derive an expression that prescribes the machine’s capacity (µ) as a function of T and λ . (Capacity is defined as the number of orders the machine can handle per day.) What happens to the required capacity when T is decreased to 0?
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A make-to-order system is well described as a basic Erlang system with a single machine. The manager of the system wants to ensure that the expected turnaround time of any order (from its placement until its shipment to the customer), in days, is T. If orders arrive at a rate λ per day, derive an expression that prescribes the machine’s capacity (µ) as a function of T and λ . (Capacity is defined as the number of orders the machine can handle per day.) What happens to the required capacity when T is decreased to 0?
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- Larry Ellison starts a company that manufactures high-end custom leather bags. Hehires two employees. Each employee only begins working on a bag when a customerorder has been received and then she makes the bag from beginning to end. The average production time of a bag is 1.8 days, with a standard deviation of 2.7 days. Larryexpects to receive one customer order per day on average. The interarrival times oforders have a coefficient of variation of one. What is the expected duration, in days,between when an order is received and when production begins on the bag?An injector machine goes down roughly 20% of the time (the injector gums up and needs to be cleaned, a quick process). One operator is assigned to service three identical such machines. Each machine can produce 100 parts/h if running properly (i.e., not down). The operator is paid $10/h and each machine costs $20/h to operate. Consider 8hr/shift a) Please fill in the table below: b) How many parts can you produce per shift? c) What is the unit cost fper part for this operation? d) If you hire another operator at the same rate to assist the first operator, what is the unit cost now? e) Is it worth hiring another operator at the same rate to assist the first operator, in case more than one machine goes down at the same time?Larry Ellison starts a company that manufactures high-end custom leather bags. He hires two employees. Each employee only begins working on a bag when a customer order has been received and then she makes the bag from beginning to end. The average production time of a bag is 1.7 days, with a standard deviation of 3 days. Larry expects to receive one customer order per day on average. The interarrival times of orders have a coefficient of variation of one. X Answer Is complete but not entirely correct. (Carry at least 4 decimal places in all intermediate calculations. Round your final answer to 2 decimal places.) What is the expected duration, in days, between when an order is received and when production begins on the bag? 30.39 8 days
- Please do not give solution in image formate thanku. We consider a level-2 IT service desk with 2 staff members. Each staff member can handle one service request in 4 working hours on average. Service times are exponentially distributed. Requests arrive at a mean rate of one request every 3 hours according to a Poisson process. What is the average time between the moment a service request arrives at this desk and the moment is fulfilled? (Show all the formulas and computations - since Lq (avg number of jobs in queue) is complex to calculate assume that it is = 1.02 (requests).)Suppose that a fire department receives an average of 24requests for fire engines each hour. Each request causes afire engine to be unavailable for an average of 20 minutes.To have at most a 1% chance of being unable to respond toa request, how many fire engines should the fire departmenthave?A graphics reproduction i rm has four units of equipment that are automatic but occasionallybecome inoperative because of the need for supplies, maintenance, or repair. Eachunit requires service roughly twice each hour, or, more precisely, each unit of equipmentruns an average of 30 minutes before needing service. Service times vary widely, rangingfrom a simple service (such as pressing a restart switch or repositioning paper) to moreinvolved equipment disassembly. The average service time, however, is i ve minutes.Equipment downtime results in a loss of $20 per hour. The one equipment attendant ispaid $6 per hour.Using i nite queuing analysis, answer the following questions:a. What is the average number of units in line?b. What is the average number of units still in operation?c. What is the average number of units being serviced?d. The i rm is considering adding another attendant at the same $6 rate. Should the i rmdo it?
- A cafeteria can seat a maximum of 20 persons. Each customer arrives in a Poisson stream with mean value 4 minutes. They are serviced at the rate of 10 per hour. For simplicity, assume that customers are serviced one at a time by one waiter. c) Suppose that two customers (with random arrival times) would like to be seated together. What is the probability that their wish can be fulfilled? Assume that arrangements can be made to seat them together as long as there are three empty seats anywhere in the cafeteria. d) Determine the expected number of customers waiting but currently not being served48. Ships arrive at a port facility at an average rate of twoships every three days. On average, it takes a single crewone day to unload a ship. Assume that interarrival andservice times are exponential. The shipping companyowns the port facility as well as the ships using that facility. The companyestimates that it costs $1000 per dayfor each day that a ship spends in port. The crew servicing the ships consists of 100 workers, each of whom ispaid an average of $30 per day. A consultant has recommended that the shipping company hire an additional40 workers and split the employees into two equal-sizecrews of 70 each. This would give each crew an averageunloading or loading time of 1.5 days. Which crew arrangement would you recommend to the company?A queuing model that follows the M/M/1 assumptions has λ = 2 and μ = 8. The average number in the system Ls is ________ and the utilization of the system is ________.
- In a multi-station serial process system, the capacity of the system is the equal to the capacity of the station that has the highest capacity among all stations. True False10. Two operators handle adjustments for a group of 10 machines. Adjustment time is exponentiallydistributed and has a mean of 14 minutes per machine. The machines operate for an average of86 minutes between adjustments. While running, each machine can turn out 50 pieces per hour.Find the following:a. The probability that a machine will have to wait for an adjustmentb. The average number of machines waiting for adjustmentc. The average number of machines being servicedd. The expected hourly output of each machine, taking adjustments into accounte. Machine downtime represents a cost of $70 per hour; operator cost (including salary andfringe benefits) is $15 per hour. What is the optimum number of operators?Mrs. Freddy Mitchell, in her lecture, stated that a transaction processing system (TPS) is software that ensures the completion of business transactions and keeps track of those business transactions. An online transaction processing system (OTPS) is an equivalent system that online merchants use for e-commerce. The TPS ensures that each transaction is successful by storing, sending, and receiving information via a database. She added that because the process is lengthy, it is broken down into cycles, which are broken further into systems and subsystems. Zara- Lee, a participant in Mrs. Freddy Mitchell’s Lecture series, got confused as Mrs. Freddy Mitchell began to elaborate on the many different systems, and Zara- Lee mentioned to YOU that she is experiencing information overload. YOU then responded that Mrs. Freddy Mitchell’s explanation was clear and concise, and YOU would explain the revenue cycle, its components, and the sub-systems that constitute that cycle after class.…