Question

C&A Pottery makes ceramic vases using a process that involves forming, drying, firing, and glazing. The 5 workers each takes on average 50 minutes to form a vase. The vases will then be loaded into an oven to dry. The oven can hold up to 100 pieces and it takes 5 minutes to load each vase. Once all the vases are loaded into the oven, it takes 24 hours to dry each load. The dried vases are then placed in a kiln that holds up to 100 pieces. It takes 6 minutes to load each vase and the vases will be fired in the kiln for 62 hours. After firing, 3 workers each take an average of 2 hours to glaze each vase. C&A receives an order of 1 vase per hour. What is the smallest batch size to ensure the process is demand-constrained?

Answer 1

C&A receives the order of 1 vase per hour, so we need to make the capacity, 1 vase per hour. Capacity is the flow rate in this case as the flow rate is the minimum of process capacity, demand, and available input.

Set up time for oven = 24 hours

(24 hours are needed to dry the load of 100 pieces)

Processing time for oven = 5 minutes = 5/60 hour

(5 minutes are required to make each vase, also known as time per unit)

Recommended batch size = (flow rate * Set up time)/ (1 – flow rate * processing time)

Batch size for oven = 1*24/ (1 – (1*5/60)) = 24/ (1-5/60) = 24/ (55/60) = 24*60/55 = 26.18

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Similarly, for Kiln,

Set up time = 62 hours

Processing time = 6 minutes = 6/60 hour

Batch size for Kiln = 1*62/ (1 – (1*6/60)) = 62/ (1 – 1/10) = 62/ (9/10) = 62*10/9 = 68.888 = 69

Minimum batch size should be 69 so the demand can be fulfilled.