Epsilon Airlines services predominately the eastern and southeastern United States. A vast majority of Epsilon's customers make reservations through Epsilon's website, but a small percentage of customers make reservations via phone.Epsilon employs call-center personnel to handle these reservations along with any problems with the website reservation system and for the rebooking of flights for customers if their plans change or their travel is disrupted. Staffing thecall center appropriately is a challenge for Epsilon's management team. Having too many employees on hand is a waste of money, but having too few results in very poor customer service and the potential loss of customers.Epsilon analysts have estimated the minimum number of call-center employees needed by day of week for the upcoming vacation season (June, July, and the first two weeks of August). These estimates are given in the following table.DayMinMondayTuesdayWednesdayThursdayFridaySaturdaySundayMinimum Number ofEmployees Needed75504570958550The call-center employees work five consecutive days and then have two consecutive days off. An employee may start work any day of the week. Each call-center employee receives the same salary. Assume that the schedule cycles andignore start-up and stopping of the schedule. Develop a model that will minimize the total number of call-center employees needed to meet the minimum requirements. (Let X; = the number of call-center employees who start work on dayi where i = 1 = Monday, i = 2 = Tuesday, etc). s.t.MondayTuesdayWednesdayThursdayFridaySaturdaySundayX1, X2, X3, X4, X5, X6, X7 20Find the optimal solution.(X₁, X2, X3, X₁1 X5, X6, X 7) = (4'Give the number of call-center employees that exceed the minimum required.(M, Tu, W, Th, F, Sa, Su) =

Linear programming is one of the mathematical techniques that is widely used by companies. This…

Answered: The call-center employees work five…

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 small bank is trying to determine how many tellers toemploy. The total cost of employing a teller is $100 perday, and a teller can serve an average of 60 customersper day. On average, 50 customers arrive per day at thebank, and both service times and interarrival times areexponentially distributed. If the delay cost per customerday is $100, how many tellers should the bank hire?
Consider the case of Conrad's Cookie Company, where he and two of his friends (Jared and Jack) are working to make and sell cookies. They have just one oven and can bake up to two dozen cookies at a time. The oven can bake two dozen cookies simultaneously (of similar or different ingredients) or one dozen only. If one dozen is baking in the oven, baking time will not be any different from baking two dozen simultaneously. The sequence of baking steps and respective durations are below. Mixing and Spooning (together) 3 mins/dozen Loading 1 minutte/dozen. Baking 8 mins. baking time for one or two dozens. Cooling 6 minutes Packing 5 mins/dozen cookies Payment (to be done after packing only) 1 minute per order If all orders are 4 dozen cookies, a) What is the best way to assign Conrad and his friends to jobs in order to maximize capacity? Find highest theoretical capacity and bottleneck of the process. b) Once system warms up, is the capacity the same…
Fast Auto Service provides oil and lube service for cars. It is known that the mean time taken for oil and lube service at this garage is 15 minutes per car and the standard deviation is 2.4 minutes. The management wants to promote the business by guaranteeing a maximum waiting time for its customers. If a customer's car is not serviced within that period, the customer will receive a 50 % discount on the charges. The company wants to limit this discount to at most 8% of the customers. What should the maximum guaranteed waiting time be? Assume that the times taken for oil and lube service for all cars have a normal distribution. Round your answer to the nearest minute.
On average, 100 customers arrive per hour at theGotham City Bank. The average service time for eachcustomer is one minute. Service times and interarrivaltimes are exponentially distributed. The manager wantsto ensure that no more than 1% of all customers willhave to wait in line for more than five minutes. If thebank follows the policy of having all customers join asingle line, how many tellers must the bank hire?
A Company that makes shopping carts for supermarkets and other stores recently purchased some new equipment that reduces the labor content of the jobs needed to produce the shopping carts. Prior to buying the new equipment, the company used 4 workers, who produced an average of 87 carts per hour. Workers receive $13 per hour, and machine coast was $32 per hour. With the new equipment, it was possible to transfer one of the workers to another department, and equipment cost increased by $18 per hour while output increased by four carts per hour.a) Compute the multifactor productivity (MFP) (labor plus equipment) under the Prior to buying the new equipment. The MFP (carts/$) = ( ) (round to 4 decimal places).b) Compute the % growth in productivity between the Prior to and after buying the new equipment. The growth in productivity = ( ) % (round to 2 decimal places)
H4. A manufacturing process consists of three processes. Step 1 requires 4 minutes per unit, step 2 requires 6 minutes per unit, and step 3 requires 7 minutes per unit. 20% of units that complete the third step require rework, which means those units must start the process over at step 2 (processing times are the same for units being reworked) and rework is always successful. Demand at the shop is 0.4 units per minute. What is the capacity of the shop (in units per minute)?
Consider two separate systems. One has an interarrival time of two hours andthe other an interarrival time of four hours. If the two systems are combined such that thecombined system’s demand is the sum of the demands from the two original systems,what is the interarrival time for the combined system?
Consider a Poisson queue with the following steady-state probabilities: po = 1/3, p1 = 1/2, p2 = 1/6, and pn = for n = 3,4,5, ... . What is the minimum number of stools that would accommodate all customers in the system at least 75% of the time in steady state? 3 stools O 2 stools none of the other choices O 1 stool
An emergency room (ER) at a Prisma Health Hospital has 10 total beds it can hold patients, i.e., the capacity of the queueing system of this ER is 10. Patients arrive to the ER at a rate of 5 per hour. Therefore, we have that λn = 6 for n = 0, 1, . . . , 9 and λ10 = 0 for this queueing system. A patient is seen by an ER doctor as the ‘service’ of this queueing system. The amount of time required for an ER doctor to treat a patient is exponentially distributed with a mean of .4 hours. We seek the minimum number of ER doctors so that the expected time of a patient waiting to be seen (so the Wq) is less than or equal to 15 minutes (.25 hours). You should begin by analyzing s = 1 and show any calculations that were used to determine Wq for each number of servers that you considered until you meet the target metric.
The utilization of baggers is Food Goblin Supermarkets use both cashiers and baggers to serve customers at check out. During the first 7 hours of each workday (Monday-Friday), 6 cashiers and 2 baggers serve approximately 25 customers per hour. A cashier and a bagger who require approximately 6 minutes at checkout and 4 minutes at bagging serve each customer. a. The utilization of cashiers is 41.7%. (Enter your response rounded to one decimal place.) %. (Enter your response rounded to one decimal place.) v an example Part 2 of 3 Get more help. O Points: 0 of 3 Clear all Check answer O
11. Automobiles arrive at a tollbooth on a highway completely at random according to a Poisson process with rate À = 4 cars per hour. Determine the following: a. The probability that the time between any two successive arrivals exceeds 20 minutes. b. The probability that exactly four cars arrive in any given hour. c. The probability that more than five cars arrive in any given hour. d. The probability that more than 10 cars arrive in any given two-hour period. e. A person working for the transportation department begins counting arrivals at the tollbooth at 8 A.M. What is the probability that he counts 20 arrivals before 12 noon? (Use a normal approximation for your calculations.)
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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