report on inventory analytics: lost revenue due to out...

Report on Inventory Analytics:Reducing Lost Revenue Due To Out Of Stock

Inventory

Igor OfenbakhIgor Ofenbakh

Founder, WizData Systems, Inc.

The ChallengeThe Challenge

Not enough inventory

Too much inventoryy

Product/size mix not optimalnot optimal

Lost RevenueMaterials copyright WizData Systems, Inc. Proprietary Technology

Problem DefinitionProblem Definition

A chain of stores sell various products.Ideally Real world

There always are the right products in the right quantities at every store.

Products can be out of stock (OOS). After that moment a seller has Lost

Lost Sales are the potential sales after an item goes OOSh ld b d if h b h i i k

the right quantities at every store. After that moment a seller has Lost Sales.

that could be made if there were be enough units in stock.

For the seller, the following business questions arise:‐What is the amount of sales that were lost?‐ Is there a better distribution of products

between stores and items?between stores and items?

Materials copyright WizData Systems, Inc. Proprietary Technology

The BenefitsThe Benefits

Lost Sales estimation;Lost Sales estimation;

Size curves tied to local demand;

Proper distribution between stores;

I i l (4% 22%)Increase in sales (4% ‐ 22%);

Universal model.


ChallengesChallengesMaterials copyright WizData Systems, Inc. Proprietary Technology

Example 1.

Si l Li D d8Sale qt. One store, one item

Simple Linear Demand

7

66

7

8(25 units in stock)

Out of Stock

5

4

34

5Sold units

Lost sales3

2

12

3Lost sales

1

0

1

1 2 3 4 5 6 7Week

1 2 3 4 5 6 7


Example 2.

R l W ld D dReal World Demand

878

9Sale qt. One store, one item

(25 units in stock)Sold units

Lost Sales

67

567 Out of Stock

2 2

1234

? ?01

1 2 3 4 5 6 7Week

? ?


Example 3.Large quantities. Size proportionsSale qt.

680700

800Sale qt.

Large blouseSmall blouseLost Sales

400

502

396 398400

500

600 Lost Sales

303

206205

332261

200 196152200

300

400

15296

0

100

1 2 3 4 5 6 7 Week


Example 4.

R l ld Si tiReal world. Size proportionsReal sales in an individual store display large variances that do not

ll f di t ti l l ti hi

1214Sale qt. Large blouse

Small blouse

allow for direct proportional relationship.

11

9 9

12

98

10

12Small blouseLost Sales

76

5

8

46

8

32

4

2

4

? ?0

1 2 3 4 5 6 7Week


Aggregating by StoresAggregating by StoresEvery store has its own size distribution.

Store 1

L 36%

Store 2

4%

29%

48% 19%M

S14%

35%

36%15%

XS

Store 3 Store 4

19%

44%11%

13%

36%10%

26% 41%


Aggregating by StyleAggregating by Style

V NECK TOP PRINTED DRESS BLOUSE

Every item has its own size distribution.

44% 20%

V NECK TOP

L 38% 19%

PRINTED DRESS BLOUSE

9%

27%

44% 20%M

S13%

29%

19%

XS

LACE BACK CAMI BEADED TANK TOP

14%

37%14%

8%42%

33%

36% 16%


Sales by WeekDue to seasonality, sales change significantly from week to week.

436391

450500

Sale qt. PRINTED DRESS BLOUSE, All stores

373 391

299300350400

200163

107100150200250

050100

1 2 3 4 5 6 7Week

1 2 3 4 5 6 7


Challengesof Lost Sales Analysis

Small quantity of weekly sales per store, size andstyle. Hence week to week deviation of the realysales is significant ;

Demand is time dependent;

Different demand for various locations and styles;

Different size proportions for different stores andp pstyles.


SolutionSolutionMaterials copyright WizData Systems, Inc. Proprietary Technology

Problem FormulationProblem Formulation

There is a network of stores selling a product (e.g. Tshirts) of various styles and sizes in different locations.For every valid combination of Style, Location, Sizeand Week we have sales data in the following forms: g

X units sold or X units sold and OOS position was reached

After OOS there is no sales or demand information available.The problem is to find demand as a function of style,i d l ti f k f th id d i dsize and location for every week of the considered period.Once this function has been found, it provides an estimation of the Lost Sales for those weeks in which the store was OOS.


Sales Data vs.True Demand

The number of units sold in a store cannot be considered the True Demand especially in the case where the number of weekly sales is small.

bl l d h llIt is impossible to accurately predict that 1 unit will be sold during week 1, 4 units during week 2, 1 unit during week 3, etc.during week 3, etc. True Demand is a function (possibly fractional) of Style, Size, Location and Week

with a high degree of variance!


Example 5.S l D t T D dSales Data vs. True Demand

44

4.5

Sale qt. One store, one itemSold units

22.53

3.5

1 1

2

1

0 51

1.52

True Demand = 1.5 units per week

00

0.5

1 2 3 4 5 6Week


AssumptionsAssumptions


Local Size CurveSize distribution of a style is assumed to be a function

of style design and location.

Store #1 Store #2 Store #3L

M

S

XS

V NECK TOP


LACE BACK CAMI


Size CurveDoes Not ChangeDoes Not Change

Size curve of a style at a given location does not change in time.

Store #1 Store #2 Store #3L

M

S

XS

V NECK TOP


LACE BACK CAMI


Weekly SalesFor every style the weekly fractions of a total demand duringa considered period are the same for different locations.

22%25%

Pct of total sales

PRINTED DRESS BLOUSE, all stores

19% 20%

15%15%

20%

10%8%

6%10%

0%

5%

1 2 3 4 5 6 7Week

1 2 3 4 5 6 7


ResultsResults

As a result of the Lost Sales algorithm wegcalculated a True Demand function, whichallows us to:Find the Lost Sales in context of styles, locations and sizes;Analyze the structure of sales during the period;Find the optimal product distribution between locationslocations.


Results – Blouse

Sale qt.

Style: PRINTED DRESS BLOUSEColor: BLACK Size: ALL SIZES

200

250

q Size: ALL SIZESStore: ALL STORES

Real sales: 1512

150

Real sales: 1512Predicted sales: 1569Lost Sales: 57 (4%)

50

100 Predicted Sales

Real Sales

0

50

1 2 3 4 5 6 7 8 9 10 11 12 13 14Week

1 2 3 4 5 6 7 8 9 10 11 12 13 14


Results – V Neck Top

Sale qt.

Style: V NECK TOPColor: IVORYSize: ALL SIZES

400

450

500

q Size: ALL SIZESStore: ALL STORES

Real sales: 2993

250

300

350

P di t d S l


100

150

200Predicted Sales

Real Sales

0

50

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 Week1 2 3 4 5 6 7 8 9 10 11 12 13 14


Results ‐ V Neck Top

Sale qt.

Style: V NECK TOPColor: IVORYSize: ALL SIZES

4

5

Sale qt. Size: ALL SIZESStore: STORE #100

Real sales: 23

3Predicted Sales


1

2Real Sales

0

1

1 2 3 4 5 6 7 8 9 10 11 12 13 14Week

1 2 3 4 5 6 7 8 9 10 11 12 13 14


ConclusionsConclusions

Lost Sales analysis is very difficult due to the small y ynumber of items sold and the very high variance of the data;

The proposed approach recognizes general regularities of the sales for different products and locations and provides the True Demand function;p ;

The amount of Lost Sales and the optimal distribution of products between storespcan be estimated by means of the

developed algorithm.


BenefitsBenefits

Lost Sales estimation can be used for future ost Sa es est at o ca be used o utu eplanning

Estimated Increase in sales (4% 22%);Estimated Increase in sales (4% ‐ 22%);

Smaller amount of merchandise sold at clearance prices

Immediate within the season responseImmediate within the season response

Our model can be used stand alone or integrated into existing systemsintegrated into existing systems


AuthorsIgor OfenbakhFounder WizData Systems IncFounder, WizData Systems, Inc.M.S. in Mathematics with concentration in operations research.

Nikolay KosarevNikolay KosarevPh.D. in MathematicsFields of interest: operations research, discrete optimization, artificial intelligenceartificial intelligence

Sergey Dobrovolskyh hPh.D. in Mathematics

Fields of interest: stability of chaotic and stochasticsystems, statistical modeling


Can we answer any questions?

You can reach Igor Ofenbakh at: 866‐949‐3282You can reach Igor Ofenbakh at: 866 949 3282or [email protected]


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