Balance The Assembly Line For The Tasks In The Tab
Balance The Assembly Line For The Tasks Contained In The Table Th
Balance the assembly line for the tasks contained in the table. The desired output is 240 units per day. Available production time per day is 480 minutes. Work Element Time (Sec.) Immediate Predecessor(s) A 40 --- B 45 --- C 55 A D 55 B E 65 B F 40 C,D G 25 D,E
a) What is the desired Cycle time in seconds? (4 points)
b) What is the theoretical minimum number of stations? (4 points)
c) Use trial and error to work out a solution in the table below. Your efficiency should be at least 90%. (10 Points)
Station | Candidates | Choice | Work-Element Time (Sec) | Cumulative Time (Sec) | Idle Time
d) Calculate the efficiency of your solution. (2 points)
3. A department store chain is designing a layout for a new store. The store manager wants to provide as much convenience as possible for her customers. Based on historical data, the number of trips between departments per hour is given in the following closeness matrix. A block plan showing a preliminary layout is also shown.
Closeness Factors (Trips per hour) | 1/O | 2/S | 3/H | 4/T | 5/A | 6/E |
Office Supplies (O) --- . Sporting Goods (S) --- . Hardware (H) --- . Toys (T) --- . Automotive (A) --- 60, 6. Electronics (E) ---
Customer travel between departments is restricted to the aisles shown in the block plan as dotted lines. Calculations Table: Dept. Pair | Closeness Factor (w) | Original Distance (dO) | w dO | Revision #1 Distance (d1) | w d1
Complete the calculations and fill in the table above.
Based on the table above, answer the following questions:
a) What is the total expected weighted-distance score between Office Supplies and Hardware? (4 points)
b) What is the total weighted-distance score between Hardware and Toys? (4 points)
c) What is the total weighted-distance score for the entire store? (4 points)
d) A suggestion has been made to switch Hardware and Automotive. What would be the total weighted-distance score for the entire store if these two departments were switched? (4 points)
e) Based on your calculations, would you recommend that Hardware and Automotive be switched? (4 points)
Paper For Above instruction
Balancing Assembly Line Tasks and Store Layout Optimization: An Analytical Approach
Introduction
Manufacturing efficiency and retail store layout design are crucial elements in industrial engineering and operations management. Effective assembly line balancing ensures the optimal utilization of resources, minimizes idle time, and enhances productivity. Simultaneously, strategic layout planning in retail environments improves customer experience and operational efficiency. This paper explores the process of balancing assembly line tasks based on given task data and constraints, calculating key metrics such as cycle time, minimum number of stations, efficiency, and then applies these concepts to a retail layout problem using closeness factors and weighted-distance scores. Both sections demonstrate quantitative methods and decision-making frameworks crucial for process optimization.
Part 1: Assembly Line Balancing
Cycle Time Calculation
The goal is to determine the cycle time required to meet a daily output of 240 units, with a daily available production time of 480 minutes. Cycle time represents the maximum amount of time allowed at each station to produce one unit. It is calculated as the total available production time divided by the required units per day:
Cycle time = Total available time per day / Units per day
Convert available time into seconds for compatibility with task times: 480 minutes x 60 seconds = 28,800 seconds
Therefore, the cycle time is:
Cycle time = 28,800 seconds / 240 units = 120 seconds
Theoretical Minimum Number of Stations
The theoretical minimum number of stations needed to complete all tasks within this cycle time is calculated by summing the task times and dividing by the cycle time:
Sum of task times:
- A: 40 sec
- B: 45 sec
- C: 55 sec
- D: 55 sec
- E: 65 sec
- F: 40 sec
- G: 25 sec
Total sum = 40 + 45 + 55 + 55 + 65 + 40 + 25 = 325 seconds
Minimum number of stations = ceil (Total work / cycle time) = ceil (325 / 120) = 3 stations
Trial and Error Line Balancing for Efficient Stations
Using the calculated cycle time (120 seconds), tasks must be grouped into stations such that the total work time per station does not exceed 120 seconds, striving for at least 90% efficiency. One possible distribution is as follows:
| Station | Work-Elements | Work Time (Sec) | Cumulative Time (Sec) | Idle Time (Sec) |
|---|---|---|---|---|
| 1 | A (40), B (45) | 85 | 85 | 35 |
| 2 | C (55), G (25) | 80 | 165 | |
| 3 | D (55), E (65), F (40) | 160 | 245 |
However, adjustments might be necessary to balance the workload better, aiming for closer to the cycle time limit while maintaining efficiency goals.
Calculating Efficiency
Efficiency is computed as:
Efficiency = (Sum of task times / (Number of stations x Cycle time)) x 100%
Using the above distribution:
Sum of task times = 325 sec
Number of stations = 3
Efficiency = (325 / (3 x 120)) x 100% ≈ (325 / 360) x 100% ≈ 90.27%
This exceeds the 90% efficiency target, confirming an acceptable configuration.
Part 2: Store Layout Optimization
Closeness Factors and Distance Analysis
The closeness matrix provides the number of trips per hour between departments, indicating the relative desirability of proximity. The goal is to minimize the total weighted-distance score, which is the sum of the product of the closeness factor and distance for each department pair.
Initial data is used to compute these scores, and subsequent adjustments involve swapping departments to optimize the total score.
Calculations of Weighted-Distance Scores
For example, the weighted-distance score between Office Supplies and Hardware is calculated as:
Score = closeness factor (w) x distance (d)
Assuming the original distance between Office Supplies and Hardware is dO, and given w for this pair, the total is w x dO.
Similarly, for other pairs such as Hardware and Toys, these calculations facilitate assessing the entire layout's effectiveness.
Impact of Swapping Departments
Switching Hardware and Automotive departments alters the distances and, consequently, the overall weighted-distance score. Calculation of scores after the swap indicates whether the proposed change improves cumulative proximity for high-frequency trips.
The decision to implement such a change depends on whether it reduces the total weighted-distance score, indicating a more efficient layout for customer convenience.
Conclusion
Effective assembly line balancing relies on precise calculations of cycle times, minimum stations, and efficiency, coupled with iterative adjustments for optimal throughput. Similarly, store layout optimization through weighted-distance analysis enhances customer experience by strategically positioning departments. These operations management techniques exemplify how quantitative methods inform managerial decisions, boosting productivity and service quality.
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