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Question: The Sun River beverage company is a regional producer of teas, exotic juices, and energy drinks. With an interest in healthier lifestyles, there has been an increase in demand for its sugar-free formulation. The final packing operation requires 13 tasks. Sun River bottles its sugar-free product 5 hours a day, 5 days a week. Each week, there is a demand for 3,000 bottles of this product each week. Using the data below, solve the assembly-line balancing problem and calculate the efficiency of your solution, assuming the line runs at the cycle time required to meet demand. Use the longest task time for your decision criteria. Use the largest number of following tasks as a secondary criterion.

Task	Performance Time (Minutes)	Task Must Follow
1	0.1	-
2	0.1	1
3	0.1	2
4	0.2	2
5	0.1	2
6	0.2	3,4,5
7	0.1	1
8	0.15	7
9	0.3	8
10	0.5	9
11	0.2	6
12	0.2	10,11
13	0.1	12

Step by step solution

01

The precedence diagram

02

Workstation cycle

We can find the workstation cycle time to produce 3000 units per day by using the below equation

$$\begin{gathered} \mathrm{Cycle}\mathrm{time}=\frac{\mathrm{Production}\mathrm{time}}{\mathrm{Desired}\mathrm{output}} \\ =\frac{1500}{3000} \\ =0.5\mathrm{minutes} \end{gathered}$$

03

Number of workstations

We can find the number of workstations by using the below equation:

$$\begin{gathered} \mathrm{Number}\mathrm{of}\mathrm{workstations}=\frac{\mathrm{Total}\mathrm{task}\mathrm{time}}{\mathrm{Cycle}\mathrm{time}} \\ =\frac{2.35}{0.5} \\ =4.7=5\mathrm{workstations} \end{gathered}$$

04

Efficiency

We can findthe efficiency of the line by using the below equation.

$$\begin{gathered} \mathrm{Efficiency}=\frac{\mathrm{Sum}\mathrm{of}\mathrm{task}\mathrm{times}}{(\mathrm{Number}\mathrm{of}\mathrm{work}\mathrm{stations}×\mathrm{Workstation}\mathrm{cycle}\mathrm{time})} \\ =\frac{2.35}{5×0.5} \\ =0.94\mathrm{or} \\ =94\% \end{gathered}$$

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