Question 1 (8 marks)

Consider the following simple assembly process:

The process is staffed by four operators with one operator assigned to each of the four machines: A, B1, B2, and C. There is no buffer between tasks. The operators of Machines A and C also handle the setup of these machines. B1 and B2 perform the same task, but B2 is newer, and hence faster than B1. Also, B1 works with a tray system where the tray requires 10 minutes setup time and at most 6 parts can be placed on the tray at once. For instance, if two parts are processed in B1, then it takes 10 minutes of setup plus 4 x 2 = 8 minutes processing (in total 18 minutes) to process two parts. If 8 parts are processed in B1, then there should be two setups taking 10 x 2 = 20 minutes plus 4 x 8 = 32 minutes of processing (in total 52 minutes). The operator of Machine B1 handles the setup of the tray. The processing time per part and setup time per batch required for each machine is given below that machine. Batches are moved together between machines, and a batch processed in A is moved to either B1 or B2 depending on the availability of these machines (note that a batch cannot be split between machines B1 and B2). Each operator receives wages of 12/hour and can work at most 8 hours. The price of the finished good is 10 per unit, cost of inputs for the good is 6 per unit of finished good, and there is unlimited demand for the good. The production starts at the beginning of the 8-hour shift (requiring the setup of task A) so there is a start-up. Any product that is unfinished at the end of the shift is scrapped.

i) Suppose that the batch size is 10. What is the capacity of the process? [2 marks]

ii) What is the batch size (if any) that balances this system? [2 marks]

iii) Suppose that the batch size is 20. Suppose that you have the option of hiring another worker to handle setups and make the setup processes external (i.e., a batch can be processed at a step while another batch is being setup).

iv) Suppose that you are going to pay a wage of 12/hour to that new worker. Is this alteration worth the additional labor cost? Justify your answer. [4 marks]

Please help with answering all question in Question 1 (I, II, III, iv)

Consider the following simple assembly process: B1 Raw Material Finished Goods V A B2 Activity Time: 1 min / part 4 min / part in B1 0.75 min/part 3 min / part in B2 Setup Time: 20 min / batch 10 min / tray in B1 25 min / batch O min / batch in B2