julian archer shannon cummings ashley green david ong
TRANSCRIPT
Sue’s Market Optimization
Julian ArcherShannon Cummings
Ashley GreenDavid Ong
Introduction Problem Statement Initial Data One Queue Model Multiple Queue Model Overall Results Conclusion
Overview
Sue of Sue’s Market has hired us a consultant firm to solve a number of issues that she has in her current store
Goal:◦ Reduce wait time for customers◦ Create a schedule that allows for worker
limitations◦ Save Sue money while creating a checkout areas
with maximum output and efficiency. ◦ Having the least amount of baggers and cashiers
working at one time to maximum profit
Introduction
Staffing of employees during peak hours◦ 2pm-10pm◦ Employees can only work 3-5 hours a day
Long lines ◦ Desired Queue Wait:
Optimal: 2-3 minutes Acceptable: 10-12 minutes
◦ Desired Queue Length: 4-5 people Minimizing Cost
Problem
Initial Data
After conducting a best fit analysis it was found that the number of items purchased per customer, on average, must be distributed empirically.
MIN: 4 itemsMAX: 149 ITEMSSample mean: 88.9
Number of Items Per Customer
From this graph we observe that the customers arrive at a lognormal distribution with a logarithmic mean of 0.00983 and a logarithmic standard deviation of 0.00308.
However, the p- value is less than 15% which tells us that we have to use the empirical distribution.
Initial DataInterarrival Times (Monday-Thursday)
Initial Data
2:00 - 2:30
2:30 - 3:00
3:00 - 3:30
3:30 - 4:00
4:00 - 4:30
4:30 - 5:00
5:00 - 5:30
5:30 - 6:00
6:00 - 6:30
6:30 - 7:00
7:00 - 7:30
7:30 - 8:00
8:00 - 8:30
8:30 - 9:00
9:00 - 9:30
9:30 - 10:00
0
20
40
60
80
100
120
140
160
180
Arrival Rate
Arrival Time
Num
ber
of
People
Arr
ivin
g
Payment Methods
Initial Data
Cash45%
Check30%
Credit Card25%
Payment Types Less Than 20 Items
Cash 20%
Check 45%
Credit Card 35%
Payment Types More than 20 Items
Initial Data: Model Flowchart
One Queue Model: Arena Model
Basic Flow◦ Assign customers amount of shopping items◦ Decides to determine customer movement
Resource Usage◦ Cashier Resources
Seized with series of delays Based on schedule
◦ Bagger Resources Bagging process
One Queue Model: Features
Initial Data Collection: Changing Resources ◦ Focused on:
Number Out of System Total Runtime Queue Wait Times and Lengths Resource Utilization and Busy Cost
[(runtime/60)*5.5*#Baggers]+[(runtime/60)*7.25*#Cashiers]
◦ Goal to Reduce: Wait times and lengths Cost Runtime
One Queue Model: Results
One Queue Model: Results
Optimal Result: 12 Cashiers & 4 Baggers
Second Stage Data Collection◦ Action:
Changed Cashier Schedule Fixed Amount of Baggers (4)
◦ Main Focus Queue wait time and length Still looked at same parameters as earlier
One Queue Model: Results
One Queue Model: Results
82.5 82.5 91 91.5 93.5 960
10
20
30
40
50
60
Average Total Wait TimeAverage Queue Length
Cashier Variance (Area Under Curve) 82.5 82.5 91 91.5 93.5 960
200
400
600
800
1000
1200
1400
cost
Cashier Variance (Area Under Curve)
Cost
Optimum 8 Hour Cashier Schedule:Max = 15 CashiersMin = 5 Cashiers
Third Stage Data Collection◦ Action:
Keep optimized cashier schedule Vary bagger schedule
◦ Main Focus: Cost Wait time and length Same parameters
One Queue Model: Results
One Queue Model: Results
26 27 28 29 29.50
200
400
600
800
1000
1200
1400
1600
Cost
Bagger Variance (Area Under Curve)
Cost
26 27 28 29 29.50
5
10
15
20
25
Total Average Queue WaitAverage Cashier Queue Length
Bagger Variance (Area Under Curve)
Optimal 8 Hour Bagger Schedule:Max = 5 BaggersMin = 1 Bagger
Final Stage of Data Collection◦ Action:
Vary cashier schedule beyond 8 hours Vary bagger schedule beyond 8 hours
◦ Main Focus Cost Queue Wait and Length Runtime Same previous parameters
One Queue Model: Results
Optimal Cashier Schedule Optimal Bagger Schedule
Total Cost: $470.84 per day◦ =((7.25*MR(Cashier)(TNOW/60)) +
(5.50*MR(Bagger)(TNOW/60))
Total Average Queue Wait: 4.21 minutes◦ Cashier Wait: 3.06 minutes◦ Bagger Wait: 1.15 minutes
Average Cashier Queue Length: ∽5 People
Total Runtime: 556.66 minutes
One Queue Model: Optimal Conditon
Multiple Queue Model: Arena Model
Ar r iv a lCu s t o m e r
Pe r Cu s t o m e rAs s ig n I t e m s
T r u e
F a ls e
I t em s ?Les s Than 10
I t e m sL e s s t h a n 1 0Sh o p p in g f o r
I t e m sM o r e t h a n 1 0
Sh o p p in g f o r
Fr om SetCas hier 1
Seiz e
Fr om SetCas hier 2
Seiz e
Fr om SetCas hier 3
Seiz e
Fr om SetCas hier 4
Seiz e
Fr om SetCas hier 5
Seiz e
Fr om SetCas hier 6
Seiz e
Fr om SetCas hier 7
Seiz e
Fr om SetCas hier 8
Seiz e
Fr om SetCas hier 9
Seiz e
Fr om SetCas hier 10
Seiz e
Fr om SetCas hier 11
Seiz e
Fr om SetCas hier 12
Seiz e
Fr om SetCas hier 13
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Fr om SetCas hier 14
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Fr om SetCas hier 15
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Fr om SetCas hier 16
Seiz e
Fr om SetCas hier 17
Seiz e
Fr om SetCas hier 18
Seiz e
Fr om SetCas hier 19
Seiz e
Fr om SetCas hier 20
Seiz e
Choos e?W hic h Lane t o
E ls e
Su b m o d e lCh e c k O u t 1
Su b m o d e lCh e c k O u t 2
Su b m o d e lCh e c k O u t 3
Su b m o d e lCh e c k O u t 4
Su b m o d e lCh e c k O u t 5
Su b m o d e lCh e c k O u t 6
Su b m o d e lCh e c k O u t 7
Su b m o d e lCh e c k O u t 8
Su b m o d e lCh e c k O u t 9
Su b m o d e lCh e c k O u t 1 0
wit h Plas t ic Bags ?Cus t om er Leav es T r u e
F a ls e
Us e dPla s t ic Ba g s
Re c o r d
L e a v e St o r eCu s t o m e r s
Ba g s Us e dRe c o r d Pa p e r
Sy s t e mSh o p p in g in
Cu s t o m e r sNu m b e r o fDe c r e m e n t
Su b m o d e lCh e c k O u t 1 1
Su b m o d e lCh e c k O u t 1 2
Su b m o d e lCh e c k O u t 1 3
Su b m o d e lCh e c k O u t 1 4
Su b m o d e lCh e c k O u t 1 5
Su b m o d e lCh e c k O u t 2 0
Su b m o d e lCh e c k O u t 1 6
Su b m o d e lCh e c k O u t 1 7
Su b m o d e lCh e c k O u t 1 8
Su b m o d e lCh e c k O u t 1 9
0 0
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00
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Single Entry
Assign Attributes and Variables
Decide Shopping Time Delay
Decide 1 of 20 Counters
Seize Cashier
Multiple Queue Model: Overview
Multiple Queue Model: Sub Model
T r u e
F a ls e
Check#1 Need Pr ice
Check#1 Pr ice
Less?I t em s is 20 or#1 Num ber of
T r u e
F a ls e
I t em sLess t han 20
Type For 20 or#1 Paym ent
4 53 0
E ls e
t han 20 I t em sType For M or e
#1 Paym ent
2 04 5
E ls e
wit h Cash#1 Paying
no Check Car d?#1 Paying wit h T r u e
F a ls e
Check Car dwit h No
#1 Paying
Car dwit h Check#1 Paying
Car dwit h Cr edit#1 Paying
Available?#1 Bagger T r u e
F a ls e
G r ocer iesBags
#1 BaggerCashier#1 Release
Help?#1 Will Cust om er T r u e
F a ls e
BaggingCashier Af t er
#1 ReleaseCust om er
wit hG r ocer ies
Bags#1 Bagger
Cust om erwit hout
G r ocer iesBags
#1 Bagger
Check O ut 1
0
0
0
0
0
0
0
0
0
0
0
0
0
Multiple Queue Model: Schedule Method
Decide Price Check Delays
Decides for Payment Type based on number
of Items Purchased
Decided If Bagger available or not
Release Resources
Exit Sub model
Multiple Queue Sub Model
◦ Decide bagging type
◦ Decrement customers
◦ Dispose Customers from system
Multiple Queue Model: Bagging Process
Overall Results
Benefits of One Large Queue
Benefits of Multiple Small Queues
Equal customer wait times
Avoid unnecessary time choosing a lane
Provides for more orderly checkout process
Allows for specialized lanes◦ Express ◦ Self check out◦ Special payment lanes
More familiar
Do not have to worry about queue placement
Optimized Bagger and Cashier Schedules◦ Adhered to 3-5 hour constraints◦ Extended schedule beyond 8 hours to account for
overtime Minimize Queue Time
◦ Preferred 2-3 Minutes, Max 10-12 Minutes Average of 6-7 Minutes
◦ Our Queue: 4.21 Minutes Minimize Queue Length
◦ Queue length less than 5 people Decreased Cost and Runtime
◦ Total Cost: $470.84◦ Total People In and Out of System: 891 People◦ Total Runtime: 556.66 Minutes
Conclusion
Questions?
Thanks for listening……