4. A process involves four activities to make a certain product. Activity A need

Question

4. A process involves four activities to make a certain product. Activity A needs 5 workers and each worker takes on average 1 hour to complete the activity. Activity B is completed through a machine that can process up to 200 units and it takes 5 minutes to process each unit. Once the entire pieces are processed through the machine, it takes 25 hours to dry each set (no matter the number of units in the set). Activity C is completed through a machine that can process up to 200 units. It takes 6 minutes to process each unit and the units (no matter the number of units in the set) will be stained in a kiln for 72 hours. After completing activity C, 4 workers each takes an average of 120 minutes to finish each unit. Assume demand is 1 unit per hour. What is the ideal batch size to minimize inventory while allowing the process to produce at maximum flow rate? Processing Time Setup Time Batch # of Workers Size Activity A Activity B Activity C Activity D 60 minutes N/A 5 minutes 25 hours 200 6 minutes 72 hours 200 120 minutes

Explanation / Answer

Flow rate of activity A = 1/(60/5) = 1 unit every 20 minutes

Flow rate of activity B = 1/(5 + 25*60/200) = 1 unit every 12.5 minutes

Flow rate of activity C = 1/(6+72*60/200) = 1 unit every 27.6 minutes

Flow rate of activity D = 1/(120/4) = 1 unit every 30 minutes

Maximum flow rate is the minimum of above = 1 unit every 30 minutes

Therefore, ideal batch size to produce to minimize inventory at maximum flow rate = Setup time of activity C /(processing time per unit of activity D - processing time of activity C) = 72*60/(30-6)

= 180 units per batch -> ANSWER

Demand rate = 1 unit per hour

ideal batch to produce to minimize inventory at the demand rate = 72*60/(60-6) = 80 units per batch

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