ram singh 0565 effect of plan o gram,inventory &vmi

8/7/2019 Ram Singh 0565 Effect of Plan o Gram,Inventory &VMI

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Effect of plan-o-gram, Inventory and VMI

M.P.Birla Institute of Management 1

A RESEARCH PAPER

Effect of Planogram, Inventory and vendor

managed inventory in VisualMerchandising

(AN EMPIRICAL STUDY)Submi t ted in par t ia l fu l f i l lment o f the

requi rem ent o f t he (MBA Degree) Bangalore

Univers i t y 2005-2007

By

Ram Singh

Reg. No. 05XQCM6072

Under the guidance of

Senio r Prof. S. Ram gopa l

M.P. Birla Institute of Management

Associate Bharathiya Vidya Bhavan#43, Race Course Road,

Bangalore-560 001


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STUDENT DECLARAT ION

I hereby dec lare that th is Research paper ent i t led

Effect of Planogram, Inventory and vendor managed inventory inVisual Merchandis ing has been under taken and comple ted byme under the valuable guidance of Senior Prof S. Ramgopal ,

M.P.B.I .M, in part ia l fu l f i l lment of Degree of MBA program is my

or ig inal w ork and no part o f t he w ork has been submi t ted for any

degree, d ip loma, fe l lowship or other s imi lar t i t le or pr izes for any

ins t i tu t ion prev ious ly, to t he best o f my k now ledge.

Date:

Place: Bangal ore (Ram Singh)


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ACKNOWLEDGEMENT

I w ou ld l ike t o express my pro found gra t i t ude to Mr . S. Ramgopal ,

Senior Professor, M.P. Bir la Inst i tute of Management whose

guidance was s ign i f icant in the successfu l comple t ion o f the

research paper.

I w ish to t hank our Dr. Nagesh Malaval l i , Pr inc i pal ,

M.P. Bir la Inst i t ute of Management for provid ing the means and

encouragement .

Date:

Place: Bangal ore (Ram Singh)


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PRINCIPAL S CERTIFICATE

This is to cer t i fy that th is repor t is the resu l t o f

Research Paper Ef fect of Planogram, Inventory and vendormanaged inventory in V isua l Merchandis ing undergone by Mr.Ram Singh bear ing the register number 05XQCM6072 under the

guidance and supervis ion of Senior Prof . S. Ramgopal This has

not formed a basis for the award of any Degree/ Dip loma of any

Univers i ty , to be the best o f m y know ledge.

Date: Dr Nagesh . Malav al l i

P lace: Bangalore (Pr inc ipal)


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GUIDES CERTIFICATE

This is to cer t i fy that th is repor t is the resu l t o f

Research Paper Effect of Planogram, Inventory and vendormanaged inventory in V isua l Merchandis ing undergone by Mr.Ram Singh bear ing the register number 05XQCM6072 under the

guidance and supervis ion of Senior Prof . S. Ramgopal . This has not

formed a basis for the award of any Degree/ Dip loma of any

Univers i ty , to be the best o f m y know ledge.

Date: Prof. S. Ramgopa l

Place: Bangal ore (Guide)


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CONTENTSExecutive Summary 8

Objective of the Study 8

Research methodology 9

Part-A

Plan-o-gram 12

1. Introduction 13

2. Recognizing and Directing Traffic Flow 14

3. Definition of plan-o-gram 16

4. Fixturing 16

5. Lighting used in retail stores 186. Graphics and Signage 19

7. Merchandising Similar Products Together 20

8. Cross-Mix Merchandising 21

9. Visual Merchandising Tools and Supplies 22

10.Plan-o-gram Examples ` 23

11.Basic Criteria for creating Plano-gram 25

12.Data analysis and interpretation 26

13.Findings 3314.Suggestions and recommendations 33

Part-B

Inventory of Retail Stores 34

1. Introduction 35

2. Model Specification and Optimality Conditions 36

3. Sales Rate Function 38

4. Inventory Decision and Cost Model 40

5. Objective Function 42

6. The Separable Sates Rate Case 43

7. Compensating Prices 45


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8. Boundary Values 46

9. Solving for the Optimal Inventory Commitment Io 47

10.Tabulated Solution and Interpretation 47

11.Interpretation of the Six Solution Cases 48

12.Two Models for Inventory Effects 50

13.Implementation Methods 52

14.Typical Price and Sales Trajectories 53

15.Conclusions 58

16.References 61

Part-CVendor Managed Inventory in Retail Industry 63

1. Introduction 64

2. Definition and Concept 65

3. Conventional Fulfillment Process from Retailer Perspective 66

4. The flow of the conventional fulfillment process 67

5. VMI Fulfillment Process from Retailer Perspective 68

6. The flow of fulfillment process using VMI 687. Activities Involved in Establishing VMI Process 69

8. EDI Documents used in VMI 71

9. Benefits of VMI Process 72

Retailer Benefits 72

Supplier Benefits 73

10. Challenges and Limitations of VMI 74

11. Overcoming the Limitations 74

12. Conclusion 74Bibliography 75


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NEED AND IMPORTANCE OF THE STUDY

Marketing products using visual merchandising system is an age-old practice but

with accelerated growth of retail industry, the art, or arguably the science, of

Visual Merchandising has gone to occupy a newfound fancy. There is a growing

recognition of the need for effective Visual Merchandising. But even as it

continues to grow, the understanding of Visual Merchandising impact and

effectiveness is still in its infancy.

The shopping behavior which governs the decision to buy is a function of three

stimuli viz., visual, auditory and kinesthetic; the visual stimulus is the easiest and

most widely used tool for attracting customers. Although Visual Merchandising

has long been an important part of retailing (clothing, house-wares, etc.) it is not

as well known or accepted within the food industry. While there is substantial

amount of research on each of the components of visual merchandising, a holistic

approach towards visual merchandising involving the consumers.

OBJECTIVE OF THE STUDY:

. Study the merchandising factors along with Plan-o-gram and inventory that

influence the consumer buying decision for product category.

Study the marketing mix for product category i.e. the product, its

characteristics and features, the price, the placement method used for product

category and promotional strategy used by this category (4ps of marketing).

Based on study of marketing mix for the product category, suggest changes in

planogram, inventory and availability that will help to increase in its sale in market.


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Research methodology

Research approach:

The research for this study is Qualitative Research

A Qualitative Research involves an in depth understanding of human behavior and the

reasons that govern human behavior. It relies on reasons behind various aspects of

behavior. It investigates the WHY and HOW of decision making.

This study based on more of Qualitative Research comprises the following.

Primary source:

Primary source of data comprises of direct interaction with people in four Big Bazaar

and different modern trade supermarkets all across Bangalore by help of past sales

record. All the required information has to be collected from this source only.

Secondary source:

Relevant additional and supplementary information will be collected from news

papers, internet, journals and past sales data.

Tools for data collection:

The approved questionnaire for interview is the main tool used for primary data

collection in this study. The interview consists of structured and unstructured questions.

The interview questionnaire tool is mainly used because:

Both qualitative and quantitative information can be gathered.

Factual survey can be done.

Opinion survey in order to secure personal opinions or on a particular matter can

be done effectively. This tool is administered through personal interview with the

target population.


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SCOPE OF THE STUDY:

The study confines itself to a few modern trade super markets and people in Bangalore

only.

SAMPLING PLAN:

1. Sampling procedure-

How should the respondents be chosen?

The sampling technique chosen are simple random sampling and stratified

Random Sampling is a sampling in which a sample is drawn probabilistically from

each group.

2. SAMPLE SIZE:-

How many respondents to be surveyed?

Due to time and other constraints, the size is 150 respondents. These samples of

Respondents are chosen randomly of different age group.

CROSS SECTIONAL STUDY:

A Cross Sectional study is a type of research design involving the collection of

information from any given sample of population elements only.


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SIMPLE RANDOM SAMPLING:

A probability sampling technique in which each element in the population has a known

and equal probability of selection. Every element is selected independently of every other

element and the sample is drawn by a random procedure from sampling frame.

STRATIFIED RANDOM SAMPLING:

A probability sampling technique is a technique that uses a two-step process to partition

the population into sub populations, or strata. Elements are selected from each stratum by

a random procedure.

ULTIMATE CONSUMER:

Ultimate consumer refers to those individuals who buy goods and services for final use or

consumption.

DATA ANALYSIS:

The data collected are analyzed and classified as required. Statistical techniques such as

frequency distribution, central Tendency, Percentages, etc, are used for analysis of

primary data. Conclusions are drawn based on the analysis and finding of primary and

secondary data.

DURATION OF THE STUDY:

The duration of the study is from 24 march 2007 to 24april 2006

LIMITATION OF THE STUDY

An attempt has been made to complete the project within the structured time

frame.

The study is limited to Bangalore only.

The study is not too substantial for want of more time.


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PLAN-O-GRAM


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Introduction: -

Going the extra distance with the display and merchandising of product throughout your

store can not only impact immediate sales but can also help you create an identity and

ambiance that work to build a loyal customer base. Unless you have a strong sense of

design, this area of your business may seem confusing. This Display and Merchandising

Guide was designed to help demystify the basics of this important facet of your retail

business by offering you new ideas and tips for general signage, directing traffic flow,

product merchandising, lighting, props and fixturing.

We have grouped our information by general topics, some of which include application

ideas for both the windows and the interior of your store. Be sure to read through thewhole guide for ideas that work best for you.

In addition to creating visual excitement, remember to keep the five senses in mind when

laying out your store. For instance, music related to your store concept and merchandise

selections will help create an overall mood. Aromatherapy can work wonders; introduce a

light scent such as perfumes or potpourri (remember to keep the scent light, a heavy odor

can drive customers away). Where appropriate, allow your customers to touch and

"experience" the merchandise.

Before you begin to adjust the design, display, and merchandising of your store you must

have a clear understanding of the image you wish to project.

To do that you will need to understand the demographics of the community in which your

store is located. What age groups are represented? What is the average income? What

lifestyle do they live or aspire to? What interests do they pursue? Within that community

you should identify the type of individual you hope to appeal to and gauge whether the

population base can support the sales volume you need to succeed. Look at competitors

within your market to see if there is a void you can fill. Whatever approach you take, a

better understanding of who you are appealing to, and the message you wish to

communicate, will make your displays more focused, more effective and easier to create.

To give you a more hands-on sense of how to display product, be sure to shop at other

stores. Whether or not the stores you visit carry like product, a trip through your local


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mall can offer adaptable ideas. When you browse through the many catalogs that reach

you through the mail, look for ideas. Vignettes and presentations pictured may be

duplicated or trigger an idea for a fabulous creation. Lastly when attending our shows,

dont forget to note the innovative exhibit display techniques you see, participate in one

of our Retail Tours or attend a Merchandising and Display seminar.

Recognizing and Directing Traffic Flow: -

In order to begin making changes to the product placement in your store you need to map

out an overall plan. To do this, you first need to recognize the current traffic flow of your

store and develop a plan to direct traffic flow so that customers will shop your entire store

and with their attention focused where you would like it to be. By strategically placing

demand/destination products and impulse items throughout the interior of your store, you

can balance the traffic flow throughout your store and increase your overall sales by

making the best use of every square foot. Start by taking the pulse of your merchandise

selection from the front to the rear of your store and follow these tips for redirecting

customer traffic to maximize your sales:

At the entry, introductory displays including graphics welcome and educate the

customer. The entry area is often referred to as the "decompression zone," where

the customer makes an adjustment to the new environment; takes off their glasses,

closes an umbrella and takes visual stock of the entire store. Sales rarely take

place in the "decompression zone" - in fact, most sales take place after the

customer passes through this area. For this reason, companies like Estee Lauder

prefer their cosmetic counters to be placed a few feet in from the department store

entry.

Once your customer passes through the "decompression zone" they look at the

price of the first item, generally to their right, that is easily accessible. This initialitem should have a price point that is not overwhelming to your customers, as this

area, called the "strike zone," offers your customer their first impression of your

store's prices. Extensive video auditing by professional retail designers has found

that in Western cultures, customers usually turn right immediately upon entering

a store into the "strike zone" and continue on their journey through your store.


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You should consider placing a compelling display of affordable products (in

relation to the price point of your overall merchandise) in the "strike zone."

Once through the "strike zone", the right wall of your store is usually your most

valuable real estate as this is the area that is generally traveled first and viewed

most thoroughly by our customers. On the right wall you may want to place

affordable items (in relation to other products within your store). This can include

products that you are promoting but which are not necessarily demand items.

Demand merchandise includes those items that the customer has made the

decision to purchase before they enter your store.

Traditionally, the cash wrap is centrally located. It is highly recommended that

you place your wrap to the left of the store entry and place impulse products

around the cash wrap. The cash wrap also serves as a security checkpoint and as

an area that can allow visibility to all parts of the store. When designing the cash

wrap area, keep in mind the many functions that will be accommodated by the

space and plan accordingly.

One of the most highly trafficked areas is the cash wrap. Add-on and impulse

merchandise should be placed above, behind and near the cash wrap where

possible. The cash wrap is the location that offers the most captive audiences (a

waiting customer) and is the point at which impulse sales are most often made. High demand products placed in the rear of the store will pull customers through

the store, increasing the visibility of other products along the way. Hallmark

stores often place their greeting cards at the rear of the store moving traffic

through seasonal, collectible and other merchandise to reach the destination area.

Add-on merchandise and impulse products are usually placed near the demand

merchandise in a highly trafficked area to suggest further purchases.

Place impulse items in the front of your store and in locations of high traffic

between the door and displays of demand products but outside of the

"decompression zone."


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Plan-o-gram: -

The placement of merchandise that is arriving to the store can be planned out on paper by

using a Plan-o-gram before the products actually arrive to the store. A plan-o-gram is a

retailer's drawing (blueprint) which visually communicates how merchandise and props

physically fit onto a store fixture or window to allow for proper visibility and price point

options. The retailer can plan to mix the new products with current items or initiate

entirely new displays. If you have more than one store this is an excellent way to

communicate to your staff how you would like displays executed.

Planogramming is a skill developed in the fields of merchandising and retail space

planning. A person with this skill can be referred to as a planogrammer.

Fixturing

Fixturing is the furniture that holds and displays the majority of your merchandise. It is

one of the more difficult subjects to address because every store has different needs to

show its merchandise. The style of fixture you choose should reflect the store's image and

include anything from hardwood custom cabinetry to inexpensive raw wood or brass and

glass shelving. Crate and Barrel became famous by using the shipping crates in which the

product arrived as fixtures for display. Depending on the type of product you sell, the

product itself can also serve as shelving. You may sell furniture pieces that, while in your

store, can act as display units. Don't overlook antiques or unique pieces of furniture that

can create a signature look to your store.

Change and rotate the fixtures within the store to add variety and excitement to the

shopping experience. Keep in mind that some fixtures can be used for display in a

window as well as on the sales floor and fixture and window rotation is up to the

individual shopkeeper. Usually, the retailer changes the interior and window displays

according to the return pattern of their typical customer within a given period of time. For

example, if a customer shops your store twice a month, make a small change twice a

month and a dramatic change once a month. A small change can consist of switching key


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merchandise in a window or interior display. A dramatic change can consist of moving

fixtures within the store or redesigning the front display window. Think about putting

your display racks on wheels so that you can easily reconfigure your departments to

emphasize and de-emphasize product categories depending on inventories, promotions

and seasons.

The most successful fixture systems are installed to be flexible and offer you the

opportunity to make major display reconfigurations with little or no additional

investment. Use the flexibility of these fixtures on a frequent basis to add interest and

excitement to your store.

Basic types of fixtures for consideration:-

Wall shelving

Floor standing shelving units

Pedestals

Tables

Bins

Revolving display stands

Wheeled carts

Security fixtures like glass showcases

Hanging fixtures

Waterfall

Faceouts

Roundracks.

Bar

Antiques Armoires

Unique pieces of furniture


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Tips for fixture selections:

Keep in mind the scale and size of your merchandise while planning your

purchase of fixtures.

Make certain the fixture you select will physically carry the weight of the product

you plan to display on it.

Include costs for shipping to your location into the overall expense of the fixtures.

Consider the cost of the fixture as compared to the possible revenue that will be

generated from it in its area of real estate within your store.

When purchasing the hardware accessories for any fixture for your store, consider

the different types of product that might be displayed on each unit. For instance,

some units offer shelving which can be removed to make way for a hang-bar. Be

sure that when someone buy the unit you purchase all the hardware necessary for

each configuration you will use.

If your store has a vendor or brand shop, the fixtures in this area may be different

than fixtures used in the rest of your store, in order to add a special cache to the

brand merchandise. Special terms sometimes apply to vendor fixturing purchased

with merchandise (i.e. free freight). These types of fixtures should be used on a

limited basis and primarily with very high-profile merchandise. Too many vendor

fixtures in varying types can detract from the store's overall ambiance.

Lighting used in retail stores: -

There are many different varieties of lighting fixtures a retailer can use in a store. Simply

changing the type of light bulb in your current fixture can make a large difference. The

lighting industry is constantly changing and introducing new variations of light bulbs to

the market. Visit your local lighting store to discover the selection of bulbs available.

Quartz halogen bulbs and compact fluorescent bulbs have recently made dramatic

additions to the market with their technologically advanced color renditions. Here are a

few lighting choices to consider and an explanation of the applications they are most

suited for:


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General lighting illuminates both the merchandise and the traffic path in a store. It is

usually not flexible

Accent lighting can accentuate merchandise and is usually designed for adjustability.

Most accent lighting is placed to highlight focal displays, or other areas of prime real

estate.

Task lighting is used in work areas, such as under the counter of the cash wrap or in a

stock room. This lighting is usually fluorescent and should not create shadows.

Graphics and Signage: -Interior graphics and signage can show brand identification of specific products, identify

classifications of product within your store, and, depending on the size of your store,

offer direction to various departments. Interior signage can be a medium for promoting a

campaign, previewing a product "coming soon" or announcing an upcoming event like a

book signing, demonstration, or a holiday promotion.

Here are a few ideas for graphics and signage:

Large graphics can reflect product style. For instance, you could use a blow-up of

a Monet floral painting behind a display of floral merchandise. For added impact,

repeat that Monet graphic within your store near the merchandise for sale. If your

store sells children's products, like educational toys, you could use a blow-up of a

little red schoolhouse or a college campus as a backdrop for the merchandise.

Large graphics can suggest a lifestyle or how your products are to be used once

purchased. For example, a graphic of a family enjoying the outdoors can beplaced behind picnic or beach items that you might have for sale. To promote a

casual summer line of clothing a recent Ann Taylor window pictured a large

graphic of a summer lighthouse behind the clothing display.


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Repetition of large graphics in one window, various windows or throughout the

store in various sizes serves as a reminder of a particular product, creates a

dramatic effect and draws your customer from the window through the store.

If you have a well designed logo, reproductions of the logo on theatre scrim,

another type of fabric or paper can be hung in your window as a backdrop to

changing product displays.

Merchandising Similar Products Together: -

Merchandising similar product together can create a dramatic impact, while quickly

educating a customer to the depth of product you carry within a given category. This type

of merchandising presents a visually clean image and makes the best use of the

customers' time in your store by making it easy to identify where the product is located.

Displaying similar products together in a window is called creating an impact window.

This type of presentation is dramatic and creates an awareness of the variety of a

particular selection inside the store. For example:

If you carry an extensive line of mugs, you could create a dramatic presentation

by simply stacking your product in the window.

Placing similar products together inside the store is called creating a shop interior,

anchor area or niche. This is sometimes called creating a store within a store.

These areas are the basic building blocks of your store and this type of interior

organization is most commonly used by retailers. When you create an anchor area,

merchandise is usually placed together with similar product, brand, color or texture. For

instance, all of your lamps will be in one section, perhaps organized by brand, while all

of your stationery will be in another. This product grouping works especially well for

demand items. It allows your customers to quickly find what they are looking for and to

see the breadth of product you offer within any given category. You may want to create a

focal point which incorporates cross-mix merchandising within each area


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Cross-Mix Merchandising: -

Cross-Mix Merchandising is displaying a variety of seemingly unrelated products

together to create a comprehensive visual story. This type of merchandising

communicates breadth of product and educates your customer about merchandise they

may be unaware that you carry.

Cross-mixing merchandise within a Window can increase the visibility of your store

image and promote the look of a certain lifestyle for customers to buy into. It illustrates

the variety of selection or breadth of product you carry.

To cross-mix you can use larger items within your product lines as props for smaller

items. Pottery Barn has created vignettes that cross merchandise items like adirondack

chairs, lanterns, outdoor dinnerware and throws. They carry the theme into the store by

creating smaller versions of the vignette throughout various departments of their store.

Williams Sonoma created a window display including a large graphic of cherries in

bushels behind a selection of product including a Cuisinart, ceramic pie plate, measuring

spoons, pastry board and checkered towels. Their theme "pie making" was stenciled on

the window. Tiffany created a cross-mix window representing a "fantasy" lifestyle. A

small picnic table, chairs and mosquito net served as prop back-drops for a selection of

high-end dinnerware, crystal, candle holders, pitchers and serving pieces. A wide-

brimmed sun hat was draped over a chair on gravel flooring and a floral arrangementcompleted the picture.

Tips for Cross-mix merchandising:

Retailers today often sell merchandise by portraying a dream lifestyle for the

customers to buy and take home. Sell your products by selling dreams.

Remember to keep your cross-mixed visual merchandising displays clean and to

the point. The average customer views a focal display of merchandise for about

one second.

Be sure to place displays featuring cross-mixed products in high traffic areas and

as focal points within a department. Don't be afraid to use both demand and

impulse items in your display.


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Visual Merchandising Tools and Supplies: -

Here is a list of visual merchandising and display supplies every store should have on

hand:

Calendar listing of all holidays and special occasions

Duct tape

Fishing line

Glass cleaner

Hammer

Hot glue gun

Hot glue sticks

Iron with board or steamer

Ladder

Light bulbs (extras)

Nails and screws (assorted)

Pencils and sharpener

Rubber bands

Scissors

Screwdrivers, flat tip and phillips head

Straight dress pins

Tape measure

Tool box

Two-faced tape

Utility/ razor knife

Velcro strips

Wire

Yellow pages


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Plan-o-gram Examples: -

Photographic Plan-o-gram: -

Plan-o-gram Block Layout: -


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Plan-o-gram Line Layout:-


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Basic Criteria for creating Plano-gram

1. Sales appeal (demand).

2. Margin (profitability).

3. Taste.

4. Flavor and size.

5. Consumer behavior.

6. Buying behavior.

7. Consumer convenience

8. Balance

a) Formal balance (placing large items with large items and small itemswith small items in display)

b) Informal balance (balancing a large item with several smaller ones)

9. Dominance. (All display should have a central point that will attract

Viewers eye)

10. Eye movement (Human eyes tend to scan from left to right and also the

mind tends to retain the last object seen by eye. We can use this psychology to

improve sales)

11. Gradation (it is the sequence in which items are arranged)

12. Height of merchandise.

13. Grouping merchandise (Place all the company products with similar need

at one place)

14. Keeping it simple and systematic

Creation of Plan-o-gram for Real juices of Dabur Foods Limited in Big Bazaar and thesales data and analysis are given below


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DATA ANALYSISANDINTERPRETATION

Real activ 1 lt. sales during year2006-07:-


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Flavour Total (1lt ) Total (330 ml.)

Apple 4242 886

Beetroot carrot 1193 273

Orange 3688 886Orange carrot 2804 631

Cucumber spinach 1238 655

Real Active 1lt.

0

1000

2000

30004000

5000

Apple Beetroot

carrot

Orange Orage carrot Cucumber

spinach

Flavour

Quantity

Apple Beetroot carrot Orange Orage carrot Cucumber spinach

Real Activ of 1 lt.

1. Apple -3 facings

2. Orange -3 facings

3. Orange carrot -3 facings

4. Beetroot carrot -2 facings

5. Cucumber spinach -2 facings

Total 13 facingsThis should keep in lower shelf because of the size and margin in rupee.


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Real active 330 ml. sales during year2006-07:-

Flavour Total

Grape 942

Guava 2133

Litchi 3951Mango 3806

Mausambi 620

Mix fruit 5223

Orange 4163

Pineapple 1189

Tomato 770

Cranberry 1344

Real Active 330 ml.

0

200

400

600

800

1000

Apple Beetroot

carrot

Orange Orange

carrot

Cucumber

spinach

Flavour

Quantity

Apple Beetroot carrot Orange Orange carrot Cucumber spinach

Real Activ of 330 ml.

1. Apple - 2 Facings2. Beetroot carrot - 2 Facings3. Orange - 2 Facings4. Orange carrot - 2 Facings5. Cucumber spinach - 2 Facings

6.Total No. of facings - 10 facings

This should keep in fridge section upper shelf because of the size and margin in

rupee and sales.


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Real Juice 1 lt. sales during year2006-07:-

Flavour Total

Grape 942

Guava 2133

Litchi 3951

Mango 3806

Mausambi 620

Mix fruit 5223

Orange 4163

Pineapple 1189

Tomato 770

Cranberry 1344

Real Juice 1 lt.

0

1000

2000

3000

4000

5000

6000

Grape

Guava Lit

chiMa

ngo

Mausambi

Mixfruit

Oran

ge

Pine

apple

Toma

to

Cranbe

rry

Flavour

Quantity

Grape

Guava

Litchi

Mango

Mausambi

Mix fruit

Orange

PineappleTomato

Cranberry

Real Juices of 1 lt.

1. Litchi -3 facings 2. Mango -3 facings

3. Guava -3 facings 4. Cranberry -3 facings

5. Grape -2 facings 6. Mix fruit -3 facing

7. Mausambi -2 facings 7. Pineapple -2 facings8. Tomato -2 facings 9. Orange - 3 facings

10. Pineapple -2 facings

Total 28 facings

This should keep in the middle shelf, since customer attraction is more for middle

shelf.


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Real Juice 200 ml. sales during year2006-07:-

Flavour Total

Grape 786

Guava 4199

Litchi 3567

Mango 2324

Mausambi 2292

Mix fruit 3760

Orange 3817

Pineapple 1319

Real Juice 200 ml.

0

1000

2000

3000

4000

5000

Grap

e

Guava

Litchi

Mang

o

Mau

sambi

M

ixfruit

O

range

Pinea

pple

Flavour

Quantity

Grape Guava Litchi Mango

Mausambi Mix fruit Orange Pineapple

Real Juice of 200 ml: -

1. Litchi -2 facings 2. Mango -2 facings

3. Guava -2 facings 4. Grape -2 facings

5. Orange -2 facings 6. Mix fruit -2 facing

7. Mausambi -2 facings 7. Pineapple -2 facings

8. Tomato -2 facings

Total -16 facings

This should keep in the middle shelf fridge section, since customer attraction is more

for middle shelf.


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Real Twist Juice 1 lt. sales during year2006-07:-

Flavour Total (1 lt.) Total (200 ml.)

Twist orange 2626 1802

Twist papaya 266 2715

Real Twist 1 lt.

0

500

1000

1500

2000

2500

3000

Twist orange Twist papaya

Flavour

Quantity


Real Twist Juice of 1 lt.1. Real Twist orange - 3 facings2. Real Twist papaya - 2 facings

Total facings - 5 facings

This should keep in side of Real juice because it attracts customer due to different

colour and packaging

Real Twist Juice 200 ml. sales during year2006-07:-

Real Twist 200 ml.

0

500

1000

1500

2000

2500

3000


Flavour

Quantity


Real Twist Juice of 200 ml.1. Real Twist orange - 2 facings2. Real Twist papaya - 2 facings

Total - 4 facings

This should keep in upper and middle shelf of fridge section and it can compete with

frooti and other soft drinks


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Coolers 1 lt. and 200 ml. sales during year2006-07:-

Flavour Total Total

Aampanna 2029 6920

Lemon barley 156 1246

Rose litchi 2106 1448

Water melon 430 2216

.

Coolers 1 lt.

0

500

1000

1500

2000

2500

Ammpanna Lemon barley Rose litchi Water melon

Flavour

Quantity


Coolers of 1 lt. (Summer juice drink)

1. Aampanna -3 facings 2. Rose litchi -3 facings

3. Water melon -3 facings 4. Lemon barley -2 facings

Total: - 11 facings

This should keep in the upper shelf and also in fridge section, due to special product

Coolers 200 ml

0

2000

4000

6000

8000


Flavour

Quality


Coolers of 200 ml.

1. Aampanna -2 facings 2. Rose litchi -2 facings3. Water melon -2 facings 4. Lemon barley -2 facings

Total: - 8 facings

This should keep in the upper shelf and also in fridge section, due to special product

for summer


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Some facts or psychology used to make a good plan-o-gram in packaged

fruit industry: -

Human eyes tend to scan from left to right and also the mind tends to retain the

last object seen by eye. We can use this psychology to improve sales.

Since most customers are right handed (about 90%) they will tend to take the

product on the right hand, instead of reaching across their body to take the

product kept in left side. So we can keep fast moving juices in right and slow

moving in left side ..

We should arrange similar brand in one shelf (horizontally).like Real juice all

flavor in one shelf.

Keep all variant vertically at one place so that accessibility and visibility will be

convenient for the customer

Suggestions and recommendations: -

First, in the upper shelf coolers and small packs of real juices and coolers

small packs, then real juice 1lt, then small pack of mango twist and

remaining real juice flavors, then real active small packs and in lower shelf

real active 1lt.

Since in big bazaar outlets and also in modern trade outlets, the shelf size is

not constant so that we have to adjust some variation in vertical

arrangement, in horizontal arrangement all outlets shelves are similar.

Total number of facing for all juices: - 95 facings in most of modern trade

outlets.


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Inventory ofRetail Stores


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Introduction

KNOWLEDGE of monthly inventory trends is a useful guide for business management

and an important factor in economic analysis and planning. Trends of orders, production,

and sales require this additional item in order to be the basis of policy-making on a large

or small scale. While some data are avail able currently on inventories in the hands of

producers and wholesalers, little is available on a monthly basis concerning the stocks of

retailers, and practically nothing concerning consumers holdings. Retailers stocks on an

annual basis or at less frequent intervals are available from the Bureau of the Census and

a number of private research organizations and trade associations. On an all-commodity

basis there are available monthly reports of the Federal Reserve Board on department

stores inventories (and to a limited degree on several other lines). The A. C. Nielsen

Company and other organizations compile retail commodity inventories, but little of this

statistical information is published. It may be said for most trades that very little is known

of the behavior of retailers inventories.

Accurate data on changes in inventories and their relation to changes in the volume of

trade would be very valuable at present to several groups of interests:

1) The inventory policy of an individual retail store may be formulated more intelligently

if its management knows inventory trends in the trade. There are approximately1,70o,ooo retail stores, whose operations might be more or less altered by the availability

of adequate information on stock movements. Both buying and selling should shift with

changes in inventory. When stocks are low, the merchant must take an active part in the

market or find himself outbid in his at tempts to replenish his shelves. Conversely,

increased competition to sell follows inventory accumulation and selling efforts

(including advertising promotion) must be quickened to offset such changes in inventory

position.

(2) The inventory position of retailers not only is a factor in their own operation but

influences schedules of producers and merchandising policies at the intermediate level of

distribution. Inherent in the more integrated phases of business is the greater importance

of single decisions. Therefore, such information is more critical to these business men in

arriving at their far-reaching decisions.


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(For the last two years, knowledge of inventory positions has been increasingly needed

by those who are directing the mobilization of national re sources in an all defense effort.

The flow of goods from producers to the armed forces, lend-lease aid, or consumers,

requires the maintenance of adequate but not overabundant inventories at each of the

several levels of production and distribution.

(In broader terms, knowledge of changes in inventories, and their relation to changes in

the volume of trade, is important to the economist because changes in inventory

accumulation and depletion assist in forecasting the direction, timing and amplitude of

cyclical changes.

Model Specification and Optimality Conditions

In developing a decision-making framework for clearance markdowns, it is important to

note at least four ways in which clearance prices differ from other types of retail pricing

decisions: (1) Clearance markdowns are

permanent, i.e., prices are not permitted to increase, (2) demand tends to decrease at the

end of the clearance period due to incomplete assortments and reduced merchandise

selection, (3) clearance prices are generally not advertised, which allows different pricing

policies to be used at different locations in the same geographic area, and (4) the

clearance period is so short that there is little time to correct pricing errors by reacting to

observed sales.

Motivated by these observations and other factors discussed below, our modeling

assumptions are as follows

Sales rate depends explicitly on price, seasonal variations, and inventory level.

Sales rate is decreased by low inventory levels but not affected by high

inventory levels.

Competition, demand uncertainty, and time discounting are not explicitly

included in the model.

Price dependence specifies the increase in sales rate as a function of the clearance

markdown. Seasonal variations capture the increase in sales rate that tends to occur


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during certain prime shopping periods, such as Christmas and back-to-school, and the

decrease that occurs at the end of the products season. When the on- hand inventory falls

below a certain level at any given store, the sales rate may drop. This is especially flue

for apparel when there is an incomplete selection of sizes and colors. In addition, for

some items, it is important to have sufficient inventory to create an attractive in-store

display to draw customers attention to the product.

A significant positive correlation between inventory levels and retail sales was found by

Wolfe (1968) and Bhat (1985). We found a similar correlation in apparel sales. However,

we argue in 3 that the inventory effects should be one sided in our applications, i.e.,

low inventory decreases sales, but high inventory does not necessarily increase sales. The

retailers we studied tend to intentionally schedule larger deliveries during periods of high

sales, implying that causality should not be attributed to high inventories, even though

positive correlation exists. On the other hand, virtually all buyers felt that inventories

below some threshold level do reduce sales, which was supported by our regression

results. Retailers often define a minimum on-hand inventory for each product, sometimes

called fixture fill, which is the quantity required for adequate presentation. We use this

threshold in defining the inventory effect in our model.

Competition and demand uncertainty are not explicitly captured in our sales rate model.

However, sales by competitors are implicitly reflected in the seasonally adjusted rate of

sale. This is appropriate as tong as competitors do not react directly to each others price

changes. For unadvertised clearance markdowns taken at the store level, competitive

reactions seem very unlikely, given that most retail chains have hundreds of stores, each

with different local competitive conditions.

Demand uncertainty clearly exists, but complicates the analysis to a great extent. Optimal

clearance pricing in the presence of gradually decreasing demand uncertainty would

require multistage pricing decisions, which would need to be jointly optimized by

stochastic dynamic programming. The state space for this problem is extremely large,

because it must capture all the possible changes in the states of information that influence

each update of the pricing policy. Because the clearance period is relatively short and

sales rates are declining, the first clearance markdown tends to be the dominant decision


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economically, thus reducing the importance of multistage optimization. The last

observation also justifies the lack of time discounting in the model, We therefore develop

a deterministic pricing formulation and allow for the possibility of revisiting the pricing

decision, at most once or twice during the clearance period.

Sales Rate Function

The sales rate is defined as a continuous function of time, price, and inventory using the

parameters listed below The decision variables are the optimal inventory commitment Io

and the optimal price trajectory p(t).

to = current time of the season,

te

=end of the season, sometimes known as the outdate,

t = an arbitrary time to t te,

Ho = on-hand inventory at time to

Io = inventory commitment at time to, Io Ho,

o = minimum required inventory, or fixture fill

In microeconomic analysis, the demand function is typically derived from a

parameterized family of customer utilities or way to pay. This is the approach taken by

Dhebar and Oren (1985) and Stoke> In the marketing literature, it is more common to

simply define a price dependent sales rate, as in I (1963)and in the literature, on

diffusion models. This paper adopts the later approach on the grounds that it is easier to

estimate sates rates directly than to estimate the underlying family of customer utilities.

p(t) = price trajectory at time t,

s(t) = cumulative sales from current time to to time t,

H(t) = the on-hand inventory at time t,

I(t) = I0 s(t) = inventory commitment at time t,

se= S(te) = total units sold by te and

x(p, H, t) = the sales rate at time t, with price p and on-hand inventory H.


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Some explanation of the difference between the inventory commitment and on-hand

inventory is war ranted. The inventory commitment I(t) is defined as the sum of the on-

hand inventory H(t) plus planned future deliveries. Thus, I(t) = Io - s(t) is always non

increasing in t, but H(t) could increase at certain points in time when shipments are

received. For the purpose of my analysis, it is useful to write the sales rate in terms of

I(t), rather than H(t), because I(t) can be expressed in terms of the cumulative sales s(t).

The value o defines the threshold at which the sales rate actually begins to be affected by

the on-hand inventory level. The following assumption allows the sales rate to be written

in terms of I(t).

ASSUMPTION 1:

If H(t) < o then I(t) = H(t). Thus x(p, H, t) = x(p, I, t).

That is, by the time sales become sensitive to the inventory level, the inventory

commitment and the on-hand inventory are equal and remain equal for the remainder of

the season. This assumption holds in general for the seasonal merchandise sold by the

retailers I studied because all deliveries of new merchandise are completed well before

the period starts. Occasionally, merchandise that is unexpectedly popular falls below the

fixture fill o before the period starts. However, planned deliveries would typically be

accelerated for this merchandise, thus satisfying the assumption.

The effect of the minimum inventory level o on the sales rate function can be illustrated

by graphing the function y(I) = x(p, I, t) / x(p, o, t), holding p and t fixed. The special

case of a linear y(I) is illustrated in Figure 1. Since inventory above o makes no

additional contribution to sales, y(I) = 1 always holds for I o Clearly


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Which can also be expressed as a differential equation for I(t):

I(t) = -x(p(t), I(t), t) for each t. . (2)

It is also required that se Io, where the unsold units Io - se = I(te) are salvaged.

Inventory Decision and Cost Model

With Io as a decision variable, the cost function must reflect the cost of changing to I o

from the current inventory commitment, which is denoted by Io:

Io= the current inventory commitment level.

The current inventory commitment Io can often be adjusted up or down within specified

limits. Planned future delivery quantities may be reduced, for example, subject to a

cancellation charge paid to the supplier or an implicit cost reflecting loss of goodwill.

Additional units may also be ordered to increase the inventory commitment within limits.

Due to the shortness of the period, this cost model does not use time discounting or time-

based holding costs for on-hand inventory. This removes the need to consider the

delivery schedule explicitly, as long as it satisfies Assumption 1. For most items, the on-

hand inventory cannot be returned once it is placed on display and it is not cost effective


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to ship on-hand units to another store. Unsold units at the end of the clearance markdown

period typically have a positive salvage value because the retailer may sell leftover

merchandise to a discounter, or donate it to charity, receiving a tax deduction.

The inventory cost therefore depends upon H0 and I0, as well as the followingparameters:

A0 = maximum possible inventory commitment,

cd= total unit cost for items delivered and displayed in the store,

ce = unit salvage value for inventory left unsold at the end of the season, and

r = unit cost for reducing the inventory commitment.

A piecewise linear function c(I0) can be defined as follows to express the total inventory

cost:

The cost c(I0) is the total cost, reflecting both sunk costs and the cost of the change from

I0 to I0 For Io Ho, cdHo is a sunk cost and Ho Io is excess inventory, which generates

revenue ce per unit. This revenue there fore appears with a negative sign in the cost

function. (In fact, it will never be optimal to adjust Io Ho because any part of the

inventory Ho that is not sold by the end of the clearance period will simply be salvaged.)

For Ho Io Io, planned future deliveries are canceled at a unit cost r, and revenue is

generated from the salvaged units Ho - Io. For Io> Io additional units are obtained up to

the limit Ao


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Objective Function

The objective is to maximize profit, defined as revenue minus cost for the remainder of

the season. At any point in time t the profit equals the revenue obtained from the I0 units

in the inventory commitment minus the cost c(Io). The profit can be expressed as:

First-order necessary conditions (FONC) for maximizing (4) with respect to p(t), subject

to the stated constraints, can be obtained from the Hamiltonian H = (p -)x, treating I(t)

as the state variable and p(t) as the control, where the Lagrange multipliers ate

= the Lagrange multiplier for the constraint Io -se = I(te) 0, and

(t) = the Lagrange multiplier for I(t) = -x(p(t),It,t) at time t.

The FONC for the optimal control p(t) are: -

(Subscripts p and I denote partial derivatives and the independent variable t has been

suppressed for notational compactness.) By substituting for p - from (6) into (5), we

obtain

By evaluating (9) at t = te and combining with (7), we obtain a boundary condition for


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The choice of the inventory commitment Io affects the FONC for p(t) only through (10),

in that only depends upon Io

The decision variable Io selected so as to maximize R(Io) c(Io) where R(Io) denotes the

revenue from (4) using the optimal price trajectory with inventory commitment Io. Sincethere is no discounting, a FONC for Io can be obtained from the fact that the marginal

revenue derived from the last unit Io must equal its marginal cost c(Io) i.e.,

Discounting is not included in this formulation because the clearance period is so short

typically three to four weeks. Fixed handling costs associated with preparing

merchandise for display can be incorporated into cd and ce. Our discussions with

retailers indicated that fixed handling and display costs are the primary drivers of store-

level inventory costs. The shortness of the clearance period also reduces the Importance

of time dependent costs. The three-part form of c(S) assumes that ce < cd r < cd.If cd r

< ce, order cancellations are never attractive and c(S) has two parts.

The Separable Sates Rate Case

Specific assumptions concerning the functional form of the sales rate x(p, I, t) allow (8),

(9), and (10) to be solved explicitly for the optimal price trajectory. A common form,

which we adopt in this paper, is a multiplicative, separable function with exponential

price sensitivity

where

k(t) = seasonal demand at time t,

y(I) = inventory effect when inventory commitment is I, and

e-p= sensitivity of demand to price p.


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Although much of this papers development can be car ried through for a more general

demand function, a closed form solution is obtained only for the separable function (12).

Exponential price sensitivity has been ap plied widely in marketing studies and has

generally been found to be superior to linear price sensitivity in empirical studies.

For the separable form (12), we have that x/xp = -1 / is a constant. From (8), it

therefore follows that p(t)= (t). Thus, (8) and (9) yield a differential equation

that can be solved for p(t)

Mathematically similar formulations have been studied in other contexts. Kalish (1983),

Dhebar and Oren (1985), and Mahajan et al. (1990) developed formula tions that are

sensitive to experience effects rather than inventory, which lead to similar conditions for

the op timal price trajectories. Rajan et al. (1992) obtain optimal price solutions for a

separable demand form that is anal ogous to (6), with a time varying y. Gallego and van

Ryzin (1994) obtain an optimal price trajectory for the case of exponential price

sensitivity and Poisson demand arrivals. These formulations do not consider the

dependence of sales on the current inventory level or seasonal variations.

Rajan et als generality is in their analysis of variable cycle length and their explicit

consideration of shrinkage and other inventory costs. They obtain closed form optimal

price trajectories for the cases of linear and exponential price sensitivities. Some

shrinkage is likely to occur in the retail environments we studied. For our analysis, we

believe that the clearance pricing period is short enough that this effect can be neglected.

Variable cycle length is used for clearance pricing of discontinued basic items by some of

the retailers we contacted. In the three applications we analyzed, however, a fixed

clearance calendar is required to coincide with the planned arrival of new merchandise.


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Compensating Prices

We solve (13) by proving that the optimal p(t) adjusts the sales rate in such a way that

x(p, I, t) is proportional to k(t) for all t. That is, p(t) should exactly compensate for any

reduction in sales due to y(I(t)). This result is stated as the following lemma.

LEMMA 1.

For the multiplicatively separable sales rate function given by (12), Equation (13) implies

tb1zt the optimal policy is to adjust p(t) so that sales remain proportional to k(t).

PROOF:- We wish to show that

is constant in t. Suppressing the dependence on t and I

from (13), after substituting I = -kye-p from (3).

Lemma 1 implies that p(t) should be selected so that

wherey. = y(I(te)), I(te) = -Io- se and pe = p(te) are the terminal values of the parameters.

Equation (15) shows that the optimal price p(t) depends upon I(t), but not upon t.

Therefore, by defining a new function P(I(t)) = p(t), (15) can be solved for the price

trajectory as a function of the inventory level I

The cumulative sales from to to t is determined by substituting (12) and (15) into (2)


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Boundary Values

The complete so of (16) requires the determination of the terminal values pe and ye. From

(17), it follows that

where K= K(to,te). Substituting (18) into (16) yields

One of two cases must hold at time te.. Either > 0 and se = Io, which gives

ye = y( Io- se) y(0). Otherwise, = 0 and pe = ce + 1/ is determined from (10), using the

fact that x/xp = -1/ for the case being considered.

For the case of > 0, the terminal price specifies the trajectory that sells precisely the

inventory I We define this price as a Function of Io

Since Pece + 1/ must always hold, it follows that

The price trajectory (19) is now completed by determining s If pe = po(Io) in (22), all units

are sold and se= Io. If pe = ce + 1/ in (22), the solution for se . is obtained by substituting

the right side of (20) for pe and rearranging terms to obtain the relationship


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Since y(Io - se) is non increasing in se and po(Io) < ce + 1/ implies y(0)Ke- ce-1 < Io it

follows that (23) must have a unique solution for se

Solving for the Optimal Inventory Commitment Io

All the FONCe obtained so far apply when I is a deci sion variable as well. From (11) the

additional relation ship pe + 1/ = c(Io) allows Io to be determined by substitution into

(22)

Since po(Io) is decreasing in Io, the solution of (24) is unique, as long as the marginal cost

c(Io) is non decreasing.

It is interesting to note that the terminal price pe and the optimal inventory commitment Io

depend only upon the minimum inventory effect value y(0) and not upon the shape of the

function y(I), except that y(I) is non- decreasing. However, to determine the price

trajectory P(I), the shape of y(I) is required. From (19), it can be seen that the initial point

on the price trajectory at t = to satisfies

This allows the optimal price trajectory to be solved for ward in time from to to te

Tabulated Solution and Interpretation

The solution of (23) is illustrated in Figure 2 and is tabulated in Table 1. Since the

marginal revenue is decreasing in 1 and the marginal cost is increasing in the step wise

manner shown in Figure 2 there must be exactly one intersection. The six possibilities

arise from the different ways in which the marginal revenue pe - 1/ from the last unit Io

can equal the marginal cost c(Io).


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Interpretation of the Six Solution Cases

The six cases can be interpreted as follows. The number of mills sold equals the total

inventory commitment in all cases except Case 1

1. The on-hand inventory is so large that it cannot all be sold using the minimum terminal

price ce + 1/ . Reduce the inventory commitment to the quantity on- hand and use the

minimum price.

2. All the on-hand inventory can be sold using a terminal price po(Ho), which is greater

than the minimum. However, the marginal Cost savings cd - r obtained by reducing the

inventory commitment is greater than the marginal revenue pe (Ho) - 1/ that can be

obtained from selling the merchandise. Therefore, reduce the inventory commitment to

the amount on-hand by cancel ling future deliveries and use the price that clears all on-

hand inventory.

3. The marginal cost cd - r of increasing the inventory commitment lies between the

marginal revenue associated with selling all the on-hand inventory and selling all the

inventory commitment. Set the inventory commitment so that the marginal revenue is

equal to cd - r and use the pricing policy that clears all this inventory.

4. The marginal revenue po(Io) - 1 / associated with clearing all the current inventory

commitment lies between the marginal cost of decreasing the inventory commitment and

the marginal cost of increasing it. Therefore, keep the current inventory commitment and

use the pricing policy that clears all inventory.

5. The marginal cost c associated with increasing the inventory commitment is less than

the marginal revenue associated with the current inventory commitment. Therefore,

increase the invent commitment until the marginal revenue equals cd and use the pricing

policy that sells all this inventory.

6. When the maximum units available Ao are sold, the marginal revenue is still greater

than the marginal cost cd. Therefore, increase the price so that exactly A0 units are sold

and set the inventory commitment to Ao


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Observations Concerning the Optimal Trajectories

The optimality conditions (23), (24), arid (25) can be used to derive some insights

concerning the behavior of the optimal price trajectory and the optimal number of units

sold. These will be discussed in terms of a parameter that measures the sensitivity of


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y(I) to inventory effects. A linear sensitivity is illustrated in Figure 1, and an exponential

sensitivity is discussed later in this section. The observations below assume only that y(I)

decreases monotonically as increases.

1. If the inventory effect is active for part of the time, total unit sales decrease as theinventory sensitivity increases. For a sufficiently high inventory sensitivity, some units

will always be left unsold at the end of the season.

2. The optimal initial price P(Io) is invariant to the inventory sensitivity, as long as all

units are sold. When not all units are sold, increasing the inventory sensitivity leads to a

higher initial price during the regular selling season.

3. When it is optimal to sell all units, an increase in the inventory commitment leads to an

equal increase in the wilts sold. When it is not optimal to sell all units, an increase in the

inventory commitment leads to (i) a fractional increase in the optimal units sold when

inventory effects are active and (ii) no change in the units sold when the inventory effects

are not active.

Proofs for these observations are given in Appendix A.

Two Models for Inventory Effects

The optimal solutions in Table 1 hold for any smooth function y(I) that is non decreasing

in I and bounded 0 y(I) 1. For the three clearance markdown applications described in

this paper, we selected a two-part linear function of the form

Where

I = the current inventory level,

o = the threshold level or minimum inventory for effective presentation, and

= sensitivity to inventory level, with 0 < < 1,

As illustrated previously in Figure 1. When substituted into (16), the linear form

(26) leads to a price trajectory that depends logarithmically on the inventory level.


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An exponential model of the form can also be used, which leads to an optimal price

trajectory that depends linearly on the inventory level. It should also be noted that (26)

and (27) are approximately equivalent when is fairly small. Both models use a

threshold level o, so that y(I) = 1 for I o. The threshold o is motivated by the

requirement for a minimum inventory for merchandise presentation, discussed

previously.

To test the correlation between sales and inventory level both with and without the

threshold, we per formed regressions on sales data from a department store that

frequently had low in-store inventories of apparel merchandise. (The regression equation

is given in 4.) Pooling sales data from four product categories over a two-year period,

we obtained the following results for the inventory effect on sales.

Parameter t Statistic Adjusted R-Square

With Threshold 0.651 8.9 0.81

Without Threshold 0.746 16.6 0.80

It is clear that inventory effects are highly significant in both cases, and that the resulting

parameter and R-square values are not greatly different. Thus, the explanatory power of

the model, as measured by the adjusted R-square, is not reduced by truncating the

inventory effect.

Wolfe (1968) and Bhat (1985) also found significant positive correlation between

inventory level and sales using a linear model analogous to (26) with no threshold level.

For our applications, the buyers felt (and we agreed) that it is not appropriate to attribute

high sales to high inventory levels, although our regression analyses found a positive

correlation. This is because retailers tend to plan deliveries of extra inventory when they

expect unusually high sales. On the other hand, low inventories do have a causal basis for


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decreasing sales due to broken assortments or poor presentation. Thus, introducing the

threshold o appears to result in a more appropriate causal model.

Implementation MethodsThe model described in this paper has been implemented in various forms at three major

retail chains. This section illustrates typical sales rate and price trajectories and discusses

methods for estimating the models parameters that are relevant for all the applications.

The applications themselves are described in the next section.

The parameters required by the model were estimated by a combination of regression

analysis and subjective inputs. We found it convenient to separate the seasonally adjusted

sales k(t) into a base weekly sales rate B, which is different for each product and each

store, and a seasonal variation V(t), which is the same for all stores and a category of

products. That is, let

V(t) = seasonal variation associated with time t,

po = regular price of the product,

B = base sales rate for this product at the regular price po, and

= the price sensitivity parameter.A normalized price sensitivity * = po was defined so that items with different regular

prices could be pooled if necessary. Thus, forecasted sales at time t with price per unit

p(t) and inventory level I(t) would be

The right side of (29) has a convenient intuitive interpretation because 1 - p(t) / po equals

the percentage markdown from the regular price po.

The optimal trajectory p(t) was not implemented directly in the three applications.

Instead, Table 1 was used to generate a solution for the optimal inventory commitment Io

and the prices pe and po(Io) The average price [pe + po (Io)]/2 was used instead of p(t). The

average price was then updated based on the information available at the next price

change (usually two to three weeks later). Since prices are not permitted to increase, the


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current price would either remain unchanged or be lowered to the tables recommended

price at each update. The discrete price approximation appears to reduce the maximum

revenue by no more than 1 percent to 2 percent based on the example calculations in the

next section.

Typical Price and Sales Trajectories

Properties of the optimal price trajectory can be illustrated by plotting the results for

sample parameter values. Figure 3 shows the underlying seasonal variation and the

optimal price and sales trajectories for one retailers private label mens dress shirts with

a regular price of po = $20.00 for the last 12 weeks of the fall season. The outdate is

February 4, and 12 weeks is the longest time window over which permanent price

reductions might be considered for this merchandise.

The top graph in Figure 3 shows the normalized seasonal variation V(t), which was also

smoothed by taking a three-week moving average. For this example,

k(t) =1,000 corresponds to V(t) = 1. For * = po = 3.2, this results in base sales B =

40.76 in (28) and K= 20,772 in (18). Other parameter values for these graphs are listed in

Table 2. The trajectories shown in Figure 3 assume that both 1 and the price are

optimized in the current week.

The optimal solution for p(t) in Figure 3 corresponds to Case 2 in Table 1, because from

(21), po(Ho) - 1/ = $8.90 - $6.25 = $2.65, which lies between ce = $2.00 and cd - r =$9.00.

It is optimal to reduce the price to $16.41 immediately. This price is held constant until

approximately December 17, when the inventory effect model (26) becomes active. After

December 17, (16) is used to specify the optimal decreasing price trajectory,


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Which stimulates sales in such a way that the cumulative sales s(t) remain unaffected by

the reduced inventory. Since poIo = $16.41, the average price is O.5*($8.90 + 16.41)=

$12.66. For the discrete approximation, this price was used in the last five weeks of

Figure 3, resulting in a total revenue during the 12 weeks of clearance of $23,432 versus

the maximum revenue obtained with the optimal price trajectory of $23,517.


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Table 2 Input Parameter Values for Example Graphs

to =0, te = 12 * =3.2 cd = $l0 ce = $2.00 pe = $20

r = $1.00 = 0.7 to =300 Ao = 2,000 Ho = 1,500 Io = 2,000

The graphs in Figure 3 are clearly dependent upon the initial inventory level and the

inventory sensitivity. Figure 4 illustrates how the optimal price trajectory is affected by

the inventory sensitivity . Notice that as increases, the optimal initial price is slightly

higher, but once the inventory effect becomes active, the optimal price trajectory declines

more steeply. For = 0.99, 75 units are not sold. For the = 0 case, it is optimal to

receive an additional Io - Ho= 306 units and lower the price immediately to $15.25, but

there is no further decline when the inventory effect becomes active. Table 3 gives the

combinations of input and out put values corresponding to these graphs. All input

parameters not listed here are set to the values shown in Table 2.

Table 3 Inputs and Optimal Values for Figure 4

=O =O.25 =O.7 =O.99

Ho 1,500 1,500 1500 1,500

Io 2,000 2,000 2,000 2,000

Io 1,806 1,500 1,500 1,500

se 1,806 1,500 1,500 1,425

po(Io) $15.25 $16.41 $16.41 $16.73


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Figure 5 gives an analogous sensitivity to the current inventory level. For lower inventory

values (H = 300 and 600), the current price of $20.00 is optimal, until the inventory effect

becomes active. For H = = 300, it is best to order 162 additional units. On the other hand,

for H = 3000 it is optimal to cut the price to $12.28 immediately and to sell only 2,904

units. A larger initial inventory also postpones the time at which the inventory constraint

becomes active. Table 4 gives the combinations of input and output values corresponding

to these graphs. In Figure 5, the full retail price of $20.00 is maintained when H = 300

and 600. When Ho = 1,500 and 3,000, it is optimal to take immediate mark downs to

$16.41 and $12.48, respectively, and then further markdowns when the on-hand

inventory falls be low fixture fill o = 300.

To evaluate the impact of the discrete price approximation, the revenues obtained from

using the optimal price trajectory were compared with the revenues obtained from using

the approximation for the combinations of parameter values given Tables 2, 3, and 4. The

reductions in revenue for the clearance period using this approximation were less than 1

percent in all cases but one (2.5 percent for the combination Ho = 300, = 0.99). Thus, it

appears that the approximation does not lead to substantial revenue losses.


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Table 4 Inputs and Optimal Values for Figure 5

Ho = 300 H = 600 H = 1,500 H = 3,000

Io 300 600 1,500 3,000

Io=se 462 600 1,500 2,904

po(Io) $20.00 $20.00 $16.41 $12.28

Parameter Estimation Equation

Taking the logarithm of the reported sales and perform ing the appropriate

transformations on the resulting coefficients, the complete regression equation is in (sales

in week t at price p with inventory level I)


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(See Smith et al. (1994) for further discussion of this regression approach) The threshold

level o was provided by the buyers. Buyers felt that sales should de cline linearly for

inventory levels below fixture fill o. Thus (26) was used as a model for inventory

effects, even though (27) is more analytically convenient.

Although we have used a regression model similar to (30) to estimate parameters for

promotion responses during the regular season for a number of retailers, the historical

data available in the three applications were only partially adequate. Additional details

are given in the next section.

Conclusions

General properties of the optimal pricing policy for merchandise that is sensitive to the

inventory level can provide guidelines for developing corporate strategies for these

products. Inventory sensitivity implies that prices should be set higher before the

clearance period begins, and then reduced more sharply during the clear ance period. For

some products, it is optimal to leave some quantity of merchandise unsold at the end of

the season, especially if it has a salvage value. In general, our optimal pricing policies

indicated that the initial clearance markdowns should be deeper than buyers were

accustomed to taking, while excessive markdowns at the end of the season should be

avoided in favor of salvaging, or even discarding, unsold merchandise.

I studied; roughly 15-20 percent of their merchandise is sold during this period. The

successful applications reported in this paper demonstrate that it is possible to build and

implement a system that achieves major financial benefits.


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Various approximations and assumptions were required in each application to apply the

regression estimation methods described in 4. Retailers POS systems have captured the

detailed information on sales transactions necessary for parameter estimation for some

time. Unfortunately, because of the expense of storing the large volume of data, who

implemented the system either aggregated the data inappropriately or discarded it too

quickly to permit estimation of the complete model. However, applications indicate that a

model based partially on subjective parameter estimates can perform effectively. Once

the data requirements for the system are known, the companys information systems can

begin to accumulate the appropriate data for improved parameter estimates. Thus, we

believe that retailers with successfully implemented systems will have the data necessary

to improve their models over time.

My response model is unique in that it includes a one-sided dependence on the inventory

level. Retail buyers in our studies, particularly in apparel products, felt that having

adequate inventory for presentation strongly affects sales and our regression analysis

found that low inventories were highly correlated with reduced sales. Adopting a

multiplicative, exponential price response function, which has previously been successful

in modeling the response to promotional, leads to an optimal price trajectory that exactly

compensates for the effects of reduced inventory, independent of the form of the

inventory sensitivity.

We believe that our model can provide the basis for further research in pricing policies

that include dependence on inventory effects. Possible enhancements, which have been

considered in other related research, include time discounted cash flows and time

dependent inventory holding costs. Another interesting generalization is the use of initial

clearance prices to elicit in formation about customers response to markdowns. When

combined with inventory adjustments and the sensitivity of sales to inventory, this

remains an unsolved problem to my knowledge.. Finally, we believe that our successfulapplications should encourage others to apply management science models in situations

that require a combination of data analysis and subjective estimates of parameters.


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Appendix A. Proofs of Properties of the Optimal Solutions

To verify Observation 1, we take the total derivative of (23) with respect to and se..

Rearranging terms this gives

Where the subscript denotes a partial derivative. Since increasing decreases y(Io -se)

for Io -se


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M.P.Birla