Consider the following two-machine manufacturing facility 

Machine A produces an intermediate product XA that can be sold directly to the market at a price $4 per unit. However, a unit can receive additional processing on machine B to get a higher quality product XB that is sold at $6 dollars per units. When machine A produces its units it can produce up to 4 units simultaneously (its maximum batch size) in a fixed amount of time and when machine B processes its units, it can process up to 2 units simultaneously (its maximum batch size) in a fixed amount of time. (From the data concerning the maximum capacity and the maximum batch size, you can compute how much time it would take to produce a batch in each one of the two machines. Of course, the maximum capacity can only be achieved with full batch sizes.)

a) If the company decides to produce product XA exclusively (shut down machine B).

- What is the capacity of the system, and what is the throughput time (flow time) for units of product XA ?
- How much total revenue will there be after 1000 hours of production?
CA = Maximum Capacity of Machine A (units /hour) = 2;
BA = Maximum Batch Size machine A can handle: (units) = 4;
CB = Maximum Capacity of Machine B (units /hour) = 1;
BB = Maximum Batch Size machine B can handle: (units) = 2

b) Suppose now that the company decides to produce only product XB.

- What is the capacity of the system and throughput time (flow time) for product XB. Which machine is the bottleneck?
- Suppose machine A uses only batches of 2 units. What fraction of the time is Machine A working and what fraction of the time is it idle?
- What happens if machine A uses batches of 4 units? What is the fraction of time that machine A is idle now?
- What is the maximum amount of revenue after 1000 hours of production in this case?

c) Suppose now that the company decides to produce both products. What is the production strategy that will maximize the revenue after 1000 hours of work? Detail your answer.

Transcribed Image Text:

Machine A CA = 2, BA=4 ΧΑ Machine B CB =1, BB=2 XB Machine A CA = 2, BA=4 ΧΑ Machine B CB =1, BB=2 XB

Answer rating: 100% (QA)

a If the company decides to produce product XA exclusively shut down machine B Capacity of the system 2 unitshour limited by Machine A Throughput time ... View the full answer