Background
To transform raw cotton into a completed order, a four-stage process is required in a
cotton textile mill. The four stages are spinning, weaving, finishing and packing. The
order of processing is represented by the following diagram:
Raw Cotton Spinning Weaving Finishing Packing Final Product
All the processes are done by machines.
The process time to spin sufficient yarn to produce a bale of finished sloth has a normal
distribution with mean and variance both equal to 180 seconds. The process times for
the weaving stage and the finishing stage also follow a normal distribution with
parameters 420 and 300 seconds, respectively. The process time for the packing stage
has an exponential distribution with mean 60 seconds.
Due to a lack of queueing spaces inside the factory, the queue for spinning is initially
set to 25 units and one unit will be added to it when one unit of final product is
produced.
The mill operates continuously on a three shifts a day, seven days a week basis. That is,
“one shift” is equivalent to an 8-hour operation.
Operational Risk – Machine Breakdown
Each machine is subjected to “breakdown”. Whenever a machine breaks down, it is
immediately sent to the repair facility (assume there are sufficient mechanists to handle
all broken-down machines at one time). The time required to repair a machine is an
exponentially distributed random variable with mean 2000 seconds.
Once a failed machine has been repaired and put into use, the amount of time it
functions before breaking down is an exponentially distributed random variable with
mean 8500 seconds.
If there is an item inside the machine when the machine breaks down, the item is
immediately processed by another idle machine (if any) for its remaining processing
time, or else it is put in priority for processing (again, for its remaining processing time)
once there is a machine available.
Problem
The management realized that if the factory is producing at its most efficient level, the idle time (in percentage) of the machine has to be minimized. As a result, the management wishes to know the relative number of machines that the factory should use at each stage in order to minimize the idle time.
As a consultant of the factory, you decide to develop a computer simulation model to solve the problem.