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Singh & Metri Estimating Retail Demand For Assortment Planning using MNL

DECISION SCIENCE INSTITUTE

ESTIMATING Retail Demand for Assortment planning using MNL model

(Full Paper Submission)

Alok Kumar Singh, Assistant Professor, Operations and Quantitative Methods,

IMI, New Delhi, India [email protected], +91-8750591115

B.A.Metri, Professor, Operations and Quantitative Methods,

IMI, New Delhi, India [email protected], +91-9871118665

ABSTRACT

Assortment planning is an important aspect of successful retail business. The critical issue faced by the retailer in the process of AP is to estimate the demand for each product and further using these demand estimates to develop a profit function and choosing the best array of products to maximize profit under various constraints (Rajaram, 2001).

Most of the earlier works in retail demand estimation are analytical. The application of the models developed and the estimation of various parameters used in the analytical work is lacking. In the present study, the validity of the MNL models has been checked and the process of estimation of the various parameters has been done in the Indian context

KEY WORDS: Retail, Demand Model, MNL, Empirical, Assortment Planning

INTRODUCTION A retailer assortment is defined as the mix of products carried by a retail store. The identification of proper assortment has become difficult in the current consumer centric environment. The increasing need of consumers in terms of variety has increased the difficulties for the retailers. The consumers have different preferences of products and retailers must offer the array of products that satisfies the needs of various consumers (Ulu, et al., 2012). The purpose of selecting a subset of products from the available products is to maximize the retailers objective e.g. profit, under consideration of constraints like limited space available for display, defined budget for the number of products and their SKU’s, inventory to be carried to meet a desired service level and last but not the least to fulfil the ever changing needs of the consumers. In the current retail merchandizing scenario, consumers have a tendency to look at the products offered by the retailers. Sometimes, the search is for the current purchase and sometimes it is done for extending the list for future buying (Morales, Kahn, McAlister, & Broniarczyk, 2005). As stated by (Quelch & Kenny, 1994), the number of products in the market for sale are increasing at a faster rate than the realized sales of the products. It is understood that the assortment selected by any retailer has a greater impact on its gross margin or sales and hence the exercise of assortment planning plays an important role in retail management. Figure 1 below shows a typical retail shelf where similar products within category are placed at same place.

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Fig 1: A typical Retail Shelf

Assortment planning (AP) is a process of selecting types and number of product to be kept from a given product line and also to determine the optimal level of inventory of these products. Poor assortment planning may lead to markdown costs due to excessive inventory of un-demanded products and lost sales due to rapid sell-outs of popular products. In the perspective of retailer, category management allows them to establish good category assortment plans as well as to make better decisions on shelf space allocation and prices and promotion in order to improve sales and profits (Arkader & Ferreira, 2004). The critical issue faced by the retailer in the process of AP is to estimate the demand for each product and by using these demand estimates, developing a profit function and choosing the best array of products to maximize profit under various constraints (Rajaram, 2001). Assortment planning is relatively a new field for both the academicians as well as practitioners in terms of specialized models for optimizing assortment. Though assortment planning always remained a point of concern for the retailer, the development of scientific methods is limited in this field. In a retail business, the products being offered are classified in categories, sub-categories and further the decision is taken on the number of SKU’s to be kept in different sub-categories. Sometimes the decision is also taken on the number of brands to be kept in a given sub-category. For example, in a FMCG store, Biscuits & Namkins are called the categories whereas different types of biscuits like butter/cream/cashew etc are called sub-categories and further how many SKU’s of the subcategories is to be carried on the shelf are the decision variables. The numbers of categories is also referred as width of the assortment while the number of sub-categories is called depth of the assortment. An example of category, sub-category and brands offering these products are shown in table 1 below. The assortment optimization problem in the literature varies because of the type of demand models considered by the authors or because of the context of the problem considered. Literature/Studies also vary in terms of the time span of study and the products under consideration.


Table 1: Example of categories and sub-categories

Category Sub-Category Available Brands

Soap Glycerin, Milk Cream, Toilet etc.

Lux, Lifebuoy, Vivel, Pears etc.

Shampoo Dandruff removing, With conditioners

Sunsilk, Head & Shoulders, Pantene etc.

Assortment planning in a retail chain largely depends on the estimation of demand of various products under consideration. Knowledge of the true demand rates and substitution rates is important for the retailer for a variety of management decisions such as the ideal assortment to carry, how much to stock of each item, and how often to replenish the stock (Anupindi, et al., 1998). The measurement of demand in a retail chain is very complex and requires a rigorous study. The complexity in demand estimation is because of the substitution behaviour of consumers. The demand of a given product comprises not only to its self-demand, but also the demand generated due to either the availability of poor substitution or unavailability of other similar products in the category. Thus, willingness of customer to switch to some other products is a major factor for assortment planning in retail. The estimation of demand is also dependent on the variables considered during the study which will accurately predict the demand. In the present study, the behaviour of multinomial logit models has been studied in two different retail categories in a big Indian retail chain. The demand using this model has been estimated and has been compared with the actual demand obtained from the store. This study will help the retailer in better assortment planning for all the categories. Most of the earlier works in demand estimation are analytical and there is lack of literature on empirical studies. The application of the model developed and the estimation of various parameters used in the analytical work is also lacking. The work has further explained the method for parameter estimation in real time which is used for demand estimation. In the present study, the variables which are more appropriate in the given context that explains the demand more accurately were also identified and used in the model. The paper is organised as follows. Section 1 gives an introduction of the topic and describes its relevance and importance for business. It also includes the objective of the research. Section 2 discusses the detailed literature review of the topic. The review has been done where assortment planning has been done considering the demand model described in literature. Section 3 describes the MNL model and the scope of the current work. Section 4 describes the methodology for parameter estimation of the MNL model. It also describes the data collection process. Section 5 shows the results of the study and includes discussion on the results. Section 6 includes conclusion, managerial implications, limitation and future scope of the work. LITERATURE REVIEW In a typical supermarket, the customers buys product without the help of any sales personal i.e. the products displayed has to sell itself (Hansen & Heinsbroek, 1979). The shelf space


utilization and assortment carried by the retailer, hence become an important factor in new business scenario. It has become important for the retailers to carry the products that minimizes the lost sales due to stock-outs and maximizes its profit Consumer reaction towards assortment carried by retailer has always remained a puzzle. In some research it has been concluded that increasing the varieties in any store increases the probability of purchase. However, in recent research (Kök, Fisher, & Vaidyanathan, 2009), it has been reasoned that the product variety has reached to its saturation and now, decrease in assortment has led to increase in profits. Similar results has been concluded by (Chernev & Hamilton, 2009). The idea is that more number of products in the assortment led to confusion in the minds of consumers, increased searching cost and hence sometimes leading to no purchase incidence. Researchers have developed models in last three to four decades to address the various objectives associated with retail shelf allocation and assortment planning. It has been observed that the demand estimation in any assortment planning problem mostly considered shelf-space and substitution parameters. In this section, the assortment problem dealt by various researchers with MNL models has been reviewed. In a retail chain, when a customer arrives and does not finds the appropriate products, he can either buy another product from the same category that is present in the store or he will not buy any of the product or he will wait for the desired product to arrive at the store and shop later. Hence if the customers are brand loyal, there will not be any substitution effect in the sales of any product. However, marketing research shows that that most of the purchase decisions are taken at the point of purchase and a large number of customer substitute for their favourite product during shopping(Europe, 1998). Hence, substitution and demand generated due to substitution is an important aspect of modelling assortment in any retail chain. In an early work, (K. J. Lancaster, 1966) used concept of utility and substitution. The process of substitution with the concept of utility was explained and concluded that a person will substitute if the utility gained from the alternative purchase in better than the utility achieved by having desired product options. (Mahajan & van Ryzin, 2001b) developed a stochastic sample path optimization model for assortment planning. In the model both type of substitution effect i.e. static as well as dynamic substitution was considered. MNL model was used in the study. Substitution based on the principle of Utility maximization was explained. Though the testing of the model was on not on real data but it showed that the retailer should carry more popular brands than unpopular brands as indicated by traditional newsboy analysis. (Cachon & Kök, 2007) studied the assortment planning problem with multiple merchandise categories and basket shopping consumers. A game theory based model was developed in which retailers choose prices and variety level in each category and consumers make their store choice between retail stores and a no-purchase alternative based on their utilities. It was concluded that category management (CM) never finds the optimal solution and provides both less variety and higher prices than optimal. It was further concluded that introduction of more products may strain the relationship between retailers and manufacturers regarding assortments. (Kok & Fisher, 2007) developed methods for demand estimation and parameter estimation. An iterative optimization heuristic was proposed for solving the assortment planning problem. A new structural property was established that related the products included in the assortment and their inventory levels to product characteristics such as gross margin, case-pack sizes, and demand variability. (Goyal, Levi, & Segev, 2009) showed that even a simple assortment planning problem is NP hard. They developed a polynomial time approximation scheme heuristics to solve these problems that too with desired accuracy. (Caro, Martinez-de-Albeniz, & Rusmevichientong, 2012) developed a formulation that considered the introduction time of short lived products. They determined the optimal assortment in each period taking considering the natural decay that occurs over time. As even the two period problems becomes a NP hard type, they relaxed problem in a way that


the relaxed problem corresponds to the situation where there are many different products of each type and approximates the original problem. For more detailed literature review on the application of MNL model in assortment planning, refer (Singh, A.K. & Kapoor, Rohit, 2013). MULTINOMIAL LOGIT MODEL FOR RETAIL DEMAND ESTIMATION DESCRIPTION OF THE MODEL The Multinomial Logit model is a discrete consumer choice model, which assumes that consumers are rational and they maximize the utility from their shopping. The model computes the probability of choosing an alternative as a function of the attributes of all the alternatives available (McFadden, University of California, & Development, 1973). The model even being stochastic in nature captures decision variables. An extension of MNL model is the locational choice model. It is also a utility-based model. This model is commonly used in marketing and economics literature (Guadagni & Little, 1983). In this model, a no purchase option is given a utility of 0. The customers arriving in the store rate the utility of different products in different way. Hence, the utility is decomposed in two parts, i.e. 𝑈𝑗 = 𝑢𝑗 + 휀𝑗 (1)

Where 𝑈𝑗 = 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑈𝑡𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑃𝑟𝑜𝑑𝑢𝑐𝑡 𝑗

𝑢𝑗 = 𝐷𝑒𝑡𝑒𝑟𝑚𝑖𝑛𝑖𝑠𝑡𝑖𝑐 𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡 𝑜𝑓 𝑈𝑡𝑖𝑙𝑖𝑡𝑦 &

휀𝑗 = 𝑅𝑎𝑛𝑑𝑜𝑚 𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡 𝑜𝑓 𝑈𝑡𝑖𝑙𝑖𝑡𝑦

The first component of the utility is considered same for all the consumers, while the second component depends on individual consumer. The random component is assumed to follow Gumbel distribution [The ε are independently distributed random variables with a double

exponential distribution given by 𝑃(ε ≤ έ) = e−e−έ. The mean and variance of this

distribution is 0.575 and 1.622 respectively] which is also called a double exponential distribution. The function can be written as

Pr( 𝑋 ≤ 휀) = 𝑒−𝑒−(

𝜀𝜂+𝛾

)

(2) Where,

𝛾 = 𝐸𝑢𝑙𝑒𝑟 ′𝑠 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 = 0.5772, & 𝜂 𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑠 𝑡ℎ𝑒 ℎ𝑒𝑡𝑒𝑟𝑜𝑔𝑒𝑛𝑖𝑡𝑦 𝑜𝑓 𝑐𝑢𝑠𝑡𝑜𝑚𝑒𝑟𝑠. This expression suggests that though the different consumers have same expected utility for a given product, the realized utility will be different. This may be due to the type of consumer base under study or it may be some other unobservable factors. The Gumbel distribution is closed under maximization. Hence, probability that a customer chooses product j from 𝑆 ∪ {0} is given by

𝑝𝑗(𝑆) = 𝑒𝑢𝑗

𝜂⁄

∑ 𝑒𝑢𝑘𝜂⁄𝑘 𝜖 𝑆∪{0}

⁄ (3)

The above expression was used by (Ben-Akiva & Bierlaire, 1999). This closed form solution makes MNL model an efficient method for modelling customer choice in analytical studies.

ESTIMATION OF PARAMETERS OF UTILITY BASED MODEL The utility based model is based on the research finding of many researchers that consumers some initial decision like selection of stores or product categories and then they make decision on the selection of product and number of SKU’s to be purchased (Lehmann, 1991). It is a type of sequential or hierarchical decision making. The total demand in this model can be written as


𝐷 = 𝐾(𝑃𝑄) (4) 𝑤ℎ𝑒𝑟𝑒

𝐷 = 𝐷𝑒𝑚𝑎𝑛𝑑 𝑜𝑓 𝑡ℎ𝑒 𝑃𝑟𝑜𝑑𝑢𝑐𝑡

𝐾 𝑖𝑠 𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑢𝑠𝑡𝑜𝑚𝑒𝑟𝑠 𝑣𝑖𝑠𝑖𝑡𝑖𝑛𝑔 𝑡ℎ𝑒 𝑠𝑡𝑜𝑟𝑒 𝑝𝑒𝑟 𝑑𝑎𝑦, &

𝑃𝑄 = 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒 𝑜𝑓 𝑎 𝑝𝑎𝑟𝑡𝑖𝑐𝑢𝑙𝑎𝑟 𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝑝𝑒𝑟 𝑐𝑢𝑠𝑡𝑜𝑚𝑒𝑟

The number of customer visiting the store 𝐾 can be can be expressed as

𝐾 = 𝜑 ∗ 𝑓(𝑇, 𝐷𝑤, 𝑃, 𝑁𝑐), .....(Kök & Fisher, 2007) (5)

𝑤ℎ𝑒𝑟𝑒

𝜑 = 𝑆𝑐𝑎𝑙𝑒 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡

𝑇 = 𝑇𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑑𝑎𝑦

𝐷𝑤 = 𝐷𝑎𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑤𝑒𝑒𝑘 &

𝑃 = 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑃𝑟𝑜𝑚𝑜𝑡𝑖𝑜𝑛 &

𝑁𝑐 = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑜𝑢𝑛𝑡𝑒𝑟𝑠 𝑂𝑝𝑒𝑟𝑎𝑡𝑖𝑜𝑛𝑎𝑙 𝑜𝑛 𝑎 𝑔𝑖𝑣𝑒𝑛 𝑑𝑎𝑦

Average number of purchase can be written as

𝑃𝑄 = 𝜋 ∗ 𝑝 ∗ 𝑞, (6)

𝑤ℎ𝑒𝑟𝑒

𝜋 = 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝑎 𝑣𝑖𝑠𝑖𝑡𝑛𝑔 𝑐𝑢𝑠𝑡𝑜𝑚𝑒𝑟 𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑖𝑛𝑔 𝑓𝑟𝑜𝑚 𝑔𝑖𝑣𝑒𝑛 𝑐𝑎𝑡𝑒𝑔𝑜𝑟𝑦

𝑝 = 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑡ℎ𝑎𝑡 𝑎 𝑔𝑖𝑣𝑒𝑛 𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝑖𝑠 𝑐ℎ𝑜𝑠𝑒𝑛 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑔𝑖𝑣𝑒𝑛 𝑐𝑎𝑡𝑒𝑔𝑜𝑟𝑦, &

𝑞 = 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑞𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝑜𝑓 𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒 𝑜𝑓 𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝑐ℎ𝑜𝑠𝑒𝑛

Purchase incidence from the category 𝜋 is modelled as a binary choice as

𝜋 = 𝑒𝛼

1+𝑒𝛼 (McFadden, et al., 1973) (7)

Where 𝛼 = 𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑢𝑡𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝑐𝑎𝑡𝑒𝑔𝑜𝑟𝑦. 𝛼 𝑐𝑎𝑛 𝑓𝑢𝑟𝑡ℎ𝑢𝑟 𝑏𝑒 𝑚𝑜𝑑𝑒𝑙𝑙𝑒𝑑 𝑎𝑠 𝑎 𝑙𝑖𝑛𝑒𝑎𝑟 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛 𝑜𝑓 𝑣𝑎𝑟𝑖𝑜𝑢𝑠 𝑑𝑒𝑚𝑎𝑛𝑑 𝑑𝑟𝑖𝑣𝑒𝑟𝑠. The equation (13) can be re-written as

1 − 𝜋 =1

1+𝑒𝛼. (8)

Dividing equation (13) by (14) we get,

𝜋

1−𝜋= 𝑒𝛼. (9)

Taking log, we have

𝐿𝑜𝑔 (𝜋

1−𝜋) = 𝛼. (10)

The expected utility of the category 𝛼 is modelled as a linear function of various demand drivers for the subcategory like temperature, days of the week, number of counters

operational on any day and average promotion on the given category. 𝛼 can be written as 𝛼 = 𝛾1 + 𝛾2 ∗ 𝑇 + 𝛾3 ∗ 𝐷𝑤 + 𝛾4 ∗ 𝑁 + 𝛾4 ∗ 𝑃 (Bucklin & Gupta, 1992) (11)


We can compute 𝜋, the probability of purchase incidence for the subcategory, from sales data as the ratio of the number of customers who bought any product in the given category to the number of customers who visited store on any day. Further, the product choice can be modelled with the MNL framework. The probability of selection a given product is given by

𝑝𝑗(𝑆) = 𝑒𝑢𝑗

𝜇⁄

∑ 𝑒𝑢𝑘𝜇⁄𝑘 𝜖 𝑆∪{0}

⁄ (12)

As earlier modelling for purchase incidence, we can write

𝐿𝑜𝑔 (𝑃𝑗

𝑃) = 𝑢𝑗 (13)

The utility derived from a given product 𝑢𝑗 can be modelled as a linear function of variables

like temperature, days of the week, difference in price of the product and the average price of products in the category and number of personnel’s helping or promoting the product at the product counter. 𝑢𝑗 can be written as

𝑢𝑗 = 𝛿1 + 𝛿2 ∗ 𝑇 + 𝛿3 ∗ 𝐷𝑤 + 𝛿4 ∗ 𝑃𝑑 + 𝛿5..(Cooper & Nakanishi, 1988) (14)

Probability of purchasing a given product can be obtained as the ratio of total number of product sold and the total number of person who bought something from the category. The average quantity purchased by a customer, 𝑞 can be obtained as the ratio of number of units of a given products sold to the number of person who bought anything in the given product category. Also, 𝑞 can be modelled as a linear function of variables like temperature, day of the week and number of personnel’s helping or promoting the product at the product counter 𝑞𝑗 = 𝜎1 + 𝜎2 ∗ 𝑇 + 𝜎3 ∗ 𝐷𝑤 + 𝜎4 ∗ 𝑁. ....(Chintagunta, 1993) (15)

As we will be able to estimate all the expression as stated above, we can calculate the demand of the product at a given store. The demand of the product can be calculated as 𝐷𝑃1 = 𝐾 ∗ 𝜋 ∗ 𝑝1 ∗ 𝑞1 (16) From the earlier work it is concluded that price, days of the week and consumer service are important variables in the selection of the store and purchase from a given store.

DATA COLLECTION The present work is an exploratory research. The cross-sectional data was collected from a hyper store located in the eastern part of the country. The store is a part of a company dealing in retail business and has almost 200 stores across India including hypermarkets and superstores. The company has almost 2 million customers per month around the country. The store selected for study is spread in almost 20000 square feet of area and carries almost 60000 SKU’s. The data was collected for a period of three months from March 2014 to May 2014. Ideally a variety of products should be tested but we narrowed down to the product categories which satisfies the following criteria. The number of product during the study period in the category did not increase or decrease. The price within the category is not going to change appreciably during the study period. The selection was also from the retailer’s categorization of the product as food and non food item. The frozen food products were discarded on the basis of limited shelf space availability. Small sized products were discarded as it was difficult to capture data for them. Based on these criteria, the two categories viz. 600 ml pet bottled soft drinks from food and mosquito repellents from non food category were chosen. The presence of competing products taking almost equal space and having prices almost similar also makes consumer substitute their initial preference. Also, these products are sometimes instantaneous purchases. For the MNL model, the number of customers entering in to the store was taken from the records of the person at the entry of the store. A single entry system is followed by the store. The person at the entry carries a machine and as and when someone enters into the store, the counter is moved by him. The number of billing of the store was recorded from the POS data which also included the number of bill generated for a given category and number of


person buying anything from the category and the sub-category. Any promotions made either by the company or the store was recorded. Any in-store advertisement done by the store or supported by the company were also recorded. The other factors recorded were number of billing counters operational each day and the number of personnel at the shelves of each product which is an indicator of the service provided by the store for the customers. The selling price and cost of the product were also recorded and any change in them at any point was recorded.

RESULT & DISCUSSION The MNL model is a hierarchical model. The ANOVA result of the number of cusmers for both the categories is shown in table 2.

Table 2: ANOVA result for Number of Consumers

df SS MS F Significance F

Regression 3.000 2551878.140 850626.0 16.717 0.000

Residual 85.000 4325075.051 50883.23

Total 88.000 6876953.191

The category selection model is a binary choice model i.e. the consumers either purchase from the category or will not purchase from the category. The ANOVA result category selection for both the category has been summarized in table 3.The product selection is modelled as MNL framework. The ANOVA result for the product purchase for all the products in category 1 and category 2 is shown is table 4 and 5.

Table 3: ANOVA result for category selection


Category 1 4.0000 2.4601 0.6150 3.9874 0.0052

Category 2 4.0000 5.3617 1.3404 16.8018 0.0000

Table 4: ANOVA result for product selection of all products category 1


Product 1 4.0000 13.6930 3.4233 12.4944 0.0000

Product 2 4.0000 11.8288 2.9572 14.1063 0.0000

Product 3 4.0000 9.2756 2.3189 6.0124 0.0003

Product 4 4.0000 9.5947 2.3987 8.6283 0.0000

Product 5 4.0000 19.0985 4.7746 16.6038 0.0000

Product 6 4.0000 11.1722 2.7930 8.8125 0.0000


Table 5: ANOVA result for product selection of all products category 2


Product 1 4.0000 16.8651 4.2163 11.3932 0.0000

Product 2 4.0000 3.5367 0.8842 5.3196 0.0007

Product 3 4.0000 16.1880 4.0470 10.3860 0.0000

Product 4 4.0000 16.5384 4.1346 9.6766 0.0000

Product 5 4.0000 20.3554 5.0889 12.1622 0.0000

The results of the models of average number of products purchased for all the products in category 1 and category 2 are shown in table 6 and 7.

Table 6: ANOVA result for Average Quantity Purchased for all products in category 1

df SS MS F

Significance F

Product 1 3.0000 0.7243 0.2414 16.5281 0.0000

Product 2 3.0000 1.0741 0.3580 24.5943 0.0000

Product 3 3.0000 0.5757 0.1919 17.0808 0.0000

Product 4 3.0000 0.7711 0.2570 20.0424 0.0000

Product 5 3.0000 0.6826 0.2275 12.9156 0.0000

Product 6 3.0000 0.3607 0.1202 10.5130 0.0000

Table 7: ANOVA result for Average Quantity Purchased for all products in category 2


Product 1 3.0000 0.7157 0.2386 22.0411 0.0000

Product 2 3.0000 0.9781 0.3260 9.3532 0.0000

Product 3 3.0000 0.3232 0.1077 13.9242 0.0000

Product 4 3.0000 0.2336 0.0779 17.3817 0.0000

Product 5 3.0000 0.1129 0.0376 22.8590 0.0000

The table 2,3,4,5,6 and 7 clearly indicates that the models developed for MNL framework for demand estimation is valid for both the product categories and the entire product in these categories. All the F values for all the models are greater than the significant values. The other results for the MNL models for all the products in category 1 and category 2 have been summarized in Appendix A.


CONCLUSION Assortment planning has been the focus of numerous industry studies. Many researchers as well as practitioners stressed upon the importance of assortment planning in retail sector. It is very important for any retailer to efficiently manage this process of assortment planning. In the present work empirical testing of MNL model has been done. The analysis showed that MNL model is valid in Indian Context for predicting the demand. As there are very limited studies in Indian context, this work will help the researchers and the practitioners to learn the nuances of retail assortment planning in the given context. The demand has been estimated from retailer’s perspective. The demand models incorporate some parameters. The estimation of these parameters using the data collected is a contribution of the work. The readers will be able to learn the method of parameter estimation. The present work can be used to estimate the demand of new products in the market and may help retailers in its selection or de-selection. Although the scope of the work has been achieved, there are many limitation of the study. The literature review and scope of the problem has been defined as per the availability of the literature on the past works that has been done on the demand model areas and assortment optimization field. The selection of the store is also a limitation of the work. The selection of the store was dependent on the approval of the store manager for carrying the research work. Also the selection of the product was also affected by the store manager. The number of product selected for the study is also affected by the approval from the store manager. In the current study, 11 products from two categories have been studied. The limited number of category for study limits the generalization of the study. In the assortment optimization problem, the values of direct and space elasticity of demand has been used from the current study. These values may improve if the duration of the study is increased. Also, if there may be some more variables which could be added to explain the phenomena more accurately, may increase the suitability of the models. The other limitation of the work includes its time frame of study. The study has been carried for almost three months from a period of March 2013 to May 2013. The 89 days of data and the analysis limits the applicability of the models and also affects the results. As there was restriction on the interaction with the consumers, the variables affecting the demand have been explored from the literature only. The interaction with consumers may give some deep insights into the factors affecting the demand. The work is limited to a single format of store and a single store. The future work can include more number of stores from different formats of stores and from different regions of the country. This may provide more insight into the process of demand estimation. Experimental study for the demand estimation can be performed. This will eliminate the problem from the retailers to conduct the study in the store. A comparative study with other demand models viz. MNL, exogenous demand model and locational choice model may give more options to the retailers. The identification of proper assortment has become difficult in the current consumer centric environment. The increasing need of consumers in terms of variety has increased the difficulty of the retailers. The purpose of selecting a subset of products from the available products is to maximize the retailers objective e.g. profit, under consideration of constraints like limited space available for display, defined budget for the number of products and their SKU’s, inventory to be carried to meet a desired service level and last but not the least to fulfil the ever changing needs of the consumers. The assortment optimization problem in the literature varies because of the type of demand models considered by the authors or because of the context of the problem considered. In the present study, the behaviour of the MNL models has been studied in two different categories in a big Indian retail chain. Most of the earlier works in demand estimation are analytical and there is lack of literature on empirical studies. The application of the model and the estimation of various parameters used in the analytical work are also lacking. In the present work, the method for parameter estimation in real time has been explained which is used for demand estimation. In the present study, the variables which are more appropriate in the given context that explains the demand more accurately were also identified and used in the model.


The results obtained from the work indicate that the model is valid in the given context. Though, some of the variables are not significant in some of the models, but they are significant in some other models. Therefore, none of the variable can be omitted from the model. The model has not fully explained the process, but it has touched upon the variables that may affect the process.

APPENDIX A

Table 8: Number of Consumers for Category 1 and 2

Regression Statistics Multiple R 0.609 R Square 0.371 Adjusted R Square 0.349 Standard Error 225.573 Observations 89.000

ANOVA df SS MS F Significance F

Regression 3.000 2551878.140 850626.0 16.717 0.000 Residual 85.000 4325075.051 50883.23

Total 88.000 6876953.191

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%

Intercept 661.524 194.730 3.397 0.001 274.349 1048.699 Temp 9.608 6.029 1.594 0.115 -2.378 21.595 Nc -7.444 18.814 -0.396 0.693 -44.851 29.963 Dw 370.681 55.910 6.630 0.000 259.517 481.845

Table 9: Probability of Purchase from Category 1




Total 88.0000 15.4165


Intercept -5.2168 0.3516 -14.8378 0.0000 -5.9159 -4.5176

Temp 0.0317 0.0108 2.9339 0.0043 0.0102 0.0533

Nc 0.0796 0.0335 2.3744 0.0199 0.0129 0.1463

Dw -0.1811 0.0980 -1.8481 0.0681 -0.3760 0.0138

Prom. -0.0442 0.1071 -0.4123 0.6812 -0.2571 0.1688


Table 10: Probability of Purchase of Product 1 from Category 1




Total 88.0000 36.7076


Intercept 1.5943 0.7005 2.2758 0.0254 0.2012 2.9874

Temp -0.0348 0.0158 -2.2009 0.0305 -0.0662 -0.0034

Nc 0.0516 0.1222 0.4222 0.6740 -0.1914 0.2946

Pd 0.6305 0.2491 2.5316 0.0132 0.1352 1.1258

N 0.7580 0.1194 6.3482 0.0000 0.5206 0.9955





Total 88.0000 29.4383


Intercept 2.4369 0.6082 4.0069 0.0001 1.2275 3.6463

Temp -0.0297 0.0130 -2.2738 0.0255 -0.0556 -0.0037

Nc 0.0182 0.1085 0.1673 0.8675 -0.1976 0.2339

Pd 0.1589 0.2195 0.7240 0.4711 -0.2775 0.5953

N 0.7316 0.1012 7.2266 0.0000 0.5303 0.9330






Total 88.0000 41.6731


Intercept 3.3171 0.8249 4.0211 0.0001 1.6766 4.9575

Temp -0.0585 0.0177 -3.3053 0.0014 -0.0937 -0.0233

Nc 0.2575 0.1471 1.7498 0.0838 -0.0351 0.5501

Pd 0.1170 0.2977 0.3931 0.6952 -0.4749 0.7090

N -0.3083 0.1373 -2.2448 0.0274 -0.5813 -0.0352





Total 88.0000 32.9467


Intercept 2.0063 0.5652 3.5498 0.0006 0.8824 3.1303

Temp -0.0364 0.0151 -2.4103 0.0181 -0.0664 -0.0064

Nc -0.0639 0.1230 -0.5197 0.6046 -0.3086 0.1807

Pd -0.2972 0.2515 -1.1817 0.2407 -0.7974 0.2030

N 0.6507 0.1182 5.5026 0.0000 0.4155 0.8858






Total 88.0000 43.2537


Intercept 2.2063 0.5725 3.8534 0.0002 1.0677 3.3448

Temp -0.0420 0.0153 -2.7440 0.0074 -0.0725 -0.0116

Nc 0.1289 0.1253 1.0294 0.3062 -0.1201 0.3780

Pd -0.1061 0.2557 -0.4148 0.6793 -0.6145 0.4024

N 0.9001 0.1154 7.8007 0.0000 0.6706 1.1295





Total 88.0000 37.7951


Intercept 2.7449 0.5999 4.5755 0.0000 1.5519 3.9379

Temp -0.0570 0.0160 -3.5682 0.0006 -0.0887 -0.0252

Nc -0.0534 0.1317 -0.4051 0.6864 -0.3153 0.2086

Pd -0.0738 0.2682 -0.2752 0.7838 -0.6071 0.4595

N 0.6063 0.1227 4.9403 0.0000 0.3622 0.8503


Table 16: Average Quantity Purchased of Product 1 from Category 1




Total 88.0000 1.9658


Intercept 0.2441 0.0883 2.7644 0.0070 0.0685 0.4196

Temp -0.0025 0.0035 -0.7179 0.4748 -0.0093 0.0044

Dw 0.0073 0.0282 0.2576 0.7973 -0.0488 0.0633

N 0.1870 0.0275 6.7905 0.0000 0.1322 0.2417





Total 88.0000 2.3116


Intercept 0.1245 0.0866 1.4384 0.1540 -0.0476 0.2966

Temp 0.0029 0.0033 0.8988 0.3713 -0.0036 0.0094

Dw -0.0274 0.0285 -0.9592 0.3402 -0.0841 0.0294

N 0.2184 0.0265 8.2552 0.0000 0.1658 0.2710






Total 88.0000 1.5306


Intercept 0.2058 0.0770 2.6741 0.0090 0.0528 0.3589

Temp -0.0022 0.0028 -0.7614 0.4485 -0.0078 0.0035

Dw 0.0010 0.0253 0.0379 0.9699 -0.0494 0.0514

N 0.1641 0.0239 6.8591 0.0000 0.1165 0.2116





Total 88.0000 1.8612


Intercept 0.0349 0.0814 0.4285 0.6694 -0.1269 0.1966

Temp 0.0043 0.0031 1.3982 0.1657 -0.0018 0.0104

Dw -0.0175 0.0264 -0.6620 0.5097 -0.0700 0.0350

N 0.1825 0.0253 7.2136 0.0000 0.1322 0.2328






Total 88.0000 2.1800


Intercept 0.0070 0.0954 0.0736 0.9415 -0.1827 0.1968

Temp 0.0039 0.0036 1.0912 0.2783 -0.0032 0.0109

Dw -0.0172 0.0312 -0.5510 0.5830 -0.0792 0.0448

N 0.1720 0.0284 6.0510 0.0000 0.1155 0.2286





Total 88.0000 1.3327


Intercept 0.2045 0.0772 2.6506 0.0096 0.0511 0.3579

Temp -0.0038 0.0029 -1.2966 0.1983 -0.0097 0.0020

Dw 0.0034 0.0249 0.1377 0.8908 -0.0461 0.0530

N 0.1331 0.0237 5.6117 0.0000 0.0859 0.1802


Table 22: Probability of Purchase from Category 2




Total 88.0000 12.0632


Intercept -2.9730 0.2438 -12.1926 0.0000 -3.4578 -2.4881

Temp -0.0018 0.0076 -0.2324 0.8168 -0.0168 0.0133

Nc -0.0337 0.0236 -1.4298 0.1565 -0.0806 0.0132

Dw -0.1982 0.0751 -2.6402 0.0099 -0.3476 -0.0489

Prom. 0.5435 0.0669 8.1282 0.0000 0.4105 0.6765





Total 88.0000 47.9510


Intercept 2.1106 0.7183 2.9384 0.0043 0.6822 3.5389

Temp -0.0448 0.0187 -2.3920 0.0190 -0.0820 -0.0075

Nc -0.4298 0.1421 -3.0240 0.0033 -0.7124 -0.1471

Pd -0.0093 0.0301 -0.3103 0.7571 -0.0691 0.0505

N 0.8379 0.1397 5.9987 0.0000 0.5601 1.1157






Total 88.0000 17.4987


Intercept 2.2934 0.3032 7.5641 0.0000 1.6905 2.8964

Temp 0.0029 0.0113 0.2533 0.8006 -0.0196 0.0254

Nc 0.1837 0.1019 1.8024 0.0751 -0.0190 0.3864

Pd 0.1626 0.0431 3.7760 0.0003 0.0770 0.2482

N 0.1616 0.0962 1.6799 0.0967 -0.0297 0.3530



ANOVA



Total 88.0000 48.9193

Coefficients Standard Error t Stat P-value Lower 95%

Upper 95%

Intercept -0.2946 0.7248 -0.4064 0.6855 -1.7360 1.1468

Temp -0.0082 0.0175 -0.4683 0.6408 -0.0429 0.0266

Nc -0.3353 0.1464 -2.2903 0.0245 -0.6263 -0.0442

Pd -0.0772 0.0526 -1.4668 0.1462 -0.1818 0.0274

N 0.8508 0.1422 5.9824 0.0000 0.5680 1.1336






Total 88.0000 52.4296


Intercept 0.5262 0.4744 1.1093 0.2705 -0.4171 1.4695

Temp 0.0047 0.0180 0.2592 0.7961 -0.0311 0.0404

Nc -0.2464 0.1577 -1.5622 0.1220 -0.5600 0.0673

Pd 0.1771 0.0704 2.5145 0.0138 0.0370 0.3172

N 0.9831 0.1600 6.1441 0.0000 0.6649 1.3013





Total 88.0000 55.5022


Intercept 0.4485 0.5684 0.7891 0.4323 -0.6817 1.5788

Temp -0.0248 0.0210 -1.1836 0.2399 -0.0666 0.0169

Nc -0.3624 0.1508 -2.4033 0.0185 -0.6623 -0.0625

Pd 0.0007 0.0340 0.0194 0.9845 -0.0669 0.0682

N 1.0766 0.1659 6.4889 0.0000 0.7467 1.4066






Total 88.0000 1.6358


Intercept 0.3804 0.0746 5.1017 0.0000 0.2321 0.5286

Temp -0.0083 0.0028 -2.9151 0.0045 -0.0140 -0.0026

Dw -0.0872 0.0243 -3.5906 0.0006 -0.1355 -0.0389

N 0.1752 0.0238 7.3750 0.0000 0.1279 0.2224





Total 88.0000 3.9412


Intercept 0.7601 0.1338 5.6797 0.0000 0.4940 1.0261

Temp -0.0028 0.0051 -0.5497 0.5840 -0.0129 0.0073

Dw 0.0205 0.0467 0.4398 0.6612 -0.0723 0.1133

N 0.2068 0.0435 4.7576 0.0000 0.1204 0.2932






Total 88.0000 0.9809


Intercept 0.0458 0.0648 0.7067 0.4817 -0.0830 0.1746

Temp 0.0013 0.0024 0.5307 0.5970 -0.0035 0.0060

Dw -0.0502 0.0206 -2.4361 0.0169 -0.0912 -0.0092

N 0.1207 0.0195 6.2027 0.0000 0.0820 0.1594





Total 88.0000 0.6143


Intercept 0.0972 0.0480 2.0258 0.0459 0.0018 0.1925

Temp -0.0003 0.0018 -0.1803 0.8574 -0.0039 0.0032

Dw -0.0467 0.0161 -2.8916 0.0049 -0.0788 -0.0146

N 0.1130 0.0158 7.1325 0.0000 0.0815 0.1445






Total 88.0000 0.2527


Intercept 0.0796 0.0291 2.7374 0.0075 0.0218 0.1374

Temp -0.0008 0.0011 -0.7014 0.4850 -0.0029 0.0014

Dw -0.0251 0.0095 -2.6494 0.0096 -0.0439 -0.0063

N 0.0815 0.0103 7.8726 0.0000 0.0609 0.1020

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