Reference no: EM131021849

Problem-1.

A manufacturing company has a production line that is composed of 5 serial stations. Inputs arrive at station 1. The output of station 1 becomes the input to station 2. The output of station 2 becomes the input of station 3, and so on. The output of station 5 is the finished product. Table below shows the cycle time at each station when there is only one employee is assigned to the station.

Station	1	2	3	4	5
Cycle time per employee	3 min. per unit	1.75 min. per unit	2.8 min. per unit	2 min. per unit	3.6 min. per unit

Here is how we interpret this information: If the worker at station 1 works non-stop, then station 1 completes processing 1 unit every 3 minutes. If the worker at station 2 works non-stop, then station 2 completes processing 1 unit every 1.75 minutes, and so on. The output of each station is proportional to the number of workers assigned to that station. That is, if there are two workers assigned to a station, the station output doubles. No work-in-process is allowed to accumulate in the system. The production line operates 40 hours per week.

NOTE: SHOW ALL YOUR WORK. USE 4 DECIMAL PLACES IN ALL CALCULATIONS.

a) What is the maximum weekly throughput rate of the process when one employee is assigned to work at each station?

b) Which station is the bottleneck of the process when one employee is assigned to work at each station?

c) Suppose the week starts and ends with no work-in-process. That is, the work starts at station 1 at the beginning of the week and all units processed at station 1 throughout the week are processed in the remaining stations and become "finished goods" before the end of the week. When one employee is assigned to work at each station, what is the weekly utilization rate of the workers at each station?

d) Suppose there are 10 cross-trained employees available to work at any station.

i. How many employees should be assigned to each station to maximize the process throughput rate?

ii. What is the resulting maximum weekly throughput rate of the process?

iii. What is the resulting weekly utilization rate of workers at each station? (Note: Compute the utilization rate for each station.)

Problem 2.

Shevrolet is considering three sites, A,B, and C at which to locate a factory to build its new electric car, Shevvy-Electra. The company prefers to build the facility at a site that has the minimum cost where cost is measured by the annual fixed cost plus variable cost of production. The data is provided below.

Site	Annual Fixed Cost ($ per year)	Variable Cost ($ per vehicle produced)
A	$15,000,000	$6200
B	$25,000,000	$3000

NOTE: SHOW ALL YOUR WORK. USE 4 DECIMAL PLACES IN ALL CALCULATIONS.

a) Shevrolet's goal is to break-even at 2500 vehicles. If site A is chosen, what should be the unit sales price of the vehicle to break even at that production volume?

b) Shevrolet's goal is to break-even at 2500 vehicles. If site B is chosen, what should be the unit sales price of the vehicle to break even at that production volume?

c) Answer the following questions to determine the minimum cost option for different production volumes:

i. For what level of production volume, would site A be the minimum cost option? Provide a range.

ii. For what level of production volume, would site B be the minimum cost option? Provide a range.

Problem-3.

On the average, 40 people arrive at a fitness center per hour. Of all the users of the fitness center, 20% do only a full body workout and the remaining 80% only do cardio exercises. People who do a full body workout spend 75 minutes at the fitness center and those who do only cardio exercises spend 60 minutes at the fitness center on the average.

NOTE: SHOW ALL YOUR WORK. USE 4 DECIMAL PLACES IN ALL CALCULATIONS.

a) What is the average number of people working out at the fitness center at any point in time doing a full body workout?

b) What is the average number of people working out at the fitness center at any point in time doing cardio exercises?

c) Suppose everyone at the fitness center uses a locker. How many lockers are used on the average at any point in time?

Problem-4.

In this question you will analyze and compare two queueing configurations that are commonly used in service industries, including grocery stores.

The historical data at a grocery store shows that the average arrival rate at the checkout lanes (cashiers) is around 90 customers per hour during rush hour. The arrivals can be modeled by Poisson distribution.There are a total of 9 cashiers (i.e., 9 checkout lanes) working during the rush hour. Each cashier can checkout 15 customers per hour on the average. The service times are known to follow an exponential distribution.

If the grocery store is designed for Configuration-1, there is a separate queue for each cashier. You can assume that the same number of customers join each queue on the average. This means that the average arrival rate to each cashier is 90/9=10 customers per hour during rush hour and there are 9 queues, each with only one server.

If the grocery store is designed for Configuration 2, there is only one queue that every customer has to join to check out. The combined queue is served by 9 cashiers. In this case, the customer that is first in line is served by the first cashier that becomes available. In Configuration 2, there is only one queue with 9 servers. The average arrival rate to the queue is the total number of customers that have to checkout, i.e., 90 customers per hour during rush hour.

NOTE: SHOW ALL YOUR WORK. USE 4 DECIMAL PLACES IN ALL CALCULATIONS.

a) What is the average waiting time in the system (in minutes) for a customer in Configuration 1?

Hint: Each cashier (hence each queue) has the same result.

b) What is the average waiting time in the system (in minutes) for a customer in Configuration 2?

c) How much time, on the average, does a customer save as he/she checks out when Configuration 2 is used instead of Configuration 1?

d) Compute the average waiting time in queue, the average number of customers waiting in line, the average number of customers in the system, the average server utilization, and probability of delay for eachconfiguration. (See the table below.)

Performance measure	Configuration 1	Configuration 2
Average wait time in queue (in  minutes)
Average number of customers in queue (per queue)
Average number of customers in system (per queue)
Average server utilization
Probability of delay

e) Suppose the grocery store decides to change the layout of the store, including the number of the checkout lanes. The store will be designed for Configuration 2. What is the minimum number of checkout lanes needed for the average wait time in the queue to be below 2 minutes during rush hour?

f) Read the New York Times article: A Long Line for a Shorter Wait at the Supermarket (https://nyti.ms/xZ10Ae). Based on the information provided in the article and your analysis in this question, why is it better to configure the checkout lanes as one combined queue instead of multiple separate queues? Explain clearly.

Problem-5.

Detailed information on the application process to register a trademark is available at the website of US Department of Patent and Trademark Office (USPTO). Let us assume that each trademark application received by USPTO is reviewed by an attorney. The attorney reviews the applications on a first-come-first-serve (FCFS) basis.USPTOreceivesan average of 995 new trademark application files per year. Assume that the submission times of applications are uncertain and variable (i.e. "arrival times" cannot be predicted with 100% accuracy) but are known to follow a Poisson distribution. The attorney, on the average, has the ability to process 1000 files a year. Theattorney's time to review a file is known to follow the exponential distribution.

a) Completethe table below to determine the impact of increasing service rates on average wait time in queues. The average arrival rate is 995 files per year. Assume 30 days per month and 12 months per year.

Average service rate (mu)	Server utilization	Wq (in days)	Lq
1000		71.6400
1050		6.2026
1100		3.1013
1150		2.0095
1200		1.4561

i. Using the data in the table, prepare a chart that plots the Wq (in days) in the y-axis and the average service rate in the x-axis. (You can do this manually or using Excel.) How does the wait time in the queue change as the service rate increases? Explain clearly. Include the chart in your answer report.

ii. Using the data in the table, prepare a chart that plots the Lq in the y-axis and the average service rate in the x-axis. (You can do this manually or using Excel.) How does the length of the queue change as the service rate increases? Explain clearly. Include the chart in your answer report.

b) Prepare the table below to determine the impact of arrival rates on average wait time in queues. The average service rate is 1000 files per year. Assume 30 days per month and 12 months per year.

Average arrival rate (lambda)	Server utilization	Wq (in days)	Lq
775			2.6694
825			3.8893
875			6.1250
925			11.4083
975			38.0250

i. Using the data in your table, prepare a chart that plots the Wq (in days) in the y-axis and the average arrival rate in the x-axis. (You can do this manually or using Excel.) How does the wait time in the queue change as the arrival rate increases? Explain clearly. Include the chart in your answer report.

ii. Using the data in your table, prepare a chart that plots the Lq in the y-axis and the average arrival rate in the x-axis. (You can do this manually or using Excel.) How does the length of the queue change as the arrival rate increases? Explain clearly. Include the chart in your answer report.

c) Suppose USPTO can employ up to three attorneys to review the trademark applications. Each attorney has the same average service rate, i.e., 1000 files per year. All attorneys work simultaneously to review the incoming files that wait in a single queue (as in Configuration 2 of Problem 5). The average arrival rate is 995 files per year. Table below shows various performance measures when there is/are 1,2, or 3 attorneys employed.

S (no. of attorneys)	Lq	Server utilization	P(0)	P(delay)
1	198.0050	0.9950	0.0050	0.9950
2	0.3273	0.4975	0.3356	0.3306
3	0.0446	0.3317	0.3655	0.0898

i. Notice that P(0)=1-(server utilization) when S=1. Why is the same relation not true when S>1? Explain clearly.

ii. Notice that P(delay)=(server utilization) when S=1. Why is the same relation not true when S>1? Explain clearly.

d) Review your analysis in parts (a), (b), and (c) to answer the following questions:

i. What is the effect of increasing utilization rates on the average wait time in the queue and the average number waiting in the queue? Explain clearly.

ii. In your opinion, what should be the utilization rate of the employee(s) for the wait times to be "acceptable" in this context? Explain clearly. Hint: First, think of how long the wait time in the queue should be to be "acceptable." Then, identify the utilization rate corresponding to the wait time.

Problem-6.

One of the most important considerations in retail operations is the amount of inventory carried for seasonal products. Matching supply with demand is not easy because some of the seasonal products are manufactured overseas and have to be ordered with a long lead time. Consider the following: The length of the season to sell a fashion apparel or shoe is less than 3 months. In contrast, the manufacturers require that orders be given at least 6 months in advance to guarantee availability of products at the beginning of a sales season. The long lead times prevent retailers from placing additional orders during the season because any additional items would not be received before the season is over. This puts department stores such as Nordstrom in a difficult situation; order too few in advance and you lose potential sales during the season, and order too much in advance and you have unsold merchandise at the end of the season.

One group of seasonal merchandise sold by Nordstrom is baby's shoes. The company gathers regional sales forecasts for the upcoming year and orders shoes from the manufacturers well ahead of the sales season. Information on two products, including the purchasing cost per unit, sales price per unit, salvage value per unit at the end of the season, mean demand, and standard deviation of demand for each item are provided below.

Item	Purchasing cost per unit (c)	Sales price per unit (p)	Salvage value per unit (s)	Demand forecast: Demand is normally distributed
				Average (mean) demand	Forecast error (standard deviation of demand)
#1 Baby Boy summer sandal (size 12-18 months)	$16.00	$24.99	$4.99	22,500	2756
#2 Baby Girl summer sandal (size 12-18 months)	$19.00	$32.99	$12.99	23,500	4550

NOTE: SHOW ALL YOUR WORK. USE 4 DECIMAL PLACES IN YOUR CALCULATIONS.

a) For many years, the company aimedat95% service level for all the items in the baby's shoes, i.e., the order quantity for each item has been determined to avoid stock-outs 95% of the time. Compute the order quantity for each item toguarantee this service level. Complete the table below. Show all your work.

Item	Target service level	Order quantity	Safety stock level	Probability of a stockout during the season P(D≥Q)
#1	95%
#2	95%

b) Should the company use the same service level for all the seasonal products? Why or why not? Discuss clearly.

c) The company decides to use the newsvendor model to maximize its expected profit during the season. Compute the following for both items using the newsvendor model. Show all your work.

Item	Unit cost of overage	Unit cost of underage	Critical fractile	Optimal order quantity	Safety stock level	Probability of a stockout during the seasonP(D≥Q)	Probability of having unsold merchandise at the end of the seasonP(D<Q)
#1
#2

d) Suppose the manufacturer of the baby sandals offers a return credit to the retailer. The manufacturer will buy back any unsold unit for $10 at the end of the season. Use the newsvendor model to determine the new optimal order quantity in this case. Complete the table below. Show all your work.

Item	Unit cost of overage	Unit cost of underage	Critical fractile	Optimal order quantity	Safety stock level	Probability of a stockout during the seasonP(D≥Q)	Probability of having unsold merchandise at the end of the seasonP(D<Q)
#1
#2

Problem-7.

Surfsports Inc. manufactures jet-skis. The most expensive component of a jet-ski is the pump. The pump costs Surfsports $2800 per unit and constitutes 40% of the total cost of the jet-ski. Surfsports sells 3500 jet-skis each year. The demand for the product has been fairly constant over the years. Currently, Surfsportsuses the EOQ model to determine how many pumps to purchase from its supplier. The ordering cost is $200 per order and the annual holding cost per unit is 20% of the variable cost of the product. The supplier's lead time is 5 days. There are 350 operating days within a year.

NOTE: SHOW ALL YOUR WORK. USE 4 DECIMAL PLACES IN YOUR CALCULATIONS.

a) Using the EOQ Model, what is the optimal order quantity for the pump?

b) Using the EOQ Model, how many orders are placed per year?

c) Using the EOQ Model, what is the total annual ordering cost?

d) Using the EOQ Model, what is the total annual inventory holding cost?

e) Using the EOQ Model, what is the reorder point for the product?

Problem 8.

You are employed as an operations and quality assurance analyst at the Darden Restaurant Group's Restaurant Support Center at Orlando, FL. Darden owns and operates more than 2000 restaurants in the United States, including the Red Lobster and Olive Garden chains. Information about Darden is available at https://www.darden.com/about/. Information about Darden's Restaurant Support Center is available at https://www.darden.com/careers/support_center.asp.

Your manager asked you to analyze customer complaint records and make recommendations to improve operations quality and increase customer satisfaction at an Olive Garden restaurant. At each restaurant, when a customer asks for a receipt, the wait staff brings the customer a blank feedback card along with the receipt. The wait staff encourages the customers to fill in the feedback cards before they leave. Most customers do not bother filling the card, but some take this as an opportunity to praise or complain about various aspects of their dining experience. The restaurant has sent the feedback cards filled by customers that dined in the restaurant in the past 4 weeks. An intern at the company copied the information provided by the customers to an Excel spreadsheet and has classified each complaint into one of several categories provided by your manager. You can see the Excel file on Blackboard. The data includes the complaints only.

a) The Pareto principle says that about 80% of operational problems are associated with only 20% of the causes. Prepare a Pareto Chart for the restaurant to show the number and frequency of quality related incidents by category. You can refer to https://ksrowell.com/blog-visualizing-data/2012/07/17/making-a-pareto-chart-in-excel/ and https://www.youtube.com/watch?v=TBtGI2z8V48 to learn how to prepare Pareto Charts on Excel. Add your Pareto Chart to your report as Figure-1 (see below).

In your Pareto Chart, the x-axis should show all categories of complaints. The primary y-axis must be the number of complaints. The primary series must be displayed as a column chart (bar chart). The columns display the categories in descending order of number of complaints (i.e, the tallest bar is the first and the shortest bar is the last displayed on the x-axis). The secondary y-axis must be the cumulative percentage of complaints (reported as percentages). The secondary series must be displayed as a line chart. These are the norms of a Pareto Chart.

Figure-1. Pareto chart of complaints

b) Complete Table-1 below and report the top three most common categories of complaints at the restaurant. The analysis you conduct to complete the Pareto chart is sufficient to complete the table; the table provides more detailed information about the top three causes of complaints at the restaurant.

Rank (from most frequent to least frequent)	Category	No. of complaints	Frequency  of incidents as a % of total	Cumulative % of incidents
1
2
3

Table-3.Top three most common quality-related incidents at the restaurant.

c) Although the goal is to minimize and eliminate the complaints at this restaurant (and all others that belong to Darden), it is impossible to tackle all problems at the same time. It is too time consuming and expensive to ensure a 100% defect-free process. The restaurant wants to identify a few areas that would have the highest impact on quality. What are the types of problems that the restaurant should target first to increase customer satisfaction? What recommendations can you make to the company to focus their efforts to minimize the number of complaints? Be very specific about your recommendations (i.e. discuss what exactly needs to be done to prevent similar complaints in the future).

Attachment:- Data_Sheet.rar