What is the raw material for evolutionary change?

The Daytona 500 racetrack in Florida has some of the best pit-crews in the world to service cars as they race for NASCAR. Each pit crew in NASCAR can contain up to 8 crew members, but only 5 are allowed in the pit at any time. In this scenario, the cars, as they stop, line up and have a crew member assigned. The crew members do not have the same service speed (see table below), but you should assume that all crew members can service a car in full regardless of title (meaning cars do not need to visit all crew members, they are serviced by 1 as they are assigned). Crew Member Pit Speed Tire Carrier 1 car per 5 min Utility Man 10 cars per hour Jackman 30 cars per 2 min Gas Man 7 cars per 15 min Tire Changer 5 cars per hour The pit-stop area (nicknamed Tartarus) is where each car is assigned a crew member and are serviced from left to right (meaning the first car is serviced first, then the 2nd car and so on). 5a. How many cars can the entire crew serve in 1 hour? (5pts) 5b. Identify the order of which the crew members should be placed in the pit (1st, 2nd, 3rd, 4th, 5th). (5pts) , , , , 5c. Identify which crew member is the bottleneck for the whole pit. (3pts) 5d. Identify each range of cars the crew members will work when the pit-stop system reaches steady state (REMEMBER: Cars arrive right to left). Please show all work on scrap paper. (10pts)

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)?