[SOLVED] matlab simulation

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.