Any system will reach steady state so long as the “traffic intensity” factor is: 

A small manufacturing system produces parts for sea kayaks in La Jolla, San Diego. The parts arrive from an upstream Poisson process with an arrival rate of 1 part every 5 minutes. All the parts that enter the system must go through a station which houses 2 prefabrication machines. A part, though, only requires to be processed by 1 of the 2 machines during prefab. The prefab time is exponentially distributed with the same mean for each of 8 minutes. If all the machines at the prefab station are busy, then the part will wait for the next available machine. . a. What is the probability that both machines are idle? Please round your answer to 3 decimal places (e.g. #.###).   (4pts) b. What is the overall system utilization? (2pts) c. What is the average number of parts waiting for prefab? (2pts) d. A floor technician suggests that the system utilization rate should be lower (less than 30%) if the company wants to maintain the life of the machines and avoid machine failures. Do you think adding a third machine with the same processing rate will achieve that goal? Please show the new utilization rate to support your answer. Please express your answer to 3 decimal places and your asnwer (e.g., #.###, yes or #.###, no) and explain why on your scratch paper. (2pts)

TRUE or FALSE: Little’s Law is not valid for all systems in steady state.

TRUE or FALSE: Little’s Law is valid for all systems and provides estimate of mean and variance of queue lengths.

TRUE or FALSE: Little’s Law is valid for all systems in steady state.

For a paced transfer line with 3 machines and without buffer, if each machine fails on average every 10 cycles and average repair time is two cycles. What is the availability of the line? (Assume that the failure and repair time follows a geometric distribution).   

For a paced transfer line with 3 machines and two buffers as shown in the following figure, it sees 20 jobs arriving per day in steady state. The average work-in-process inventory level at each buffer (B1 and B2) is 40 jobs. Jobs can require anywhere from 4 to 10 operations and processing time per operation, and can take anywhere from 60 minutes to 3 hours. Machines may fail and require 4 hours to several days to repair. Assume each day has 8 effective working hours. On average, how long does it take a job to go through the line?

A manufacturing cell with Kanban control produces 16 different types of cylindrical metal rods that are used in several assembly cells spread across a 1,000,000 sq. ft. complex consisting of four buildings.  One particular rod (A3416) is used by three different assembly cells for a consistent total demand rate of 60 rods per hour.  The rods are moved in containers that hold 5 rods.  It typically takes 5 hours to replenish a container of rods but that time varies by up to 20%. How many kanbans should be used for the production of rod (A3416)? 

TRUE or FALSE: The main requirement of a good heuristic is that it provides solutions that agree with past decisions made by the problem owner.

Age-related changes in the respiratory system include a decrease in lung elasticity and a reduction in the efficiency of gas exchange.