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- September 13, 2020
- By menge

Please help give full solutions for this MBA OM homework.

I. Process Analysis: Answer ANY ONE of I.1 or I.2 below (either Process Mini-case or Yum and Yee)

1. Somewhat open-ended Process Analysis mini case (30 Points): Consider the situation of an

entrepreneurial student (yourself) who is starting his or her own business operations, baking make-toorder cookies. Cookies differ in ingredients but all follow the same production process. The process,

shown in the flow diagram below, consists of the following steps: 1. Receive order 2. Wash & mix dough

3. Spoon dough 4. Set oven timer 5. Bake cookies 6. Unload 7. Cool cookies 8. Pack cookies 9. Accept

payment. The key resources are: you, your friend, a baking oven. Answer the questions below. You?s&

Cookies:&

Process&

Flow&

Chart&

Y

ou) Y

ou) C puter)

om Spoon

Dough Wash and

Mix Dough Receive

Order (2 min./dz) (Setup time =

6 min; up to 3

dz) (0 min) F

riend) Oven)

&) Load and

Set Timer

Setup time = 1 min. Oven) Bake

Run&

7me& 9&

=& min./dz;&

max& dz& oven&

1& in& F

riend) Pack (0 min) F

riend) Accept

Payment F

riend) Unload (1 min./order) (2 min./dz.) Cool

(5 min.) Notes on the Process Flow Diagram:

dz = dozen; one ?tray? of cookies holds a

dozen.

In the Mix Dough step, the electric mixer can

hold and mix ingredients for up to three-dozen

cookies. This step takes 6 minutes for washing

and mixing, regardless of how many cookies are

being made in the batch. (This is equivalent to

setup time = 6 minutes, process run time = 0.)

Assume there is one oven. Total baking time is

10 minutes, during the first minute of which

3&

your friend is busy loading & setting the oven. Page 1 of 8 Miscellaneous additional information: You and your friend already own all the necessary capital equipment: a

high-capacity professional-grade electric mixer, cookie trays, and spoons. Your apartment (location of this home

business) has a small oven that will hold one tray at a time. Your landlord pays for all the electricity and is OK

supporting your business venture. The variable costs, therefore, are merely the cost of the ingredients (estimated

to be $0.60/dozen), the cost of the box in which the cookies are packed ($0.10 per box; each box holds a dozen

cookies), and your time (what value do you place on your time? Let?s assume the labor rate is 20$/hour for each

worker and paid only for productive time, not idle time). In case of confusion, state assumptions made.

a. (10 points) Capacity: In order to design a good system for pricing, accepting orders, and production, you

want to know how many cookies you can expect to complete in a night, assuming your cookie company is

open four hours each night for ?steady-state? production. Start by completing the following process

capacity analysis; use it to answer the aforementioned capacity question. Note: There two columns in the

table below with order size 1 dz and 2 dz because some of the processing does not depend on order size

and some does. So some capacity numbers in a row will change with order size and some do not.

Resource Order size = 1 dz. Order size = 2 dz. Capacity

(dz./hr.) Capacity

(dz./hr.) You

Oven

Friend Which resource will be the bottleneck with the highest utilization? ____________________________

Number of dozens of cookies you can expect to complete in a night, assuming your company is open for four

hours of steady-state operation each night (steady-state operation allows you to ignore start-up and shut-down

effects):

b. (*10 points) Resources: Assuming ample demand, ceteris paribus, how many electric mixers and baking

trays will you need? [Note: Each baking tray is in use during the spoon dough, load, bake, unload, and

cool part of the process. If useful, you may visualize the problem using a Gantt chart.] c. (*10 points) Planning / Improvement: What is the effect of adding another oven and how much would

you be willing to pay per day to rent an additional oven, assuming there is ample demand and half the customer orders are for one dozen cookies and half for two dozen cookies? What changes / improvements

would you make in your production plans that will allow you to make better cookies or more cookies in

less time or at lower cost? 2. Based on Chapter 7 on Batching (30 Points): A new Yum and Yee food truck near the business school

serves customers during lunch hour by taking orders and making fresh batches of stir fry. Customers have

only one choice during the lunch hour, since the objective is to maximize the number of customers served.

Assume that each customer places just one lunch order, and all lunch orders are the same size ?one unit of

stir-fry. The stir-fry cooking works in this manner: First, one Yum and Yee employee cooks a batch of orders

in a wok. The cooking depends upon the number of orders in the batch. The time to cook just one order is 3

minutes. For each additional order in the batch, it takes 0.5 minutes more to cook. Thus, cooking two orders

in a batch takes 3.5 minutes, cooking three orders takes 4 minutes, and so on. The other process is bagging

and accepting payments (done by a separate employee), which takes 0.75 minutes per order.

a. (10 points) Capacity: If Yum and Yee operates with batch sizes of 8 units, what is their process capacity

(in orders per minute)? b. (6 points) Batch-size: Calculate the batch size (in orders) that will maximize the overall flow rate

(assume there is ample demand)? Do NOT round the batch size (i.e., assume for this calculation that a

non-integer batch size is possible). c. (8 points) EOQ: Yum and Yee owner Sarah must purchase a secret ingredient (SI) for her stir-fry

business. She needs 1 pound (lb) of SI per day on average. The supplier charges a $30 delivery fee per

order (which is independent of the order size) and $5 per lb. of SI. Sarah?s annual holding cost rate is

25%. Assume 40 working weeks per year and 5 days per week. If Sarah wants to minimize inventory

holding and ordering costs, how much SI should owner Sarah purchase with each order (in lbs.)? d. (6 points) Quantity Discounts: Sarah?s supplier is willing to sell her SI at a 5% discount (i.e. at 0.95 x 5

= 4.75$/lb) if she purchases 150 lbs at a time. Given this sourcing-discount information, how much SI

would you recommend Sarah purchase with each order (in lbs)? Why? II. Variability and Waiting Times Chapter 8 (35 Points): This question is intended to build and test your

intuition on the design of waiting lines with variability and two identical streams of customer arrivals (e.g.,

men and women). The three systems being considered are shown below, where the arrow denotes flow with

arrival rate Rak, for stream k = 1, 2, the triangle represents the waiting line or queue and the rectangles

represent processing by a server with specified average unit processing time ? the two rectangles inside a

larger rectangle in System B corresponds to a two-server station; System C is a single-server station with

average unit process time cut by 50%; assume values for rak and p, for instance, take Ra1 = Ra2 = 0.9

customers per hour, p = 1 hour. Unless otherwise stated, assume all coefficients of variation are 1.0. 1. (5 points) Utilization: Calculate the utilization of the three systems, A, B, and C. Show your work. 2. (15 points) Time in Queue: Calculate the average time in queue in the three systems. Show your data

values / approach. 3. (10 points) CTq and CT comparison: Which system has the lowest average time in queue, CTq? Which

system has the lowest time in system, CT? Explain qualitatively (in layman?s terms) why the pooled

system B has lower CTq than the independent system A. Will the choice of which system has the lowest

CT continue to hold if the variability factor, V, is not 1 but could be large (e.g., V = (Ca2 + Ce2 )/2 = 2.5,

corresponding to Ca2 = 1, and Ce2 = 5)? Explain your Yes / No choice. 4. (5 points) Queuing Process Design: Consider the following three process designs to organize a call

center with 12 employees. The center handles calls for two customer types. Type 1 customers call with

credit card related questions and type 2 customers call with questions related to the online account

opening. On a busy day the call center receives 60 calls per hour from type 1 customers and 30 calls per

hour from type 2 customers. It takes on average 2 minutes to service both kinds of calls.

Process design 1: 6 employees handle type 1 calls; the other 6 employees handle type 2 calls

Process design 2: 8 employees handle type 1 calls; 4 employees type 2 calls.

Process design 3: 12 persons (cross-trained) handle all calls. Which of the three process designs leads to the shortest (longest) average waiting time for a random

incoming request?

a.

b.

c.

d.

e.

f.

g.

h.

i. 1 is the shortest, 2 is the longest

2 is the shortest, 1 is the longest

3 is the shortest, 2 is the longest

2 is the shortest, 3 is the longest

3 is the shortest, 1 is the longest

1 is the shortest, 3 is the longest

3 is the shortest, 1 and 2 are the same

Cannot be determined (explain why)

None of the above (explain why) III. Decision-making under Uncertain Demand (30 points): Answer ANY 30 Points from the questions

below, while answering at least one of the * / italicized questions. Answer the Bonus Points question for

2 extra points. Technical Note: The Cumulative Distribution Function, CDF, F(Q), and Loss Function, L(Q), can be

obtained using Excel for Normal and Poisson distributions; one implementation in Excel is posted on Blackboard->

Course Docs, Revenue Management folder, file Poisson_Normal_TablesN.xlsx. 1. Newsvendor Chapter 12 for Montanso (20 Points) Montanso is a large bio firm that sells genetically

modified seed to farmers. Montanso needs to decide how much seed to put into a warehouse to serve

demand for the next growing season. They will make one quantity decision. It costs Montanso $16 to make

each kilogram (kg) of seed. They sell each kg for $90. If they have more seed than demanded by the local

farmers, the remaining seed is sent overseas. Unfortunately, they only earn $6 per kg from the overseas

market (but this is better than destroying the seed because it cannot be stored until next year). If demand

exceeds their quantity, then the sales are lost ? the farmers go to another supplier. As a forecast for demand

they will use a normal distribution with a mean of 300,000 kgs and a standard deviation of 106,000 kgs.

a. (10 points) Newsvendor Quantity: How many kilograms (kgs) of seed should they place in their

warehouse before the next growing season to maximize their expected profit? b. (*10 points) A senior executive at the company asks the following ?Suppose we were to place 500,000

kilograms in this warehouse. What is the probability that our total revenue will be at least

$36,000,000?? Don?t forget that revenue comes from both local sales and overseas sales. Furthermore,

you are concerned with revenue and not profit, so you can ignore costs . [Hint: Write the total revenue as a

function of the realized demand value.] 2. Revenue Management Chapter 16 for Inn at Penn (30 Points) Inn at Penn has 200 rooms. For regularfare customers, rooms are priced at $300 per night while the rooms are priced at $700 per night for the highpaying customers who generally arrive at the last minute. The demand for such high fare customers is

distributed normally with mean 60 and standard deviation 50. Assume that there is ample demand for

regular-fare customers.

a. (10 points) What should the protection level for the high fare be to maximize expected profit? b. (*10 points) Suppose that Inn at Penn operates with the protection level of 80 rooms for high fare

customers. On average, how many high-fare customers are turned away because of lack of rooms? c. (*10 points) Suppose again that the Inn at Penn operates with the protection level of 80 rooms for high

fare customers. What is the probability that there are at least 5 rooms left unoccupied? d. (2 BONUS points) In your opinion, what is wrong with the data provided in the first paragraph of this

problem?