Optimizing Location and Production Efficiency

Questions:

a. Where is the best location using the center-of-gravity method?

b. If half of the customers from Segment 4 are expected to move to Segment 2, where should the drugstore shift?

c. What is the hourly capacity of each production stage and which stage is a bottleneck?

Answers:

a. The best location using the center-of-gravity method is determined by calculating the weighted center coordinates. By multiplying the coordinates of each market segment by the number of potential customers in that segment, summing up these values, and then dividing by the total number of customers, we can find the optimal location.

b. If half of the customers from Segment 4 move to Segment 2, we need to recalculate the weighted center coordinates using the updated number of customers to determine the new optimal location.

c. To determine the hourly capacity of each production stage, we calculate the time required to produce one unit at each stage and multiply by the desired output rate. The stage with the lowest capacity is considered the bottleneck stage.

Optimizing Location Using Center-of-Gravity Method:

The center-of-gravity method is a technique used to find the optimal location for a facility based on the distribution of customers in different market segments. In this case, we have four market segments with varying numbers of potential customers and coordinates. To find the best location:

Segment 1: (2, 18) * 1,000 = (2, 18,000)

Segment 2: (15, 17) * 600 = (9, 10,200)

Segment 3: (2, 2) * 1,500 = (3, 3,000)

Segment 4: (14, 2) * 2,400 = (33, 4,800)

Total x-coordinate = 47, Total y-coordinate = 36,000, Total customers = 5,500

Center-of-gravity coordinates = (47/5,500, 36,000/5,500)

Shifting Location:

If half of the customers from Segment 4 move to Segment 2:

Segment 2: (15, 17) * (600 + 1,200) = (15, 34,200)

Segment 4: (14, 2) * (2,400 - 1,200) = (14, 2,400)

Total x-coordinate = 34, Total y-coordinate = 57,600, Total customers = 4,300

Updated center-of-gravity coordinates = (34/4,300, 57,600/4,300)

Production Efficiency and Bottleneck Analysis:

By analyzing the production stages of Peter's Paper Clips, we can identify the bottleneck stage and determine the hourly capacity of each process stage:

Cutting: 0.0067 minutes per unit

Inner bending: 0.0071 minutes per unit

Outer bending: 0.0091 minutes per unit

Cutting: 2.23 units per hour

Inner bending: 2.37 units per hour

Outer bending: 3.03 units per hour

Conclusion:

Optimizing location and production efficiency plays a crucial role in the success of businesses. By using methods like the center-of-gravity technique and identifying bottleneck stages, organizations can make informed decisions to enhance performance and meet customer demand effectively.