Question

Question 2:

(a) A Muscat Tools company manufactures toolkits and supplies to the local and overseas market within the GCC region. In the assembly line, the kits are packed in the tool boxes. The company produces the specified demand rate of toolkit in 8 hours per daywithtasks, description of tasks, and time for each task shown in Table Q2a.

(i) Draw the precedence diagram anddetermine the cycle time,and number of workstations;

iii) Balance the line using the longest task time rule,and determine the line efficiency.

Table Q2(a)
Demand rate (units/day)	1225
Task	Time (sec)	Predecessors	Description
A	15	-	Open tool box and place on assembly line
B	9	A	Place spanner in tool box
C	7	A	Place spark plug spanner in tool box
D	7	A	Place screw driver in tool box
E	7	B, C, D	Close internal lid
F	18	E	Place jack in tool box
G	6	E	Place jack handle in tool box
H	7	Place polishing cloth in tool box	E
I	10	Close tool box	F, G, H
J	21	Shrink wrap tool box	I

(b) A company is unable to satisfy customer demand for one of their products. The ratios for mixing the outputs from processes C, D and E are 2, 1 and 1 respectively. The ratio for the departments F and G is 3 and 1, and the ratio for departments H and I is 4 and 1. Using Table Q2(b), Determine;

(i)The system capacityand bottleneck;

(ii) How much system capacity can be gained by adding capacity to the bottleneck

Table Q2(b)
Department	Capacity (liters/hour)	Predecessors
A	400	-
B	A	400
C	B	350
D	-	200
E	-	200
F	700	C, D and E
G	250	-
H	900	F, and G
I	300	-
J	1000	H and I
K	1300	J

Answer 1

2. a)

i) Given,

Total time = 8 hours = 8 x 60 x 60 seconds = 28800 seconds

Demand = 1225

=> Target cycle time = Total time available / Demand = 28800/1225 = 23.51 seconds $\approx$ 24 seconds

Composite work content (Total time taken for tasks) = 15 + 9 + 7 + 7 + 7 + 18 + 6 + 7 + 10 + 21 = 107 seconds

=> Minimum number of workstations (
Nmin
) = Composite work content / cycle time = 107/23.51 = 4.55 $\approx$ 5

The precedence diagram along with workstation distribution is shown below:

| Workstations 18 7 Workstation 1. A -- 6 e- - »I JA ro - workstation 5 7 Workstations workstation 4

ii) The Line is balanced and workstations are assigned using longest task time rule, i.e. the longest tasks available in precedence is added to a workstation. After the longest tasks are assigned, the shorter tasks are assigned to next workstation.

Hence, we have,

Workstation 1: Task A and Task B

Time = 15 + 9 = 24 seconds

Workstation 2: Tasks C,D and E

Time = 7 + 7 + 7 = 21 seconds

Workstation 3: Task F

Time = 18 seconds

Workstation 4: Tasks G,H and I

Time = 6 + 7 + 10 = 23 seconds

Workstation 5: Task J

Time = 21 seconds

Line balance efficiency = Sum of task times / Number of workstations x cycle time

= 107/ 24 x 5 = 107/120 = 0.891667 = 89.17%

2.b)

i) Bottleneck resource is the one that limits the overall process capacity or output.

We shall analyze how many liters of output from each resource is required for an input of 1 unit to the subsequent department.

Units of output per hour = Capacity/units required

For example,

For Department C,

Capacity = 350 liters/hour

units required = 2

Units of output per hour = 350/2 = 175 liters/hour of output

Department Capacity (liters/hour) Predecessors units required Units of output per hour A 400 1 400 B 400 A 1 400 350 B 2 175 D 200 1 200 E 200 1 200 F 700 C,D,E 3 233.3333333 250 1 250 T 900 F.G 4 225 1 300 1 300 1000 HI 1 1000 K 1300 1 1300

Because the output per hour for department C is the least i.e. 175 liters, Department C is the bottleneck.

For process capacity:

We know C is the bottleneck and can contribute to making 175 liters of input for Department F.

Now, the 3 units of F are required to make 1 unit of H.

Hence, input for H = 175 / 3 = 58.33 Liters/hour

Now, the 4 units of H are required to make 1 unit of J.

Hence, input for J = 58.33 / 4 = 14.58 Liters/hour

Hence, process capacity = 14.58 Liters/Hour

ii) Now, we can add capacity to the existing bottleneck resource until the bottleneck gets shifted to the next limiting capacity of the resource.

Here, C is the existing bottleneck, and D and E are the next limiting resources.

So, we can add capacity to C till it matches the output from D and E.

C currently generates 175 liters of output per hour for which it requires a capacity of 350 liters.

We can increase C's output to 200 liters per hour, for which it will require 200 * 2 = 400 liters per hour of capacity.

Hence, additional capacity requirement = 400 - 350 = 50 liters/hour

Now,

the revised input to F will be 200 liters/hour

Now, the 3 units of F are required to make 1 unit of H.

Hence, input for H = 200 / 3 = 66.67 Liters/hour

Now, the 4 units of H are required to make 1 unit of J.

Hence, input for J = 66.67 / 4 = 16.67 Liters/hour

Hence, revised process capacity = 16.67 Liters/Hour

The gain in process capacity = 16.67 - 14.58

The gain in process capacity = 2.09 liters/hour

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