Operations Mgmt POM 601

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POM 601

1) A network consists of the activities in the following list. Times are given in weeks.

Activity Preceding Time
A 8
B 3
C A 7
D A, B 3
E C 4

Draw the network diagram.

8 weeks

7 weeks 4 weeks

3 weeks

3 weeks

Calculate the ES, EF, LS, LF, and Slack for each activity.

Activity Preceding Time ES EF LS LF Slack
A 8 0 8 0 8 0
B 3 0 3 13 16 13
C A 7 8 15 8 15 0
D A, B 3 8 11 16 19 8
E C 4 15 19 15 19 0

What is project completion time? Project completion time = A-C-E = 8+7+4= 19 weeks

2) A toy manufacturer makes its own wind-up motors, which are then put into its toys. While the toy manufacturing process is continuous, the motors are intermittent flow. Data on the manufacture of the motors appears below.

Annual demand (D) = 50,000 units

Daily subassembly production rate = 1,000

Setup cost (S) = $85 per batch

Daily subassembly usage rate = 200

Carrying cost = $.20 per unit per year

To minimize cost, how large should each batch of subassemblies be?

Q*P = √ 2DS = √ 2 * 50000 * 85 = 7288.68 = 7289 units

H – (1 –d/p) .2 (1 – 200/1000)

Approximately how many days are required to produce a batch? 7289/1000 = 7.289 = 7.3 days

How long is a complete cycle? 7289/200 = 36.445 = 36 days

What is the average inventory for this problem? (Solve for maximum inventory first)

Q*{1/d-p} = 7288.7*{1-200/1000} = 5830.96 = 5831 units; Average inventory = 5831/2 = 2915.5

What is the total inventory cost (rounded to nearest dollar) of the optimal behavior in this problem?

TC= 50000 * 85 + 5831 *.2 = 583.07 + 583.10 = $1166.17

7289 2

3) A very simple product (A) consists of a base (B) and a casting (C). The base consists of a plate (P) and three fasteners (F). There are currently 30 castings and 100 bases on hand. Final assembly takes one week. The casting has a lead time of three weeks. All other parts have one week lead times. There are no scheduled receipts. All components are lot-for-lot. The MPS requires 80 units of product A in week 5 and 120 in week 8. Produce the MRP for the upcoming eight weeks. Produce a list of all planned order releases.

Indented Bill of Material (BOM)

Component Level # per Parent Indented BOMA 0 1 AB 1 1 BP 2 1 PF 2 3 FC 1 1 CTotal Components 5
Gross Requirements   0 0 0 0 80 0 0 120      
Scheduled Receipts                        
On-hand Inventory   0 0 0 0 0 0 0 0      
Net Requirements   0 0 0 0 80 0 0 120      
Planned Order Receipts   0 0 0 0 80 0 0 120      
Planned Order Releases   0 0 0 80 0 0 120 0      
Gross Requirements   0 0 0 80 0 0 120 0      
Scheduled Receipts                        
On-hand Inventory 100 100 100 100 100 20 20 20 0      
Net Requirements 0 0 0 0 0 0 0 100 0      
Planned Order Receipts 0 0 0 0 0 0 0 100 0      
Planned Order Releases 0 0 0 0 0 0 100 0 0      
Gross Requirements   0 0 0 80 0 0 120 0      
Scheduled Receipts                        
On-hand Inventory 30 30 30 30 30 0 0 0 0      
Net Requirements   0 0 0 50 0 0 120 0      
Planned Order Receipts   0 0 0 50 0 0 120 0      
Planned Order Releases   50 0 0 120 0 0 0 0      
Gross Requirements   0 0 0 0 0 100 0 0      
Scheduled Receipts                        
On-hand Inventory   0 0 0 0 0 0 0 0      
Net Requirements   0 0 0 0 0 100 0 0      
Planned Order Receipts   0 0 0 0 0 100 0 0      
Planned Order Releases   0 0 0 0 100 0 0 0      
Gross Requirements   0 0 0 0 0 300 0 0      
Scheduled Receipts                        
On-hand Inventory   0 0 0 0 0 0 0 0      
Net Requirements   0 0 0 0 0 300 0 0      
Planned Order Receipts   0 0 0 0 0 300 0 0      
Planned Order Releases   0 0 0 0 300 0 0 0      

4) Fred’s Fabrication has the following aggregate demand requirements and other data for the upcoming four quarters.

Quarter Demand   Previous quarter’s output 800 units
1 700   Beginning inventory 0 units
2 900   Stockout cost $100 per unit
3 1200   Inventory holding cost $10 per unit at end of quarter
4 600   Hiring workers $20 per unit
      Laying off workers $40 per unit
      Subcontracting cost $200 per unit
      Unit cost $100 per unit

Which of the following production plans is better: Plan A: chase demand by hiring and layoffs; Plan B: pure level strategy; or Plan C: 700 level with the remainder by subcontracting?

Production Plan B is best as it has the lowest costs.

Plan A

  Demand Regular Time Capacity Regular Time Production Units Increase Units Decrease
Initial Inventory          
Q 1 700 1200 700 0 100
Q 2 900 1200 900 200 0
Q 3 1200 1200 1200 300 0
Q 4 600 1200 600 0 600
Total Units 3400 4800 3400 500 700
      @$100/unit @$20/unit @$40/unit
Subtotal     340,000 10,000 28,000
Total $378,000        

Plan B

  Demand Regular Time Capacity Regular Time Production Inventory (end) Shortage (end) Units Increase
Initial Inventory       0    
Q 1 700 1200 850 150 0 50
Q 2 900 1200 850 100 0 0
Q 3 1200 1200 850 0 250 0
Q 4 600 1200 850 0 0 0
Total Units 3400 4800 3400 250 250 50
      @$100/unit @$10/unit @$100/unit @$20/unit
Subtotal     340,000 2,500 25,000 1,000
Total $368,500          
  Demand Regular Time Production Subcontracting Production Regular Time Production Subcontracting Inventory (end) Units Decrease
Initial Inventory           0
Q 1 700 700 0 700 0 0 100
Q 2 900 700 200 700 200 0 0
Q 3 1200 700 500 700 500 0 0
Q 4 600 700 0 700 0 100 0
Total Units 3400 2800 700 2800 700 100 100
      @$100/unit @$200/unit @$10/unit @$40/unit  
Subtotal       280,000 140,000 1,000 4,000  
Total $425,000              

5) A Methods and Measurements Analyst needs to develop a time standard for a certain task. The task involves use of ruler, square, and portable electric saw to mark and cut the “notch” in a rafter (a standard carpentry task of home construction). In a preliminary study, he observed one of his workers perform this task five times. The observations were made in an air-conditioned, well-lighted training facility, at ground level, with all tools and equipment clean and readily available.

Observation: 1 2 3 4 5
Task time (seconds): 82 74 80 83 76

What is the actual average time for this task? 82+74+80+83+76/5 = 79 seconds

What is the normal time for this task if the employee worked at a 20% faster pace than is typical for adequately trained workers? 79*1.20= 94.8 seconds

What is standard time for this task if allowances are 8% constant and 6% variable?

d) If the analyst then thought more carefully about his experiment, and decided that the variable allowances needed to be increased to match the real (outside, un-air-conditioned) work environment, and that the proper variable allowance was not 6% but 12%, what is the revised standard time? 94.8 / (1-.20) = 118.5 seconds

  • 94.8 / (1-.14) = 110.23 seconds



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