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?

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?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter5: Network Models

Section: Chapter Questions

Problem 71P

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7. 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?b. An employee has proposed adding new equipment that would speed up the loading rate to 6trucks per day. The equipment would cost $100 per day for each dock. Should the managerinvest in the new equipment?
On average, 100 customers arrive per hour at GothamCity Bank. It takes a teller an average of two minutesto serve a customer. Interarrival and service times areexponentially distributed. The bank currently has fourtellers working. The bank manager wants to compare thefollowing two systems with regard to the average numberof customers present in the bank and the probability that acustomer will spend more than eight minutes in line.■ System 1: Each teller has his or her own line (andno moving between lines is permitted). Arrivingcustomers are equally likely to choose any teller.■ System 2: All customers wait in a single line forthe first available teller.If you were the bank manager, which system wouldyou prefer?
Consider the Dynamic Program formulation of the n-class optimal booking problem with sequential arrivals. In thisproblem, show some monotonicities of the value function.• Jt(x) − Jt(x − 1) is non-decreasing in t, ∀x.• Jt(x) − Jt(x − 1) is non-increasing in x, ∀t.Consider that the second property implies the first property. To prove the second property, given Dt, consider the discrete concavity of Ht(Dt, x) = max0≤u≤min{Dt,x} (pt)u + Jt−1(x − u) in x, i.e., Ht(Dt, x + 1) − Ht(Dt, x) ≤ Ht(Dt, x) − Ht(Dt, x − 1) for any x ∈ Z+ for any t. Image attatched for clarity.
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?
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 small mail-order firm Sea’s Beginning has onephone line. An average of 60 people per hour call inorders, and it takes an average of one minute to handlea call. Time between calls and time to handle calls areexponentially distributed. If the phone line is busy, Sea’sBeginning can put up to c 2 1 people on hold. If c 2 1people are on hold, a caller gets a busy signal and calls acompetitor. Sea’s Beginning wants only 1% of all callersto get a busy signal. How many people should it be ableto put on hold, that is, what is the required value of c?
A shipping company operates 10 container ships that can each carry 5000 containers oneach journey between ports. They want to be able to load and unload 20,000 containerseach week. Assume their ships always travel fully loaded. What is the longest averagetravel time between ports that allows them to meet their goal of 20,000 containers perweek?
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?
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. a) What is the annual transportation and holding cost if TopOil ships a full truckoad each time a customer is running out of stock? How many days of inventory is carried at each customer under this policy.
A refiner in city Q serves three customers near city Wand maintains consignment inventory (owned by the refiner) at each location. Currently, the refiner uses TL (truckload) transportation to deliver separately to each customer. Each truck costs $650 plus $300 per stop. The refiner is considering aggregating deliveries to city Won a singletruck. The demand ofthe first customer is 96 tons a year, the demand of the second customer is 24 tons per year, and the demand of the third customer is 9.6 tons per year. Product cost is $7,700 per ton, and it uses a holding cost of 15%. Truck capacity is 15tons. a.What is the annual transportation and holding cost if the refiner ships a full truckload each time a customer is running out of stock? How many days of inventory is carried at each customer under this policy? b.What is the optimal delivery policy to each customer if the refiner ships separately to each of them? What is the annual transportation and holding cost? How many days of inventory…
A medical clinic performs three types of medical tests that use the same machines. Tests A, B, and C take 15 minutes, 30 minutes, and 1 hour, respectively, with respective profits of $120, $240, and $500. The clinic has four machines and four workers available. One person is qualified to do test A, two to do test B, and one to do test C. If the clinic has a rush of customers for these tests, how many of each type should it schedule in a 10-hour day to maximize its profit?
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?