“Optimizing Production Capacity and Inventory Management in Wood Bowl Manufacturing: A Case Study of Wavy Wood Works in Portland, Oregon”

QUESTION

In their Portland, Oregon, facility, Wavy Wood Works makes several types of wood bowls from coastal driftwood. To make a bowl, the first step is to clean the driftwood. Each piece of driftwood makes a single bowl. There is one cleaning machine. It takes 35 seconds to load each piece of wood, and the machine can hold up to 33 pieces. Once all of the pieces are loaded into the machine, it takes 50 minutes to clean the set (no matter the number of pieces in the set). Once the wood is cleaned, 11 skilled artisans carve the bowls; each one takes, on average, 92 minutes to produce each bowl. After carving, bowls are finished with a stain. It takes 29 seconds to load each bowl into the stain machine. The staining machine holds up to 36 bowls. Once all of the bowls are loaded, they are soaked for 84 minutes. After staining, bowls are unloaded onto drying racks. There is plenty of space on the drying racks.

a. What is the maximum capacity (bowls per hour) of this process?

Note: Do not round intermediate calculations. Round your answer to 2 decimal places.

b. Suppose Wavy wants to operate with the same number of bowls in each batch that are cleaned or stained. For example, if it cleans in batches of 29, then it stains in batches of 29 as well. What batch size (in bowls) minimizes its inventory while allowing the process to produce at the maximum flow rate?

Note: Use unrounded capacities from Part a.

ANSWER

The maximum capacity of the process can be calculated by identifying the bottleneck in the production flow. The bottleneck is the step that limits the overall production rate. In this case, the bottleneck is the cleaning machine since it takes the longest time to process a set of driftwood pieces.

First, let’s calculate the time it takes to clean one batch of driftwood pieces:
Time to load one piece into the cleaning machine = 35 seconds
Number of pieces the machine can hold = 33 pieces
Time to clean one batch of 33 pieces = 35 seconds/piece * 33 pieces = 1155 seconds

Now, let’s convert this time to hours:
Time to clean one batch in hours = 1155 seconds / 3600 seconds per hour = 0.32 hours

Next, let’s calculate the number of batches that can be cleaned in one hour:
Number of batches cleaned per hour = 1 / (Time to clean one batch in hours) = 1 / 0.32 ≈ 3.13 batches per hour

Now, let’s calculate the number of bowls in one batch:
Number of bowls per batch = Number of pieces the machine can hold = 33 bowls

Finally, we can calculate the maximum capacity of the process:
Maximum capacity (bowls per hour) = Number of batches cleaned per hour * Number of bowls per batch
Maximum capacity = 3.13 batches/hour * 33 bowls/batch ≈ 103.29 bowls per hour

So, the maximum capacity of the process is approximately 103.29 bowls per hour.

b. To find the batch size that minimizes inventory while allowing the process to produce at the maximum flow rate, we need to balance the cleaning and staining steps. Since the cleaning machine has a maximum capacity of approximately 103.29 bowls per hour (as calculated in part a), we should aim for a batch size that matches this rate.

Therefore, the optimal batch size would be 33 bowls, which is the same as the cleaning machine’s capacity. This allows the cleaning and staining steps to operate in harmony, ensuring that neither step accumulates excessive inventory while maximizing the overall flow rate of the process. This balance minimizes the cost associated with holding excess inventory and ensures efficient production.