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LOADING A COCA-COLA VENDING MACHINE BASED ON A STATISTICAL DESIGN.

ABSTRACT

Softdrink vending machines are installed in almost all businesses, universities, high schools, and other facilities. All businesses like to improve their profits and service to their customers. The softdrink vending business is not any different. In this paper, we present a statistical study based on a survey of our students to show that Coca-Cola vending machine businesses can improve their customer service and in turn their profits by loading spring water and more regular Coca-Cola as compared to Diet Cola. We analyzed the data obtained using the [3.sup.6] availability design and the statistical software programs Foxlogit [11] and Minitab [10]. Our study finds that the Diet Cola should be removed from the vending machine as it received the lowest percentage and should be replaced by Coca-Cola that received the highest percentage. Mr. Pibb had the second lower percentage and thus should be replaced by spring water.

INTRODUCTION

These days, softdrink vending machies are installed almost every where even where people least expect them. The last one we saw was installed under the sun, with no cover, on the side of a walking track of a middle school. The vending machine business is growing fast, however, service to the customer has not changed much.

A softdrink vending machine is usually loaded with one kind of drink in each column. As some softdrinks are preferred over others, a better way to load a vending machine would be based upon the consumers' preference. Many times a consumer turns around and leaves if he/she does not find his/her favorite drink in the machine. In this paper, we present a statistical study based on a survey of our students to show that Coca-Cola vending machine businesses can improve their customer service and in turn their profits by loading spring water and regular Coca-Cola as replacing Diet Cola.

We conducted a survey of 420 students. We analyzed the data obtained using the statistical software programs Foxlogit [11] and Minitab [10].

In order to study the customers' preferences on the choices available to them, we used the [3.sup.6] availability design [5, 6]. An availability design is a discrete choice set experiment [2, 3] that allows the estimation of the availability and effects of the components. Using these estimates the utility of each component is computed. We then use the utilities to compute the market share [8] for each component.

SOFTDRINK VENDING MACHINES

The vending machine business depends largely on customer preference. If a vending machine business can figure out customers' preference, it may improve profits. In one of the buildings on our campus, we have several Coca-Cola machines. The price of a softdrink is 50 cents. The machines carry six products: Coca-Cola, Diet Cola, Sprite, Root Beer, Mr. Pibb, and Mello Yello.

My first preference is Coca-Cola. If the machine is out of Coca-Cola, I get Sprite which is my second and last preference. If the machine is out of both, I turn around and leave. I also prefer to spend 50 cents rather than 75 cents. Using an experimental design, we analyze behavior of other consumers as well. The price is used as an attribute and it has two levels: low price and high price.

STATISTICAL DESIGN

In Table II below, we present the [3.sup.6] availability design, [5, 6] in eighteen choice sets. The [3.sup.6] availability design is an orthogonal design and comes with 18 rows. Orthogonal designs provide uncorrelated estimates. Each of the eighteen rows in the design represents a choice set.

Each column represents one of the six products. The first column represents Coca-Cola, column 2 represents Diet Cola, column 3 Sprite, column 4 Root Beer, column 5 Mr. Pibb, and column 6 Mello Yello. The 0 in a row means the product is not available; 1 means the product is available with the low level price (50 cents); 2 means the product is available with the high level price (75 cents). For example, the set {2, 1, 0, 1, 0, 0} indicates that Coca-Cola is available with the high price level (75 cents), Diet Cola is available with the low price level (50 cents), Spring is not available (N/A), Root Beer is available with the low price level (50 cents), Mr. Pibb is not available (N/A), and Mello Yello is not available (N/A). Hence the first choice set in the availability design translates to the following table and represents the first choice set in our survey. Spring water was given as a choice in case the students preferred spring water versus any of the soft drinks. Therefore, every choice set contains the c hoice spring water for 50 cents in the survey.
Coca-Cola Diet Cola N/A Sprite N/A N/A Spring Water
75 cents 50 cents 50 cents 50 cents


We continued this process and obtained the survey given in Table III below. Four hundred and twenty students completed the survey. Each student was instructed to circle one and only one choice from each choice set.

MARKET SHARE AND UTILITY MODEL

The model for computing the market shares [4] for the products is the well known multinomial distribution [9], equation 1 below.

P ([product.sub.i]/[product.sub.i], [epsilon] [A.sub.[kappa]]) = exp([v.sub.i])/[[sigma].sub.j[epsilon]A] exp([v.sub.j]) (1)

This model computes the market share for product 8 provided that product is part of the choice set. We need to estimate the utility component, [V.sub.i], for each product i. The model equation [5] for the utility of product i is given in equation 2 below,

[V.sub.i] = [[alpha].sub.1] + [[beta].sub.i][XL.sub.i] + [[sigma].sub.i'[neq]i] ([[gamma].sub.ii][XL.sub.i], + [[delta].sub.ii][Z.sub.i],) (2)

where

[[alpha].sub.1] = Intercept for Product i

[[beta].sub.i] = Price Effect for Product i

[XL.sub.i] {-1 if Product i is present with Price level 1 1 if Product i is present with Price level 2

[[gamma].sub.ii], = Price Cross effect of product i' on Product i

[[delta].sub.ii], = Availability Cross Effect of Product i' on Product i

[Z.sub.i] = {-2 if Product i' is present 1 if Product i' is present with Price level 1 or 2

The values for Z and XL are well known orthogonal codings for providing uncorrelated estimates.

We need to estimate a total of 72 parameters, 12 parameters for each product. These include all price effects, 6, all intercepts, 6, all price cross effects, 30, and all availability cross effects, 30. The price effects and the price cross effects are given in Table IV. The main diagonal elements represent the price effects. In Table IV, the numbers 1, 2, 3, 4, 5, and 6 represent Coca-Cola, Diet Cola, Sprite, Root Beer, Mr. Pibb, and Mello Yello, respectively. The product intercepts and the availability cross effects are given in Table V. The main diagonal elements represent the product intercepts.

In Table IV, the price effect and the price cross effects are either negative or positive. Any product appearing at the low price gains utility from negative price effects and price cross effects and loses utility if appearing at the high price. If the price effect and price cross effects are positive the effect is opposite. In Table V, if the intercept is negative, the product is chosen less often than the spring water. If the availability cross effect is negative, the utility of product I ([V.sub.i]) increases if product i' is not available, and it decreases if product i' is available. If the availability cross effect is positive the effect is the opposite. In both Tables IV and V, the price and the availability cross effects are read from the columns to the rows.

Now that the parameters are estimated, we can use the utility model, equation 2, to compute the utilities for each product under different scenarios. We first concentrate on the following two scenarios [1] all products are present with the low price level (50 cents) and [2] all products are present with the high price level, 75 cents. After we compute the utilities and the market shares [8] for the products under these scenarios, we would consider some other interesting scenarios.

When all the products appear with the low price level (50 cents), the utility for each product is given by

[V.sub.1]=[[alpha].sub.1]+(-1)[[beta].sub.1]+(-1)[[gamma].sub.12]+(-1 )[[gamma].sub.13]+(-1)[[gamma].sub.14]+(-1)[[gamma].sub.15]+(-1)[[gam ma].sub.16]+(1)[[delta].sub.12](1)[[delta].sub.13](1)[[delta].sub.14] (1)[[delta].sub.15](1)[[delta].sub.16]

[V.sub.2]=[[alpha].sub.2]+(-1)[[beta].sub.2]+(-1)[[gamma].sub.21]+(-1 )[[gamma].sub.23]+(-1)[[gamma].sub.24]+(-1)[[gamma].sub.35]+(-1)[[gam ma].sub.26]+(1)[[delta].sub.21](1)[[delta].sub.23](1)[[delta].sub.24] (1)[[delta].sub.25](1)[[delta].sub.26]

[V.sub.3]=[[alpha].sub.3]+(-1)[[beta].sub.3]+(-1)[[gamma].sub.31]+(-1 ) +[[gamma].sub.32]+(-1)[[gamma].sub.34]+(-1)[[gamma].sub.45]+(-1)[[gam ma].sub.36]+(1)[[delta].sub.31](1)[[delta].sub.32](1)[[delta].sub.34] (1)[[delta].sub.35](1)[[delta].sub.36]

[V.sub.4]=[[alpha].sub.4]+(-1)[[beta].sub.4]+(-1)[[gamma].sub.41]+(-1 )[[gamma].sub.42]+(-1)[[gamma].sub.43]+(-1)[[gamma].sub.55]+(-1)[[gam ma].sub.46]+(1)[[delta].sub.41](1)[[delta].sub.42](1)[[delta].sub.43] (1)[[delta].sub.45](1)[[delta].sub.46]

[V.sub.5]=[[alpha].sub.5]+(-1)[[beta].sub.5]+(-1)[[gamma].sub.51]+(-1 )[[gamma].sub.52]+(-1)[[gamma].sub.53]+(-1)[[gamma].sub.54]+(-1)[[gam ma].sub.56]+(1)[[delta].sub.51](1)[[delta].sub.52](1)[[delta].sub.53] (1)[[delta].sub.54](1)[[delta].sub.56]

[V.sub.6]=[[alpha].sub.6]+(-1)[[beta].sub.6]+(-1)[[gamma].sub.61]+(-1 )[[gamma].sub.62]+(-1)[[gamma].sub.63]+(-1)[[gamma].sub.64]+(-1)[[gam ma].sub.65]+(1)[[delta].sub.61](1)[[delta].sub.61](1)[[delta].sub.62] (1)[[delta].sub.64](1)[[delta].sub.65]

When all the products appear with the high price level, the utility for each product is given by

[V.sub.1]=[[alpha].sub.1]+(1)[[beta].sub.1]+(1)[[gamma].sub.12]+(1)[[ gamma].sub.13]+(1)[[gamma].sub.14]+(1)[[gamma].sub.15]+(1)[[gamma].su b.16]+(1)[[delta].sub.12](1)[[delta].sub.13](1)[[delta].sub.14](1)[[d elta].sub.15](1)[[delta].sub.16]

[V.sub.2]=[[alpha].sub.2]+(1)[[beta].sub.2]+(1)[[gamma].sub.21]+(1)[[ gamma].sub.23]+(1)[[gamma].sub.24]+(1)[[gamma].sub.35]+(1)[[gamma].su b.26]+(1)[[delta].sub.21](1)[[delta].sub.23](1)[[delta].sub.24](1)[[d elta].sub.25](1)[[delta].sub.26]

[V.sub.3]=[[alpha].sub.3]+(1)[[beta].sub.3]+(1)[[gamma].sub.31]+(1)[[ gamma].sub.32]+(1)[[gamma].sub.34]+(1)[[gamma].sub.45]+(1)[[gamma].su b.36]+(1)+[[delta].sub.31](1)[[delta].sub.32](1)[[delta].sub.34](1)[[ delta].sub.35](1)[[delta].sub.36]

[V.sub.4]=[[alpha].sub.4]+(1)[[beta].sub.4]+(1)[[gamma].sub.41]+(1)[[ gamma].sub.42]+(1)[[gamma].sub.43]+(1)[[gamma].sub.55]+(1)[[gamma].su b.46]+(1)[[delta].sub.41](1)[[delta].sub.42](1)[[delta].sub.43](1)[[d elta].sub.45](1)[[delta].sub.46]

[V.sub.5]=[[alpha].sub.5]+(1)[[beta].sub.5]+(1)[[gamma].sub.51]+(1)[[ gamma].sub.52]+(1)[[gamma].sub.53]+(1)[[gamma].sub.54]+(1)[[gamma].su b.56]+(1)[[delta].sub.51](1)[[delta].sub.52](1)[[delta].sub.53](1)[[d elta].sub.54](1)[[delta].sub.56]

[V.sub.6]=[[alpha].sub.6]+(1)[[beta].sub.6]+(1)[[gamma].sub.61]+(1)[[ gamma].sub.62]+(1)[[gamma].sub.63]+(1)[[gamma].sub.64]+(1)[[gamma].su b.65]+(1)[[delta].sub.61](1)[[delta].sub.61](1)[[delta].sub.62](1)[[d elta].sub.64](1)[[delta].sub.65]

After computing the utilities, we now compute the market share for each product using equation 1. Using the utilities given above and equation 1, we computed the market shares for all the products. The market shares are given in Table VI below.

When all the products are at the low level (50 cents) the highest market shares are 36.9%, 19.0%, 11.3% and 10.1%, for Coca-Cola, Sprite, spring water, and Mr. Pibb, respectively. The lowest market shares are 8.6%-Mello Yello, 7.4%-Diet Cola, and 6.7%-Root Beer.

When all the products are introduced at the high price (75 cents) the spring water dominated the market, with a 47.6% market share. The next two highest market shares are 16.1%-Coca-Cola, and Spring-12.6%. The lowest market shares are 5.5%-Diet Cola and 1.2%-Root Beer.

From the above result, we can see the students' choices are influenced by the price. The students will buy more soft drinks versus spring water if the price is at the low level (50 cents). We will continue our analysis based on the scenario that all the products are introduced at the low level price (50 cents).

Obviously, Coca-Cola is more in demand than anything else. Is it possible for the machine to have two rows of Coca-Cola, instead of one, and row of spring water? The question is which soft drinks should be replaced by the Coca-Cola and the spring water? From Table VI, the two lowest market shares are 6.6% for Root Beer and 7.4% for Diet Cola. It's not very clear at this point that Root Beer and Diet Cola are the ones to be replaced by an extra row of Coca-Cola and spring water.

In Table VII, we introduce a few other scenarios that will help us make the correct decision.

Scenario 1 tells us how the market share of the Coca-Cola is distributed among the other products when the machine is out of Coca-Cola. Even though Root Beer had the lowest market share in Table VI, under Scenario 1 it gained enough market share to beat Mr. Pibb and Diet Cola. Obviously, Root Beer is not one of the products to be replaced, but possibly Diet Cola with a market share of 7.9% and Mr. Pibb with 14.1%

Scenarios 2 through 5 tell us the distribution of the next highest market share of a product. For example, in Scenario 2, Coca-Cola and Sprite are not available. Diet Cola and Mr. Pibb have the lowest market shares at 8.7% and 15.7%, respectively. This trend continues in the remaining scenarios, Diet Cola gets the lowest market share and Mr. Pibb gets the next lowest. It is obvious now, that Diet Cola and Mr. Pibb should be replaced by Coca-Cola and spring water.

CONCLUSION

Our study finds that based on the choice behavior of the students on our campus and the availability designs, Diet Cola should be removed from the vending machine since it received the lowest percentage and replaced by Coca-Cola which had the highest percentage. Mr. Pibb had the second lowest percentage and should be replaced by spring water which had the third highest percentage.

If vendors make use of the suggestions provided by this study, they will provide better service to the students on our campus and may in turn improve their profits.

Some readers may have reservations about the results we obtained in this study. Our study does have limitations. The data is confined to the students on our campus and the beverage selection available. The statistical analysis was performed using availability designs on the empirical data collected. The results may not be extrapolated to include general public beyond our campus. A study using different data may not produce the same results.

REFERENCES

(1.) Anderson D and Wiley JB: Efficient choice set designs for estimating cross-effects models. Marketing Letters 3: 4, 357-370, 1992.

(2.) Batsell RR and Lodish LM: A model and measurement methodology for predicting individual consumer choices. Journal of Marketing Research 18: 1-12, February, 1981.

(3.) Batsell RR and Louviere JJ: Experimental Choice Analysis. Marketing Letters: July, 1991.

(4.) Batsell RR and Polking JC: A New Class of Market Share Models. Marketing Science 4: 177-198, 1985.

(5.) Lazari A: "Designs for discrete choice experiments including availability and attribute cross effects," University of Wyoming, Dissertation Abstracts, p. 35, 1991.

(6.) Lazari A and Anderson D: Designs of Discrete Choice set Experiments for estimating both Attribute and Availability Cross Effects. Journal of Marketing Research 31: 375-383, August, 1994.

(7.) Lazari A: 3m Availability Designs. Decision Sciences Institute Proceedings 2: 1062-1063, 1995.

(8.) Lazari A and Meghabghab G: Comparison of Market Estimates for Neural Networks vs. The Maximum Likelihood Function of Availability Designs. Georgia Journal of Science 53 No. 2: 89-100, 1995.

(9.) McFadden: Conditional Logit Analysis of Qualitative Choice Behavior. Frontiers in Econometrics. P. Zarembka ed. New York: Academic Press: 105-142, 1994.

(10.) Minitab inc. "Minitab Reference Manual," State College, PA, p. 1-16, 1996.

(11.) Woodworth G: "Foxlogit Reference Manual," University of Alberta, Canada, p. 3, 1985.
 The six products with the Low and High Prices
Product Low High
Coca-Cola 50 cents 75 cents
Diet Cola 50 cents 75 cents
Sprite 50 cents 75 cents
Root Beer 50 cents 75 cents
Mr. Pibb 50 cents 75 cents
Mello Yello 50 cents 75 cents
 Availability Design
2 1 0 1 0 0
0 0 2 2 2 1
1 2 1 0 1 2
2 2 1 1 2 1
0 1 0 2 1 2
1 0 2 0 0 0
2 0 1 2 1 0
0 2 0 0 0 1
1 1 2 1 2 2
2 1 2 0 1 1
0 0 1 1 0 2
1 2 0 2 2 0
2 2 2 2 0 2
0 1 1 0 2 0
1 0 0 1 1 1
2 0 0 0 2 2
0 2 2 1 1 0
1 1 1 2 0 1
 The Survey
Coca-Cola Diet Cola Sprite Root Beer Mr. Pibb Mello Yello
Coca-Cola Diet Cola N/A Root Beer N/A N/A
75 Cents 50 Cents 50 Cents
 N/A N/A Sprite Root Beer Mr. Pibb Mello Yello
 75 Cents 75 Cents 75 Cents 50 Cents
Coca-Cola Diet Cola Sprite N/A Mr. Pibb Mello Yello
50 Cents 75 Cents 50 Cents 50 Cents 75 Cents
Coca-Cola Diet Cola Sprite Root Beer Mr. Pibb Mello Yello
75 Cents 75 Cents 50 Cents 50 Cents 75 Cents 50 Cents
 N/A Diet Cola N/A Root Beer Mr. Pibb Mello Yello
 50 Cents 75 Cents 50 Cents 75 Cents
Coca-Cola N/A Sprite N/A N/A N/A
50 Cents 75 Cents
Coca-Cola N/A Sprite Root Beer Mr. Pibb N/A
75 Cents 50 Cents 75 Cents 50 rents
 N/A Diet Cola N/A N/A N/A Mello Yello
 75 Cents 50 Cents
Coca-Cola Diet Cola Sprite Root Beer Mr. Pibb Mello Yello
50 Cents 50 Cents 75 Cents 50 Cents 75 Cents 75 Cents
Coca-Cola Diet Cola Sprite N/A Mr. Pibb Mello Yello
75 Cents 50 Cents 75 Cents 50 Cents 50 Cents
 N/A N/A Sprite Root Beer N/A Mello Yello
 50 Cents 50 Cents 75 Cents
Coca-Cola Diet Cola N/A Root Beer Mr. Pibb N/A
50 Cents 75 Cents 75 Cents 75 Cents
Coca-Cola Diet Cola Sprite Root Beer N/A Mello Yello
75 Cents 75 Cents 75 Cents 75 Cents 75 Cents
 N/A Diet Cola Sprite N/A Mr. Pibb N/A
 50 Cents 50 Cents 75 Cents
Coca-Cola N/A N/A Root Beer Mr. Pibb Mello Yello
50 Cents 50 Cents 50 Cents 50 Cents
Coca-Cola N/A N/A N/A Mr. Pibb Mello Yello
75 Cents 75 Cents 75 Cents
 N/A Diet Cola Sprite Root Beer Mr. Pibb N/A
 75 Cents 75 Cents 50 Cents 50 Cents
Coca-Cola Diet Cola Sprite Root Beer N/A Mello Yello
50 Cents 50 Cents 50 Cents 75 Cents 50 Cents
Coca-Cola spring water
Coca-Cola spring water
75 Cents 50 Cents
 N/A spring water
 50 Cents
Coca-Cola spring water
50 Cents 50 Cents
Coca-Cola spring water
75 Cents 50 Cents
 N/A spring water
 50 Cents
Coca-Cola spring water
50 Cents 50 Cents
Coca-Cola spring water
75 Cents 50 Cents
 N/A spring water
 50 Cents
Coca-Cola spring water
50 Cents 50 Cents
Coca-Cola spring water
75 Cents 50 Cents
 N/A spring water
 50 Cents
Coca-Cola spring water
50 Cents 50 Cents
Coca-Cola spring water
75 Cents 50 Cents
 N/A spring water
 50 Cents
Coca-Cola spring water
50 Cents 50 Cents
Coca-Cola spring water
75 Cents 50 Cents
 N/A spring water
 50 Cents
Coca-Cola spring water
50 Cents 50 Cents
 Price Cross Effects
 1 2 3 4 5 6
1 -.456 -.331 -.432 .077 -.208 .304
2 -.159 -.356 -.229 -.074 -.071 .025
3 -.168 -.054 -.671 -.043 -.020 -.077
4 -.048 -.381 -.314 -.947 .126 -.011
5 -.163 -.034 -.122 .127 -.585 -.067
6 -.014 -.072 -.156 0.47 .088 -.582
 Availability Cross Effects
 1 2 3 4 5 6
1 -.527 .293 -.134 .167 .171 .079
2 .072 -1.508 .091 -.011 .062 .008
3 -.031 -.036 -.411 -.002 .111 -.036
4 -.124 .109 -.005 -2.121 .157 -.123
5 -.017 .053 .119 -.045 -1.071 .003
6 -.113 .034 .050 -.050 .115 -1.001
 Products Market Share
 Scenario Scenario
 Low Level High Level
Coca-Cola 36.9% 16.1%
Diet Cola 07.4% 05.5%
Sprite 19.0% 12.6%
Root Beer 06.7% 01.2%
Mr. Pibb 10.1% 07.9%
Mello Yello 08.6% 09.1%
spring water 11.3% 47.6%
 Products Market Share Under Difference Scenarios
 All Products are at the
 Low Price (50 Cents)
 1 2 3 4 5
Coca-Cola N/A N/A N/A N/A N/A
Diet Cola 7.9% 8.7% 10.5% 14.1% 16.9%
Sprite 27.5% N/A N/A N/A N/A
Root Beer 14.3% 19.2% 33.2% N/A N/A
Mr. Pibb 14.1% 15.7% 17.7% 33.0% N/A
Mello Yello 18.5% 24.6% N/A N/A N/A
spring water 17.7% 31.8% 38.6% 53.9% 83.1%
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Author:Lazari, Andreas; Goel, Sudhir
Publication:Georgia Journal of Science
Date:Dec 22, 2000
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