Paper details THIS CLASS PROJECT INCLUDES TWO CASES, BOTH OF WHICH MUST BE COMPLETED

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Deadline: 3 Nov, 01:11 PM (6:30pm

Academic level:College (1-2 years: Freshman, Sophomore)
Subject or discipline:Management
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Paper details THIS CLASS PROJECT INCLUDES TWO CASES, BOTH OF WHICH MUST BE COMPLETED

FOR FULL CREDIT. YOU CAN WORK IN GROUPS OF UP TO SIZE FIVE PEOPLE, OR

INDIVIDUALLY IF YOU PREFER. MAKE SURE TO INDICATE THE MODEL YOU USED IN

EVALUATING EACH CASE, AND SUMMARIZE THE PURPOSE OF YOUR EVALUATION

FOR EACH CASE. INCLUDE A SUMMARY AND CONCLUSIONS, MAKING SURE TO

ANSWER ANY QUESTIONS POSED WITH THE CASES. MAKE SURE TO ENTER THE

NAMES OF ALL GROUP MEMBERS ON YOUR PROJECT. THE FINAL REPORT SHOULD

BE SUBMITTED AS A HARD COPY. NO E- MAIL OR OTHER ELECTRONIC MEDIA

SUBMISSION FORMATS WILL BE ACCEPTED!!!!!!!!!

Solution

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                                    Case1: The Twelve-Stars Amusement Park

Summary

            This first analysis is a case study of the Twelve-Star Amusement Park which has recently begun its operations in the East Bay. Patrons arrive at an estimated rate of 40% and have to pass through different points before finally leaving the park. We are to determine for the park, the expected number of patrons waiting at the admission gate, exit gate as well as at each ride. We also aim to determine how long the patrons will wait at each location within the park and also to help the owners know where to place an additional worker.

Analysis:

Assuming a single que system with M/M/1 standard assumptions:

 Average time of waiting time of the patrons in the system is Ws=(μ-λ) ^-1

Average waiting time in the Queue is Wq= (λ/ μ) (1/((μ-λ))

From Little’s law, L= λ*W

Average number in the queue Lq= λ*Wq

Average number in the system Ls= λ*Ws

Average server utilization x= λ/ μ

Number of Servers(n)

Where λ is the arrival rate and μ is service rate. Time are expressed in hours. The respective values of λ and μ are:

Entry gate: λ = 40, μ = 45;

Ferris: λ = 40% of 40 =16, μ = 18;

Roller Coaster: λ = 30% of 40 =12, μ = 15;

Zombie House: λ = 30% of 40 =12, μ = 16;

House of Mirror: λ = 16+40% of 12 =20.8, μ = 25;

Exit Gate: λ = 20.8 + 60% of 12 + 12 =40, μ = 42

Summary of Results: The following tables illustrate the model to evaluate the amusement park:

 Entry Gate    
ParameterValue ParameterValue
M/M/1  x0.8889
λ40 Lq7.111
μ45 Ls8
n1 Wq0.1778
   Ws0.2
At Ferris    
ParameterValue ParameterValue
M/M/1  x0.8889
λ16 Lq7.111
μ18 Ls8
n1 Wq0.444
   Ws0.5
At Roller C.    
ParameterValue ParameterValue
M/M/1  x0.8
λ12 Lq3.2
μ15 Ls4
n1 Wq0.2667
   Ws0.3333
Zombie H.    
ParameterValue ParameterValue
M/M/1  x0.75
λ12 Lq2.25
μ16 Ls3
n1 Wq0.1875
   Ws0.25
At House M.    
ParameterValue ParameterValue
M/M/1  x0.832
λ20.8 Lq4.120
μ25 Ls4.952
n1 Wq0.1981
   Ws0.2381
At Entry Gate    
ParameterValue ParameterValue
M/M/1  x0.9524
λ40 Lq19.04
μ42 Ls20
n1 Wq0.4762
   Ws0.5

Where to place additional worker: since the average waiting time in the queue and the number of patrons in the waiting at the Exit gate is higher, an additional worker is necessarily posted at the gate to increase the number of servers.

The park limitation the number of matrons is met because, at any given time, the number in the system does not exceed the limit of 45.

Case 2: The Main Street Deli – Rotisserie Chicken

DaysDaily Demand (D)Baked chicken (B)Selling price (P)Cost ($)Excess baked(Eb) Eb=B-DUnmet demand Daily(Du) Du=D-BProfit ($)
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Averages       
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