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The Houston Port Authority has engaged you as a consultant to advise it on possible changes in the handling of wheat exports. It is interested in...

Good morning,
I've attached some homework questions that I answered incorrectly for my Operations Management class. The exam is on Sunday so I need to know the correct answers today so I can study tomorrow. Please let me know if you can help!
Thanks!
5. The Houston Port Authority has engaged you as a consultant to advise it on possible changes in the handling of wheat exports. It is interested in evaluating three alternatives as follows. System A: This is the current system. Presently, TWO crews of dock workers are assigned to the task of unloading hopper cars containing wheat onto cargo ships. On the average, each crew takes 25 minutes to unload a hopper car and the wages per crew are $80 per 8 hour shift. System B: The first option is to add a THIRD crew to decrease the number of cars waiting to be unloaded. The third crew will also be paid the same wages as each of the first two crews and will work as efficiently (i.e., will also take 25 minutes to unload a hopper car). System C: The second option is to automate the unloading process. The proposed system (referred to as the pneumatic handling system) can unload cars to the ships at the constant rate of 6 cars per hour (or 10 minutes per car) and will require a skilled operator who will be paid $6.50 per hour. The initial investment of such a system (amortized over the life of the system) is expected to be $ 403 per day. When analyzing Systems A and B, it is reasonable to assume that there is a single “queue” of waiting hopper cars and the first idle crew starts work on unloading the next hopper car in queue. Given the following additional information, help the port authority decide which of the three systems should be chosen so that total expected costs are minimized: The railroad bringing the hopper cars into the dock area charges the port authority $4 per hour from the time of arrival to the time when the hopper car is returned empty (i.e., this cost is a function of the average cycle time in the system and the number of hopper cars which arrive per day). This cost is referred to as a demurrage cost. The hopper car unloading times by the crews are assumed to follow an exponential distribution. The hopper car arrivals average 12 per shift and follow an exponential distribution. The port is operated 24 hours a day. 8. The local hospital’s emergency department has 6 trauma bays. On average, patients requiring a trauma bay arrive every 30 minutes (with a coefficient of variation of 1, no seasonality exists). If the hospital has an available trauma bay, it is immediately allocated to a needy patient. If there are no trauma bays available, the patient is sent to another hospital. On average, a patient’s length of stay in a trauma bay is 1.5 hours (with a standard deviation of 1.5 hours). The hospital’s emergency department operates 24 hours a day. (a) What fraction of the patients requiring trauma bays end up being sent to another hospital? (b) How many patients are treated in the trauma bays on an average 24 hour day? (c) The hospital updated the operating procedures for its staff. This led to a reduction in the coefficient of variation of the length of stay in a trauma bay from 1.5 to 1.25 and a reduction in
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the mean to 1 hour. How will this training program affect the number of patients who have immediate access to a trauma bay? (d) New state regulations require that every emergency department be able to accommodate at least 90% of all patients needing a trauma bay without any waiting. What is the minimum number of trauma bays necessary to meet this requirement? (Assume that the time spent in the trauma bay cannot be changed) 9. A company has started a phone service that uses overseas doctors to provide emergency medical consultations. The responding doctors are based in a country with low wages but with a highly skilled pool of physicians. Responding to each call takes on average 15 minutes. At any given time, there are 4 doctors overseas on duty. Calls arrive every 5 minutes on average (standard deviation is 5 minutes). The company receives $50 from the patient’s insurance company for each consultation. If one of the 4 overseas doctors is available, the firm pays $20 to the doctor and makes $30 in profit. If no doctor is available overseas, the call is rerouted to the U.S. where a local physician answers the question. A local physician is always available to take a call. In this case, the firm pays the $50 to the local physician, so there’s no profit for the company. (a) What is the probability of a call being answered by a physician in the US? (b) What would be the additional revenue per hour obtained if the company managed to have 10 doctors overseas on duty at any given time? (c) What would be the additional profit if the company managed to have 10 doctors overseas on duty at any given time?
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Measures of Performance with a single capacity unit NOTE: IF THE ARRIVAL PROCESS IS EXPONENTIAL, THEN THESE EXPRESSIONS PROVIDE EXACT ESTIMATES OF SYSTEM PERFORMANCE. IF NOT, THEN THESE EXPRESSIONS PROVIDE APPROXIMATE (BUT "GOOD") ESTIMATES OF SYSTEM PERFORMANCE. THIS WORKSHEET IS USED ONLY WHEN m=1. a = average interarrrival time σ = standard deviation of average interarrival time p = average service time σ = standard deviation of average service time I_q = Inventory in queue I_p = Inventory in service I = Inventory in system T_q = cycle time for queue T = cycle time for system Enter a (average interarrival time) 4.00 (standard deviation of average interarrival time) 4.00 Enter p (average service time) 3 (standard deviation of average service time) 3 Enter n (number of customers) 0 Average Capacity Utilization 75.00% Inventory in system 3.00 Inventory in queue 2.25 Inventory in service 0.75 Cycle Time in system 12.00 Cycle time for queue 9.00 Probability of n customers in the system - P(n) 0.25000 Enter σ Enter σ Enter inputs in these yellow cells. Read results in these orange cells.
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Measures of Performance with multiple capacity units - approximations NOTE: THESE EXPRESSIONS PROVIDE APPROXIMATE ESTIMATES FOR SYSTEM PERFORMANCE FOR THE CASE WHEN THE ARRIVAL AND SERVICE PROCESSES DO NOT NECESSARILY FOLLOW AN EXPONENTIAL DISTRIBUTION AND THERE ARE 1 OR MORE CAPACITY UNITS. THIS WORKSHEET IS MORE USEFUL WHEN m > 1. a = average interarrrival time σ = standard deviation of average interarrival time p = average service time σ = standard deviation of average service time I_q = Inventory in queue I_p = Inventory in service I = Inventory in system T_q = cycle time for queue T = cycle time for system m = number of capacity units = probability of exactly n customers being in the system Enter a (average interrarival time) 4 (standard deviation of average interrarival time) 4 Enter p (average service time) 3 (standard deviation of average service time) 3 Enter m (number of capacity units - m > 1) 1 Average Utilization per capacity unit 75.00% Inventory in system 3.00000 #VALUE! Inventory in queue 2.25000 Inventory in service 0.75000 Cycle time in system 12.00000 Cycle time in queue 9.00000 P n Enter σ Enter σ Enter inputs in the  yellow cells. Read the results of the  model from these  orange cells.
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