In a service facility, a manager wants to find “Optimal Service Level” by employing a trade-off graph (a graph of costs vs level of services) between waiting costs and service costs. Describe and show the optimal service level on this graph
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In a service facility, a manager wants to find “Optimal Service Level” by employing a trade-off graph (a graph of costs vs level of services) between waiting costs and service costs. Describe and show the optimal service level on this graph
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- The following information pertains to telephone calls to a motel switchboard on a typical Tuesday.PeriodIncoming Rate(calls perminute)Service Rate(calls per minuteper operator)Number ofOperatorsMorning 1.8 1.5 2Afternoon 2.2 1.0 3Evening 1.4 0.7 3a. Determine the average time callers wait to have their calls answered for each period and theprobability that a caller will have to wait for each period.b. For each case in the previous problem, determine the maximum line length for a probability of96 percent.The director of Burtonsville Civil Defense Agency has been ordered to draw up a disaster plan for assigning casualties to hospitals in the event of a serious earthquake. For simplicity, we will assume that causalities will occur at two points in the city and will be transported to three hospitals. It is estimated that there will be 300 casualties at point A and 200 at point B. Travel times to hospitals 1, 2, and 3 are 25, 15, and 10 minutes, respectively; from point B they are 20, 5, and 15 minutes. Hospital capacities for emergency cases are 250, 150, and 150 patients. How should the victims be assigned to hospitals to minimize the total time lost in transporting them? Disaster Point Hospital Total Casualties 1 2 3 A 25 15 10 300 B 20 5 15 200 Maximum Capacity 250 150 150 Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You…We are in a M/M/1/3 queueing system in which we wish to determine the cost of operating the system. Each customer in the queue costs us $100 per hour and each customer being served costs us $50 an hour. Customers arrive at a rate of 4 per hour and the server can serve customers at a rate of 5 per hour. The following table in the picture provides Pn values, W, and Wq:
- The manager of a regional warehouse must decide on the number of loading docks to request fora new facility in order to minimize the sum of dock costs and driver-truck costs. The manager haslearned that each driver-truck combination represents a cost of $300 per day and that each dockplus loading crew represents a cost of $1,100 per day.a. How many docks should be requested if trucks arrive at the rate of three per day, each dockcan handle five trucks per day, and both rates are Poisson?Food Goblin Supermarkets use both cashiers and baggers to serve customers at check out. During the peak hours, 8 cashiers and 6 baggers serve approximately 75 customers per hour. On average, a cashier spends 6 minutes at checkout and a bagger spends 4 minutes at bagging to serve a customer. Calculate the utilization of cashiers and their capacity cushion during a peak hour. Calculate the utilization of baggers and their capacity cushion during a peak hour. Calculate the overall average utilization of cashiers and baggers during a peak hour.A supermarket has just added a new cash register to reduce the waiting times of the customers during weekends. Since a new cash register is added, the customers expect that their waiting time will be less than the waiting time before the cash register was added. Suppose the sample variance of the waiting times for 25 customers before adding the new cash register is sĩ = 4.8 minutes, while the sample variance of the waiting times for 25 customers after adding the cash register is sź = 2.2 minutes. The manager of the supermarket believes that the waiting times are normally distributed and that the two samples are drawn independently. What is the conclusion? Given that all other criteria are satisfied, should the supermarket continue with the new cash register?
- A local bank has generated the following metrics: an arrival rate of 18 customers per hour with a service time of 3 minutes per customer, and wait times Wq = 0.45 hours for s = 1, Wq = 0.0127 hours for s = 2, and Wq = 0.0017 hours for s = 3. The goal is to solve the following argument: argmin $7s + $49Lq. What is the optimal service level?A catering company must have the following number of clean napkins available at the beginning of each of the next four days: day 1: 15, day 2: 12, day 3: 18, and day 4: 6. After being used, a napkin can be cleaned by one of two methods: fast service or slow service. Fast service costs $0.10 per napkin, and a napkin cleaned via fast service is available for use the day after it is last used. Slow service costs $0.06 per napkin, and a napkin cleaned via slow service is available two days after they were last used. New napkins can be purchased for a cost of $0.20 per napkin. Part A: Formulate the problem as a minimum cost transportation problem.A catering company must have the following number of clean napkins available at the beginning of each of the next four days: day 1: 15, day 2: 12, day 3: 18, and day 4: 6. After being used, a napkin can be cleaned by one of two methods: fast service or slow service. Fast service costs $0.10 per napkin, and a napkin cleaned via fast service is available for use the day after it is last used. Slow service costs $0.06 per napkin, and a napkin cleaned via slow service is available two days after they were last used. New napkins can be purchased for a cost of $0.20 per napkin. Part A: Formulate the problem as a minimum cost transportation problem. Part B: Solve the problem (provide exact values for all variables and the optimal objective function).
- CarpetPlus sells and installs floor covering for commercial buildings. A CarpetPlus account executive, was just awarded the contract for five jobs. This executive now must assign a CarpetPlus installation crew to each of the five jobs. Because the commission, the executive will earn depends on the profit CarpetPlus makes, This executive would like to determine an assignment that will minimize total installation costs. Currently, five installation crews are available for assignment. Each crew is identified by a color code, which aids in tracking of job progress on a large white board. The following table shows the costs (in hundreds of dollars) for each crew to complete each of the five jobs. Crew 1 2 3 4 5 Red 30 44 38 47 31 White 25 32 45 44 25 Blue23 40 37 39 29 Green 26 38 37 45 28 Brown 26 34 44 43 28 (a) Develop a network representation of the problem. (b) Formulate and solve a linear programming model to determine the minimum cost assignment..opOil, a refiner in Indiana, serves three customers near Nashville, Tennessee and maintains consignment inventory (owned by TopOil) at each location. Currently, TopOil uses TL transportation to deliver separately to each customer. Each truck costs $800 plus $250 per stop. Thus delivering to each customer separately costs $1050 per truck. TopOil is considering aggregating deliveries to Nashville on a single truck. Demand at the large customer is 60 tons per year, demand at the medium customer is 24 tons per year, and demand at the small customer is 8 tons per year. Product cost for TopOil is $10,000 per ton and they are using a holding cost of 25 percent. Truck capacity is 12 tons. What is the optimal order quantity to each customer assuming TopOil develops a tailored aggregation policy?TopOil, a refiner in Indiana, serves three customers near Nashville, Tennessee and maintains consignment inventory (owned by TopOil) at each location. Currently, TopOil uses TL transportation to deliver separately to each customer. Each truck costs $800 plus $250 per stop. Thus delivering to each customer separately costs $1050 per truck. TopOil is considering aggregating deliveries to Nashville on a single truck. Demand at the large customer is 60 tons per year, demand at the medium customer is 24 tons per year, and demand at the small customer is 8 tons per year. Product cost for TopOil is $10,000 per ton and they are using a holding cost of 25 percent. Truck capacity is 12 tons. What is the optimal order quantity to each customer assuming TopOil aggregates shipments to each of the three customers on every truck that goes to Nashville?