 5 14 16 11 8 7 1.78 9 16 9 16 0 9 4 0.44 9 13 12 16 3 10 4 0.44 13 17 21 16 8 11 9 1.00 16 25 16 25 0 12 4 4.00 15 27 15 25 2

Where;

Expected activity times (ES); Earliest start and finish times (EF); Latest start and finish times (LS); Activity Slack (LF); and Critical Path (S)

However, the expected project duration and standard deviation are:

Project duration = sum of each activity time (durations) = 59 days

Standard Deviation = sum of all standard deviations = 12.54 days

References

Cleland, D. I., & King, W. R. (2013). Project Management Handbook. New York, NY: Prentice Hall Publishing.

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