A warehouse has 2 docks for unloading. The arrival rate of trucks at the warehouse is 5 trucks perhour (Poisson distributed). The unloading rate is 4 trucks per hour (Poisson distributed). The driver-truck combination represents a cost of S275 per day. Each dock plus labor represents a cost of $900per day. What's the minimum dock-crew and driver-truck cost (pick nearest answer)?a. 2364.10b. 0.75c. 1345.00d. 2670.76e. 0.25

The utilization rate of the docks to understand how efficiently they are being used. Determine the…

Answered: A warehouse has 2 docks for unloading.…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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A supplier ships goods from Richmond, VA to three market places in 3 cities (Chicago, IL; Athens, GA; St. Luis, MO). The supplier can ship every day, every other day, or every third day. There is a penalty of $0.30/cwt for each day delayed. Consolidating shipments allows for lower transportation costs from larger loads, but incurs penalty costs due to the delay. Transportation Rate (S/cwt) Shipment City Weight/day LTL 50,000 lb 50000 lb Chicago, IL 18,000 lb (180 cwt) 1.50 1.25 Athens, GA 15,000 lb (150 cwt) 1.35 1.00 St. Luis, MO 12,000 lb (120 cwt) 2.00 1.50 Total 45,000 Ib = 450 cwt Find what is the cost for the following: Shipping Every Day Shipping on the alternate Day (every two days) Shipping every three Day
A city would like to know how many vehicles it could move through its streets in an emergency. The most likely situation is an evacuation starting at the school and ending at the park. The connections between these two locations, plus their capacity and direction, is shown below. Oak Street F A Street School Park Elm Street 2nd Street E Path A В D E F Сaрacity 15 15 10 10 25 10 10 (Round your answer to the nearest whole number.) Maximum Flow
Pete's Market is a small local grocery store with only one checkout counter. Assume that shoppers arrive at the checkout lane according to a Poisson probability distribution, with an arrival rate of 20 customers per hour. The checkout service times follow an exponential probability distribution, with a service rate of 25 customers per hour. The manager’s service goal is to limit the waiting time prior to beginning the checkout process to no more than five minutes. Also the manager of Pete's Market wants to consider one of the following alternatives for improving service. Calculate the value of Wq for each alternative. Hire a second person to bag the groceries while the cash register operator is entering the cost data and collecting money from the customer. With this improved single-server operation, the service rate could be increased to 33 customers per hour. Round your answer to three decimal places. Do not round intermediate calculations.Wq = 2.797 minutes Hire a second person to…
Ted Glickman, the administrator at D.C. General Hospital emergency room faces the problem of providing treatment for patients who arrive at different rates during the day. There are 4 doctors available to treat patients when needed. If not needed, they can be assigned other responsibilities (such as doing lab tests, reports, X-ray diagnoses) or else rescheduled to work at other hours. It is important to provide quick and responsive treatment, and Ted feels that, on the average, patients should not have to sit in the waiting area for more than 4 minutes before being seen by a doctor. Patients are treated on a first-come, first-served basis and see the first available doctor after waiting in the queue. The arrival pattern for a typical day is as follows: Time Arrival Rate 9 A.M.−3 P.M. 8 patients/hour 3 P.M.−8 P.M. 3 patients/hour 8 P.M.−midnight 13 patients/hour Arrivals follow a Poisson distribution, and treatment times, 12…
The VBO grocery store has a checkout counter with a full-time cashier. Customers arrive randomly with an average rate of 20 per hour. The distribution of service time is exponential with an average of 2 minutes. Occasionally, this situation causes a long queue and customer complaints. Since there is no room for another cashier, the manager plans to hire another person to help pack the groceries and reduce the expected service time to 1.5 minutes, still with exponential distribution. The manager wants the percentage of time when there are more than 2 customers at the cash register to be less than 25%. He also wants no more than 5% of customers to have to wait 5 minutes or more before starting service or 7 minutes or more before finishing service. a) Use the formulas from the M/M/1 model to calculate L, Lq, W and Wq, π0, π1 and π2 of the current transaction. What is the probability that there are more than 2 customers at the cash register? (b) Repeat (a) for the helper alternative.
During the evening hours, an average of 52 customers can be found in Sachi’s Sports Bar. About 40 customers arrive each hour. Using Little’s Law, how long does each customer stay at Sachi’s?
3. The Friendly Neighbor Grocery Store has a single checkout stand with a full-time cashier. Customers arrive randomly at the stand at a mean rate of 20 per hour. The service-time distribution is exponential, with a mean of 2 minutes. This situation has resulted in occasional long lines and complaints from customers. Therefore, because there is no room for a second checkout stand, the manager is considering the alternative of hiring another person to help the cashier by bagging the groceries. This help would reduce the expected time required to process a customer to 1.5 minutes, but the distribution still would be exponential. The manager would like to have the percentage of time that there are more than two customers at the checkout stand down below 25 percent. (a) Use the formulas for the M/M/1 model to calculate L, W, W₁, Lq, Po, P₁, and P₂ for the current mode of operation. What is the probability of having more than two customers at the checkout stand? (b) Repeat part (a) for this…
A grocery store has three open checkout counters. There is a single queue leading up to these three counters. On average, 45 shoppers arrive at this queue. The coefficient of variation of the interarrival time is equal to 1. The average service capacity of each of the three servers is 18 customers per hour, and the coefficient of variation of service time distribution for each server is 3. (a) (3 points) What is the percentage decrease in capacity utilization when one more checkout lane is added to the system? (b) (7 points) On average, how many customers are waiting in the queue?
A retail catalog operation employs a bank of six telephone operators who process orders using computer terminals. When a terminal breaks down, it must be disconnected and taken to a nearby electronic repair shop, where it is repaired. The mean time between terminal breakdowns is six working days, and the mean time required to repair a terminal is two working days (both exponentially distributed). As a result of lost sales, it costs the mail-order operation an estimated $50 per day in lost profits each day a terminal is out for repair. The company pays the electronics repair shop $3000 per year on a service agreement to repair the terminals. The company is considering the possibility of signing a new service agreement with another electronics repair shop that will provide subsitutute terminals while the broken ones are at the repair shop. However, the new service agreement would cost the mail-order operation $15,000 per year. Assuming that there are 250 working days in a year, determine…
A mom and pop car wash with 1 drive through lane gets an average of 4 cars per hour, with a Poisson distribution. The washing and drying process has a mean of 12 minutes, M= exponentially distributed, and a car cannot enter the lane until the car in front of it is finished drying (there can only be one car in the lane at one time). Due to the location, there is only space enough to hold 5 cars in line waiting to get washed. However, they rent space from the empty lot next door that is large enough to hold as many cars as needed. They decided to rent a section that will hold only 3 cars. a) If they decide to rent a section that will hold 3 cars, what will you solve for to determine the probability that they will still turn cars away? b) They promise each customer their money back ($10) if it takes longer than 30 minutes to get their car washed (from the time they enter). They are open 8 hours per day. How much money can they expect to give away per day?
A study-aid desk staffed by a graduate student has been established to answer students' questions and help in working problems in your OSCM course. The desk is staffed eight hours per day. The dean wants to know how the facility is working. Statistics show that students arrive at a rate of four per hour and the distribution is approximately Poisson. Assistance time averages 10 minutes, distributed exponentially. Assume population and line length can be infinite and queue discipline is FCFS. Calculate the percentage utilization of the graduate student. Note: Round your answer to 1 decimal place. Calculate the average number of students in the system, including the graduate student service desk. Note: Round your answer to the nearest whole number. Calculate the average time in the system. Note: Round your answer to the nearest whole number. Calculate the probability of four or more students being in line or being served. Note: Round your intermediate calculations to 3…
A supplier ships goods from Richmond, VA to three market places in 3 cities (Chicago, IL; Athens, GA; St. Luis, MO). The supplier can ship every day, every other day, or every third day. There is a penalty of $0.30/cwt for each day delayed. Consolidating shipments allows for lower transportation costs from larger loads, but incurs penalty costs due to the delay. Transportation Rate (S/cwt) Shipment City Weight/day LTL 50,000 lb 50000 lb Chicago, IL 18,000 lb (180 cwt) 1.50 1.25 Athens, GA 15,000 lb (150 cwt) 1.35 1.00 St. Luis, MO 12,000 lb (120 cwt) 2.00 1.50 Total 45,000 Ib = 450 cwt Find what is the cost for the following: Shipping Every Day Shipping on the alternate Day (every two days) Shipping every three Day

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