Q1. (20%) As the Cottrell Bicycle Co. of St. Louis completes plans for its new assembly line, it identifies 25 different tasks in the production process. VP of Operations Jonathan Cottrell now faces the job of balancing the line. He lists precedences and provides time estimates for each step based on work-sampling techniques. His goal is to produce 1,000 bicycles per standard 40-hour workweek.

 

Task Time

(sec)

Immediate Predecessors Task Time

(sec)

Immediate Predecessors
K3 60 E3 109 F3
K4 24 K3 D6 53 F4
K9 27 K3 D7 72 F9, E2, E3
J1 66 K3 D8 78 E3, D6
J2 22 K3 D9 37 D6
J3 3 C1 78 F7
G4 79 K4, K9 B3 72 D7, D8, D9, C1
G5 29 K9, J1 B5 108 C1
F3 32 J2 B7 18 B3
F4 92 J2 A1 52 B5
F7 21 J3 A2 72 B5
F9 126 G4 A3 114 B7, A1, A2
E2 18 G5, F3      

 

  1. Balance this operation using shortest operation time rule and compute the ef ficiency of the line. (10%)
  2. Discuss the results obtained in (a) including the maximum efficiency we can a chieve and how this balance could be improved. (10%)

 

 

Q2. (20%) Manager Chris Channing of Fabric Mills, Inc., has developed the forecast shown in the table for bolts of cloth. The department has a normal capacity of 275 bolts per month, except for the seventh month, when capacity will be 250 bolts. Normal output has a cost of £40 per bolt. Workers can be assigned to other jobs if production is less than normal. The beginning inventory is zero bolts.

 

Month 1 2 3 4 5 6 7 Total
Forecast 250 300 250 300 280 275 270 1,925

 

  1. Develop a chase plan that matches the forecast and compute the total cost of your plan. Over time is £60 per bolt, and backlogs are not allowed. (5%)
  2. Would the total cost be less with regular production with no overtime, but using a subcontractor to handle the excess above normal capacity at a cost of £50 per bolt? Backlogs are not allowed. The inventory carrying cost is £2 per bolt. (5%)
  3. Compare and contrast two simple pure strategies, i.e., chase strategy and level strategy, for capacity planning. (10%)

 

 

Q3. (20%) Emery Pharmaceutical uses an unstable chemical compound that must be kept in an environment where both temperature and humidity can be controlled. Emery uses 200 pounds per month of the chemical, estimates the holding cost to be £3.33 (because of spoilage), and estimates order costs to be £10 per order. The cost schedules of four suppliers are as follows:

 

Vendor 1 Vendor 2
Quantity Price/LB (£) Quantity Price/LB (£)
1-49 35.00 1-74 34.75
50-74 34.75 75-149 34.00
75-149 33.55 150-299 32.80
150-299 32.35 300-499 31.60
300-499 31.15 500+ 30.50
500+ 30.75    
Vendor 3 Vendor 4
Quantity Price/LB (£) Quantity Price/LB (£)
1-99 34.50 1-199 34.25
100-199 33.75 200-399 33.00
200-399 32.50 400+ 31.00
400+ 31.10    

 

  1. What quantity should be ordered, and which supplier should be used? (10%)
  2. Discuss factor(s) should be considered besides total cost. (10%)

 

Q4. (20%) A process considered to be in control measures an ingredient in ounces. A quality inspector took 25 samples, each with 5 observations as follows:

 

Samples Observations
1 2 3 4 5
1 51 50 49 50 50
2 45 47 70 46 36
3 50 35 48 39 47
4 55 70 50 30 51
5 49 38 64 36 47
6 59 62 40 54 64
7 36 33 49 48 56
8 50 67 53 43 40
9 44 52 46 47 44
10 70 45 50 47 41
11 57 54 62 45 36
12 56 54 47 42 62
13 40 70 58 45 44
14 52 58 40 52 46
15 57 42 52 58 59
16 62 49 42 33 55
17 40 39 49 59 48
18 64 50 42 57 50
19 58 53 52 48 50
20 60 50 41 41 50
21 52 47 48 58 40
22 55 40 56 49 45
23 47 48 50 50 48
24 50 50 49 51 51
25 51 50 51 51 62

 

  1. Using this information, obtain three-sigma (i.e., z=3) control limits for a mean control chart and control limits for a range chart, respectively. It is known from previous experience that the standard deviation of the process is 8.46. (10%)
  2. Discuss whether the process is in control or not. (10%)

 

Q5. (20%) The Model 5 is a new custom-designed electric car. An analysis of the task of building the Model 5 reveals the following list of relevant activities, their immediate predecessors, and their duration:

 

Job Description Immediate Predecessors Normal Time (Days)
A Start 0
B Design A 8
C Order special accessories B 0.1
D Build frame B 1
E Build doors B 1
F Attach axles, wheels, gas tank D 1
G Build body shell B 2
H Build transmission and drivetrain B 3
I Fit doors to body shell G, E 1
J Build engine B 4
K Bench-test engine J 2
L Assemble chassis F, H, K 1
M Road-test chassis L 0.5
N Paint body I 2
O Install wiring N 1
P Install interior N 1.5
Q Accept delivery of special accessories C 5
R Mount body and accessories and chassis M, O, P, Q 1
S Road test car R 0.5
T Attach exterior trim S 1
U Finish T 0

 

  1. Identify the project duration stating the critical path. (10%)

If the Model 5 had to be completed 2 days earlier, then discuss ideas about how to reduce the project