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 P

eopl

e Ar

rivin

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

200400600800

1000120014001600

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 ?Less Than 10

I t e m sL es s t h an 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 op 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 SetCashier 10

Seiz e

Fr om SetCas h ier 11

Seize

Fr om SetCas h ier 12

Seize

Fr om SetCas h ier 13

Seize

Fr om SetCas hier 14

Seize

Fr om SetCas h ier 15

Seize

Fr om SetCas h ier 16

Seize

Fr om SetCas h ier 17

Seize

Fr om SetCas h ier 18

Seize

Fr om SetCas hier 19

Seize

Fr om SetCashier 20

Seiz e

Choo s e?W hic h Lane t o

E ls e

Su b m o de lChe c k O u t 1

Sub m o d e lCh e c k O u t 2

Sub m o d e lCh e c k O u t 3

Sub m o d e lCh e c k O u t 4

Sub m o d e lCh e c k O u t 5

Su b m o de lChe c k O u t 6

Sub m o d e lCh e c k O u t 7

Sub 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 Plast ic Bags ?Cust om er Leav es T r u e

F a ls e

Us edPlas t ic Bag s

Re c o r d

L e av e St or eCu s t o m e r s

Ba gs 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 ofDe c r e m e nt

Su bm o d e lChe c k O u t 11

Su bm o d e lChe c k O u t 12

Su bm o d e lCh e c k O u t 1 3

Su bm o d e lChe c k O u t 14

Su bm o d e lChe c k O u t 15

Su b m o de lCh e c k O u t 2 0

Sub m o d elCh e c k O u t 1 6

Sub m o d elCh e c k O u t 1 7

Su b m o de 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

0

0

0

0

0

0

0

0

0

0

00

0

0

0

0

0

0

0

0

0

0

0

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 ResultsBenefits 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……