Batch sizing: resources which can perform different activities (e.g. produce different parts) often have a set-up time required. For example, in an automobile production line, the car bodies are produced with dies and the metal is stamped into the correct shape using these dies (to see this for Tesla: https://www.youtube.com/watch?v=8_lfxPI5ObM). These set-up times eat into the capacity, because nothing can be produced during the set-up time. If the set-up times are long, then it makes sense that the machine be set up to produce one part, let it run for a certain time, then change the machine over to the other part, and then repeat. This repeating sequence is called a production cycle. In each production cycle, the parts are produced in groups or "batches, and we use the term batch production process. 1. Choosing the Optimal Batch Size: For automobile production, we have the following production flow: For each car, there are 2 different parts that need to be stamped using the same Die Stamping machine. Between each of these 2 different car parts, we have a set-up time of 30 minutes at the Die Stamping. For one production cycle, this is a total setup time of 30 + 30 = 60 minutes. As we learned: Die Stamping: the capacity will depend on the batch size. Assembly: there is no need for batching, and a car can be assembled in 20 minutes/unit capacity at Assembly = 1/20 units/min We learned that the optimal batch size is the smallest batch size that does not constrain the flow rate of the process. What is the flow rate of our process? This is fixed at Assembly at 1/20 units/min. Here we want our Die Stamping to have a capacity equal to the Assembly Process capacity = 1/20 units per minute. What is the optimal batch size for Die Stamping? 1a. Using the equation below, solve for the optimal batch size at Die Stamping: (Hint: maximum capacity = 1/20 : Continue this to solve for the optimal batch size.) Maximum capacity = batch/(setup + batch size * processing time) 1/20=x1(60+x*10) 60+10x=20X 60+10x X=6

1b. What is the (negative) impact to the process if the batch size is smaller than this optimal batch size?

1c. What is the (negative) impact to the process if the batch size is larger than this optimal batch size?

ONLY NEED QUESTIONS 1B and 1C