More challenges, more analysis! Samba Sneakers You are learning that there's alwaysa new challenge that needs your analysis and attention. You returned from aquick lunch to find another e-mail...

Question One:
Customer service standards
Cynthia Crowninshield invites you into the Shuzworld small conference room to discuss your
involvement in a new customer service project.
"As you may know," she begins, "We're looking for Shuzworld to grow over the next five years by
opening small retail stores in major malls around the country. We want to have a boutique feel to these
stores, and we're going to stock them with our best selling brands and with our most profitable lines."
She pauses for a moment. "Here's the question. What should the staffing levels be? We want the
customer to feel special when she comes to the Shuzworld store. Say she comes to the store over the
lunch hour: she needs to be able to find her shoes, make her purchase, and get back to the office."
Crowninshield slides a store layout plan to you across the conference room table. "We will staff these
stores with salespeople on the floor and we think one full-time cashier will be sufficient. Our pilot test
showed that we can expect a sale every ten minutes on the average and each transaction at the register
takes an average of five minutes."
"The pilot team looking at customer service standards put together a list of questions they need
answered." She hands a copy of the list to you.
Shuzworld Mall Store Customer Service Standards
1. How many customers will be in the system (waiting in line or being served), on average?
2. What is the average time a customer will spend in the system (waiting in line and being served)?
3. How many customers will be in line on average?
4. How long will customers wait in line on average?
5. What is the probability of no one being in line or being served?
Crowninshield stands up and walks around the conference room. "We really need this customer service
approach to work in the mall stores. It's vital to our long-term strategy. I'd like to know the answers to
the pilot team's questions and I'd also like to
consider another scenario. Suppose we add a second cashier and nothing else changes. A sale is still
expected every ten minutes. If each transaction at the register still takes an average of five minutes, and
customers wait in a single line until one of the cashiers is free, what will this do to our customer service
performance? How different will the answers to the team's five questions be?"
She sits down and scans the customer standards list again. "We need the hard numbers to make the
decision," she says. "Can I count on you for the analysis and for a recommendation?"
 This is what I have to solve for this question above: Thanks
D. Compare the characteristics (e.g., number of customers waiting, waiting time, total checkout
time) of one-cashier and two-cashier waiting-line systems.
1. Recommend a one-cashier or two-cashier waiting line system, utilizing the appropriate
decision analysis tool.
2. Submit a copy of the output from your decision analysis tool of choice.
a. Explain why you chose the decision analysis tool you used.

Single Server Model i.e. One Cashier Model:
On an average a sale is expected every 10 minutes. Therefore, λ = 6.
On an average a transaction takes 5 minutes at the register. Therefore, µ = 12.
Customers in the System Ls= λ/ (µ - λ) = 1 per hour
Waiting Time in the system Ws= 1/ (µ - λ) = 10 minutes
Average Customers in Queue Lq= λ
2
/ µ (µ - λ) = 0.5 per hour
Average waiting time in Queue Wq= λ/ µ (µ - λ) = 5 minutes
Probability of no one being in queue or served P0= 1 - λ/ µ = 0.5
Multiple Server Model i.e. Two Cashier Model:
On an average a sale is expected every 10 minutes. Therefore, λ = 6.
On an average a transaction takes 5 minutes at the register. Therefore, µ = 12.
No. of cashier M = 2.
Probability of no one being in queue or served P0= 0.6
Customers in the System Ls= λ µ (λ/ µ) ^M / (M – 1)! (Mµ - λ)
2
P0 + λ/ µ = 0.5333 per hour
Waiting Time in the system Ws= Ls/ λ = 5.33 minutes
Average Customers in Queue Lq= Ls λ/ µ = 0.0333 per hour
Average waiting time in Queue Wq= Lq/ λ = 20 seconds
I think from the calculations, we see that the improvement achieved by employing one more cashier is
not worth the cost associated with it. The company can deploy one cashier system at their stores and
gradually move to two cashier system if needed.
QUESTION 2
Transportation issues
"We have one other pressing challenge that you could review for us," Alistair Wu says. "As you
know, the Shanghai plant was our first facility in China, but we also have two other production
plants, at Hangzhou and Fuzhou. We call them the Shuzworld H and Shuzworld F."
"One of our major lines of women's shoes is produced at all three plants. In turn, the shoes are
sent to Shuzworld's three central warehouses for further distribution to regional warehouses and
then to the stand-alone retail and mall stores."
Wu reaches into his elegant leather briefcase and produces two charts, which he hands to you.
"This first chart shows our monthly production capacity for these shoes at each of our factories and
our monthly requirements to meet demand at each of our warehouses," he explains. "We are
producing at normal capacity at all three factories in order to meet our current demand."
Factory Capacity Warehouse Requirements
Shanghai 1300 1 2500
Shuzworld H 2300 2 1500
Shuzworld F 2200 3 1800
Totals 5800

5800
He asks you to look at the next chart. "Here you can see what it costs us to ship on a per unit
basis. For example, our most expensive route is to ship from Shuzworld F to Warehouse 3 and
costs $6 per shipping unit."
To/From Warehouse 1 Warehouse 2 Warehouse 3
Shanghai $4 $3 $3
Shuzworld H $3 $4 $2
Shuzworld F $2 $4 $6
"We've decided to increase production at Shanghai from 1,300 units to 2,800 units," Wu continues.
"There's no increase in demand right now, by the way, but this will enable us to meet the growth
we expect in the near future. Meanwhile we will have some flexibility in case we have a problem at
one of the factories. This move may also mean we can change our transportation schedule in the
event that turns out to be advantageous. We want to know what the lowest possible monthly
transportation cost can be and what shipping plan we should adopt to achieve that. Can you help
us with this?"
THIS IS WHAT I HAVE TO ANSWER FOR THIS QUESTION.
A. Develop a distribution pattern that meets availability and demand constraints and
minimizes total shipping costs for Shuzworld, utilizing the appropriate decision analysis
tool.
1. Submit a copy of the output from your decision analysis tool of choice.
a. Explain why you chose the decision analysis tool you used.
THIS IS MY ATTEMPT TO SOLVE IT BELOW
intuitive Lowest-Cost Approach
From\ To

Warehouse 1 Warehouse 2 Warehouse 3 Factor Capacity
Shanqhai

$4 1300 $3 $3 1300
Shuzworld H

300 $3 200 $4 1800 $2 2300
Shuzworld F

2200 $2 $4 $6 2200
Warehouse
Requirements
2500 1500 1800 5800
From To Shoes Shipped Cost per Unit Total Cost
Shanghai Warehouse 2 1300 $3 $3900
Shuzworld H Warehouse 1 300 $3 $900
Shuzworld H Warehouse 2 200 $4 $800
Shuzworld H Warehouse 3 1800 $2 $3600
Shuzworld F Warehouse 1 2200 $2 $4400
$13600
I chose to use the intuitive Lowest-Cost Approach because it focuses on the lowest cost associated with the
transportation of the shoes in questions and does not just give a solution which satisfies supply and demand
constraints like the North west corner rule does.
We will begin answering the problem addressed by using the northwest corner rule. This specific rule begins
where one starting in the upper left hand cell of a table (the northwest corner), and systematically...