Project Questions:
1. In an auto assembly line the major subassemblies (engine, hood, wheels, transmission, and doors) are added in a progressive manner to the chassis. The chassis arrives from the fabrication department at the rate 5 per hour (exponentially distributed). The chassis is mounted on an assembly fixture (mounting time is normally distributed with a mean of 8 min and standard deviation of 4 min). All the following major sub-assemblies arrive to the respective assembly stations at the rate 5 per hour (exponentially distributed).
The times for adding sub-assemblies to the chassis are as follows:
Sub-assembly
Engine
Hood
4x wheels Transmission 4x Doors
Assembly Time
Normal (mean: 10, std. dev: 3) min Triangular (max: 12, mean: 10, min: 6) min Uniform (8 ~ 12) min
Normal (mean: 12, std. dev: 2) min Uniform (8 ~ 15) min
After the assembly is completed, they go on to an inspection station. The inspection time is uniformly distributed between 6 to 12 minutes. Five percent of the assemblies are sent back to the beginning of the line for rework and are processed similar to new assemblies. Rest of the assemblies that pass inspection, go on to the shipping dock where they are dismounted from the assembly fixtures and shipped to the dealers. The assembly fixtures are returned to the beginning of the assembly line.
There is a buffer for waiting cars only at the start of the assembly line. There is no other waiting space in between various sub-assembly stations or between sub-assembly stations and the inspection station. Run the model for 200 hours.
Respond to the following questions:
1. Utilization of the sub-assembly stations and the inspection station. Which one is the bottleneck of the process?
2. What is the production rate of auto assemblies per hour?
3. What is the work-in-process inventory of semi-finished auto assemblies?
4. What is the throughput time (from start of assembly till shipping)?
5. Make a time plot of the work-in-process inventory and comment on whether the system is stable and in steady state or not? How can you tell?
6. How many assembly fixtures do we need? Why?
4. Sweet Bake Shop is famous for its cupcakes. Customers arrive to Sweet Bake Shop with mean inter-arrival time of five minutes, exponentially distributed. The number of cupcakes that each customer picks up from the store shelves is uniformly distributed between 2 and 12. The time that it takes to decide on a cupcake and pick up is normally distributed with mean 3 min and standard deviation of 1 min. Note that each customer can spend different amount of time for different cupcakes she chooses. A Kanban is attached to each cupcake.
After picking up the cupcakes, they are sent to a queue to cashier for check out. The checkout time takes a time that is normally distributed with mean .8 min and standard deviation .1 min. The cashier also collects all the M-kanbans and returns them to the storage room.
In the storage room, an associate detaches the P-kanban from a fresh cupcake and sends the P- kanban back to the kitchen. The storage room associate also attaches the M-kanban to a fresh cupcake. The detaching of the P-kanban and attaching the M-kanban takes an average of 2 minutes (normally distributed with standard deviation 1 minute). The cupcakes are then sent to the shelves where the move time has a normal distribution with mean 2 min and standard deviation 1 minute.
The baking staff in the kitchen on receiving the P-kanban produces another fresh cupcake. Time to bake a cupcake is normally distributed with mean 4 min and standard deviation 1 min. The P- kanban is attached to this fresh cupcake. The packer in the kitchen puts the cupcake in a decorative box. Time to box and wrap is normally distributed with mean 2 min and standard deviation 0.5 min. Then the box (with the P-kanban attached to it) is moved to the storage room. The moving time is normally distributed with mean 2 min and standard deviation 0.5.
Try various combinations of numbers of M-kanbans (12 ~36) and P-kanbans (12 ~ 36) and analyze how they affect the performance of the store. What would be the ideal number of M- and P-kanbans and why?