Consider the following batch process and assume the demand rate is 15 units per hour. After task 1 is completed, the production unit is divided into two parts (top and bottom). Tasks 2 and 7 are done on the top of the unit and tasks 3, 4, 5 and 6 are done on the bottom of the unit. Tasks 3, 5 and 6 are currently done by the same robot, which is operated by one worker (Fiona for task 3, Erin for tasks 5 and 6). Preparing the robot for tasks 3 and 5 takes (virtually) no time. However, setting it up for task 6 takes 10 minutes before every batch. Task 4 consists of having the bottom part of the flow units cool down on a cooling rack. The cooling rack can hold up to 20 units at the same time. Task 7 can be done either by Bob or by Chloe, who each have their own machine. Task 8, which consists of reassembling the top and bottom parts of the units, is currently done by Adam using a screwdriver. Task 9 is done with machine 3 operated jointly by Adam and George. The setup time and the actual production for task 9 require the presence of both workers. Machine 3 can only process one unit at a time. All setups are required between two batches. The production is currently done in batches of 10 units. Here is the process flow diagram of the process : (a) What is process capacity and what is (are) the bottleneck(s) of the process? What is the cycle time? Is the process supply‐ or demand‐constrained? Show all your work. (b) The manager of the process wants to increase profits (i.e., revenues minus costs). What do you think of the following options: (i) Increasing the batch size to 20 units. (ii) Buy a new robot to replace the existing one (and throw away the old one). The new robot can do task 3 in 1 minute per unit instead of 2 minutes (but the time it takes to do tasks 5 and 6 is as before). (iii) Lay off Fiona and have Adam replace her. So in the new process Adam would do tasks 1, 3, 8 and 9. (iv) Reorganize the process so tasks 2 and 7 can be done at the same time on the same flow unit. (v) Have Fiona work with Dorothee on task 2 so task 2 would only take 3 minute per unit instead of 6. So in the new process Fiona would be doing tasks 2 and 3 and Dorothee would still be doing task 2. (vi) Advertise to increase the demand rate to 20 units per hour. (vii) Increase the selling price of the units. This will decrease the demand rate to 10 units per hour.

a) Process capacity is the maximum units it can produce. As the cooling rack can hold maximum 20 units at a time so that will be the capacity of this process.

The bottleneck operation is the the step which takes maximum time, here step 4 i.e cooling rack takes maximum time of 50 mimutes so it is the bottleneck operation

cycle time is the time required to convert raw material into finished goods. it is 50 minites here, as the demand is 15 but supply is done at 10 per hour so itis supply constrained.

b) I think increasing the batch size to 20 will lead to less setup time required after every batch and thus increased throughput in less costs thus more revenue.

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