Job shop processes are used, for example, in the manufacturing of machine parts, in the maintenance of jet engines, and for the care of patients in a hospital. Job shops typically have a different variety of work stations and can make a variety of different products. With so many In what order should jobs be processed at each machine? We consider this question in Example types of jobs moving through a job shop at a time, an important question becomes the following: 23. Example 22: Pharmaceutical manufacturing A pharmaceutical company makes a number of products in pill form. Two such products, Aspirin A and Aspirin B, have a high and steady demand and a single machine has been dedicated to making them. This machine can only make one type of pill at a time and must be thoroughly cleaned (i.e.. setup) when it switches from making one type of pill to another. Management must decide how much of each type of pill to make at a time to satisfy 90% of the demand for each product; in operations lingo, management must decide on the best batch sizes, Let us simplify the process as follows. First, assume we have as much raw material (chemicals in powder form) as we need. (Once we design the rest of the process, we can arrange with our supplier to deliver the quantities we need, when we need them.) The raw materials can be grouped into batches of anywhere from 100 to 500 lbs (in increments of 100 lbs). Batches are sent to the machine that creates the pills (pills are created by applying enormous pressure to the chemicals placed into pill-shaped molds). Every time the machine finishes a batch, it must be washed out before a batch of the other product can be started. The setup times are normally distributed with a mean of 3 working hours and a standard deviation of .5 hours. Actual processing times for a batch are the same for each product and are provided in the following table. Processing Times (hr) 100 Nor(1..5) 200 Batch Sizes (lbs.) 300 Nor(2..6) Nor(3.7) 400 Nor(4,.8) 500 Nor(5.9) After processing, the pills go into a storage area with a very large capacity. Pills are removed from the storage area as demand dictates: The time between shipments for Aspirin A is exponentially distributed with a mean of 20 working hours and each shipment is 300 lbs (or as much as is available); the time between shipments for Aspirin B is exponentially distributed with a mean of 10 working hours and each shipment is 300 lbs (or as much as is available). Management is considering the following scenarios, or combinations of batch sizes. Scenarios (batch sizes in lbs) 1 2 3 4 5 6 Aspirin A Aspirin B 100 100 200 300 300 400 200 300 300 400 500 500 88