> DCM Portfolio Optimization

DCM Portfolio Optimization

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A case study: Consumer Response to Marketing Information

A bank ... sent out 60,000 letters to existing clients saying "Congratulations! You're eligible for a special interest rate on a new loan." Like a drug trial, the interest rate was randomized. In line with traditional economics, the people who received the high interest rate were less likely to take up the offer.
But the bank also randomized other aspects. For some letters, a photo of a bank employee, ..., a variety of tables, some complex and others simple, ..., deadlines, ..., and the chance to win prizes.
The results were stunning. People appeared to be influenced by factors other than the actual interest rate. ... The letter with just one example of a loan size and term with its monthly repayments was more successful than the letter with four examples ...

[ From once a public source on http://www.med.govt.nz, shortened ]

Problem

A common task in marketing engineering is to set up a product portfolio or a line of products that maximize a desired criterion such as reach, choice frequency, acceptance value, competitive potential, etc. Confusion from a too large selection of products has been named "tyranny of choice". It often makes a potential customer postpone the purchase, especially in the category of durables requiring high involvement. A too narrow portfolio, on the other hand, may discourage some customers as little representative. In FMCG category it is important to offer a sufficiently broad spectrum of products to satisfy individual desires and needs but, at the same time, to keep the production and distribution costs low. Clearly, finding a optimal portfolio composition is a frequent research tasks. 

A method known as TURF - Total Unduplicated Reach and Frequency is often used. It allows to find a set of items that manifest a satisfactory reach by allowing a sufficient diversity of choices for potential users. The method suffers from two major deficiencies.

1. The TURF method makes use of dichotomous acceptance. Whatever data is exploited, each item in a portfolio is given an acceptance value either 1 - acceptable or 0 - unacceptable. This is a very crude approximation since personal preferences are never so distinct. A substantial amount of information, e.g. that obtained from a preference study, is left unused.
   
2. When an item is added to a choice set of any size the reach or frequency never falls. The final number of items in a portfolio must be either known in advance, or some additional criteria such as cost of the addition, or (most often) some expertise must be applied.

Solution

A process of making choice from a set of several items can be viewed quantitatively from the standpoint of the following DCM characteristics of the set.

1. Inclusive value (IV)
   It is the overall utility of the set computed as logarithm of the sum of the odds of the products in the set. It is known as "logsum value" in nested logit models. When an arbitrary item is added to a set, the inclusive value of the set is always increased. 
• Inclusive value is always higher than the utility of the most preferred option in the set.
• Inclusive value is a semantic equivalent to the frequency in the TURF method.
2. Expected value (utility)
   When only one choice from a selection of options is supposed the chooser must resign on all other options which makes the process of choosing risky. Such a situation can be described by expected utility that refers to the whole set of options with uncertain outcomes, and reflects the balance of risk versus reward. 
• Expected value cannot exceed the utility of the most preferred option in the set. 
• Expected value is a semantic equivalent to the reach in the TURF method.
3. Persuasive value
   The theoretically optimal size of a consideration set at the time of making a decision is a set of 3 items. A higher number of items with similar acceptance makes the choice decision more difficult and thus leads to confusion in the decision maker's mind. The more similar to each other the electable items are the higher the doubt or dilemma which one to choose. The persuasive value of a set has been defined as its expected value decreased by a value equivalent to the information entropy of the choice set. It is useful for developing a narrow but more efficient portfolio of items.
• Persuasive value is always lower than the utility of the most preferred item in the set.
• Persuasive value does not have an equivalent in the TURF method.

As aside

• As decisions of individuals are mutually independent the contributions to the likelihood of "faith" or "doubt" in the choice can be aggregated over the sample. 
• Intuitively, expected utility of a choice set evoking no confusion should be close to the highest utility of an item in the set. The equality would occur if and only if the "just noticeable differences" between items [Luce and Suppes (1965); Tversky (1971)] were infinitely small or, equivalently, the utility scaling factor (steepness of the discrimination function) infinitely large. Such conditions are nonexistent in the real market.
• On the assumption that all items with utilities above a certain threshold value have acceptance equal to 1 (100 %) and all the other items have acceptance equal to 0 (zero), the sum of expected acceptances is identical to the TURF reach, and sum of acceptances derived from inclusive values is identical to the TURF frequency. The DCM Portfolio optimization based on expected values can be viewed as an enhanced version of the standard dichotomy-based TURF - Total Unduplicated Reach and Frequency method.

Properties of the method

• Concurrent choices (typically consumption goods - CPG/FMCG)
• A choice of one item does not preclude a choice of another one in some quantity from the same choice set at the same time.
• Choices usually proceed with low effort and involvement.
• Confusion from a broad selection is usually low.
• Autonomous choices (typically durables and infrequently bought products) 
• A choice, having been made, precludes a choice of another item from the choice set.
• Choices are usually preceded with relatively high involvement and effort related to identification and evaluation of a number of product aspects. 
• Confusion from a broad selection is usually high.

While utilities are not additive and should not be averaged across individuals, choice probabilities and consumption quantities are. Therefore, optimization of a set of items in respect to a sample should be be done by maximizing the portfolio acceptance, consumption or spend related to the expected or persuasive value across the individuals in the target. Acceptances can be computed from the standard logit formula.

Individual inclusive value is not very helpful in portfolio optimization as it always grows with an item added to the set. It is eligible only in the case when the number of items in the portfolio is known beforehand.

Individual expected value of a choice set is often only slightly lower than the value of the most preferred item in the set. Optimization by expected values for a sample usually leads to a relatively broad set tending to satisfy all important population segments with several products being chosen concurrently.

A portfolio of products perceived as too similar might make the products to cannibalize one on another. The strategy should be to make the portfolio narrower but possibly not too much because of psychological reasons. This may be achieved by introduction of controlled dose of choice "confusion", i.e. information entropy. In the case of low choice probabilities (and sales), one might "give a chance" to a higher number of apparently different products.

Low involvement FMCG/CPG consumer goods are the candidates for optimization of a portfolio by its expected value. 

In contrast, optimization by aggregated acceptance derived from individual persuasive values gives a substantially narrower portfolio. The unaccepted items are understand as simply ignored by the individual and do not influence persuasive value of the set. In contrast, multiple items with acceptances close to the most accepted item decrease the persuasive value of the set for an individual by the increased information entropy equivalent to the doubt which of the offered items to chose. If the products are of the same brand a substantial decrease of cannibalization may be achieved. 

Durables or other infrequently purchased products with many decisive aspects requiring high involvement of the decision maker, or consumer goods purchased infrequently or occasionally in small quantities, are the candidates for the optimization by persuasive value of the portfolio.

There are two fundamental approaches in application of the portfolio optimization method.

• A portfolio is optimized with no respect to any other fixed sets of products such as those from competition.
  An optimal choice set can be found using interval scaled utilities, e.g. raw (uncalibrated) utilities from a DCM exercise. Utility location factor is irrelevant but scaling factors (sensitivities) for individuals should have correct values. CBC, MXD or SCE are eligible sources of the utilities. Product acceptances can be computed with the reference point set at expected utility of the complete set of candidates for the portfolio.
  This approach is typical in searching for an optimal portfolio of a seller offering products of several brands or makes.
• A portfolio is optimized in respect to the current market with competing sets of products present.
  Ratio scaled, i.e. calibrated utilities are preferable for the candidate and competing products. By calibration we mean that stated product acceptances are available for all individuals in the sample. If calibrated utilities are not available, the reference point is set as expected utility of all items in the set of competing products.
  This approach is most useful in searching for an optimal setup of lines or extensions common to a brand. 
  

Estimation of the optimal choice set can take account of some known factors used as weights. Total consumption quantities are often used for concurrently purchased products. When the candidate products have final price tags the method can be enhanced to an optimization based on maximization of estimated total revenues. An appropriate interviewing format (e.g. SCE – Sequential Choice Exercise or CBC - Choice Based Conjoint) and sufficiently representative sample are essential.

Example: Hypothetical car choice set

Referring to the demonstrative example of car preferences in the two person target discussed in the chapter on what-if simulations it is intuitively clear that the car provider should offer German and French cars for the given target. For the 3 items (cars by origin) there are 2³ - 1 = 7 possible combinations. The choice characteristics averaged over the two potential buyers for the 7 portfolio combinations are in the following table.

As aside

• This table is provided just as an oversimplified demonstration. Averaged utility values instead of correct averaged acceptances derived from individual values are shown since no acceptance can be derived from inclusive value we wanted to show.

The best values in the table are marked with light green background. For a set with a single item, the confusion is none by definition, and the inclusive, expected and persuasion values are the same. For sets with two items, the set composed of German and French cars (shown in bold) is the best. Confusion value (the difference between expected and persuasive values) is very small as a person who prefers one of the cars is fully uninterested in the other one and simply ignores it. While the inclusive value of the set with all three cars is the best one, its persuasion value is perceptibly lower than its expected value. This is because the alternative of a Japanese car is included in the process of making decision but is not going to be actually chosen by any individual from the sample.

Example: Acquirement benefit set

A telecommunication company had an intention to attract new users to their Internet services by offering invitation benefits. The data come from the example given on page MXD - Maximum Difference Scaling. The goal was to find a small and efficient set of benefits to offer. As the benefits were clearly low involvement ones, expected value was used as the criterion. Results for sets with 2, 3 and 4 benefits in decreasing order of expected acceptance (from top to bottom) are in the table below. The best sets for fixed number of items are shown in light green.

The best set set composed of 2 benefits contains the two items found as best in MXD. However, replacing "Computer price discount" for "Print of photos" makes the set only slightly worse and should be worth of consideration. "Internet installation" enters the second-best set with 3 items. That, extended by "Print of photos" benefit makes the best set with 4 items.

Example: Snacks portfolio

The producer of the First brand snacks was considering introduction of a smaller packaging for a presumably significant segment of users. The problem was to decide if an introduction of packages containing either 1 or 3 pieces (servings) of the snack would increase reach and/or share with or without replacement of the current 4 piece packages. The major competing brands Second and Third were available only in 4 piece packages. Each competing brand was represented by 3 flavor varieties. A conjoint brand-price study was run in a design equivalent to that in the class-based demo to outweigh the disbalance in representation of the brands.

Prices of the products were set so that when price of a piece was 100% in a 4-piece package, the piece prices in 3-piece and single piece packages were 96% and 111 %, resp. The competitive acceptances derived from persuasive values of all 511 combinations (2⁹–1) of the nine First brand products were computed and sorted from best to worst. The results for 3 item portfolios are shown in the picture below.

Evidently the best portfolio of 3 products with persuasive acceptance 0.4304 is composed of 3-piece packages. Adding the 4-piece packages, thus making a portfolio of 6 products, would increase persuasive acceptance only to 0.4372 and, therefore, would make no sense. This result is a rare example of "one size fits all".

The improvement of the switch from the current portfolio of 4-piece to 3-piece packaging is demonstrated in the pictures of competitive potential below.

The top-box of competitive potential (product acceptance > 0.95) of the current 4-piece portfolio is quite low as only about 6% of the sample would "definitely" choose the First brand and 60% one of the other brands. The switch to 3-piece packaging of the First brand products should change these numbers to 26% and 29%, resp. The increase of average acceptance of the First brand from 0.20 to 0.46 suggests more than doubling the choices. Even with the price decreased to 72% for the 3-piece package the revenues might increase by about 40%. 

Example: Energetic drinks

A producer of energetic drinks asked to suggest portfolios of their products for some types of sales points. The market was represented with brands A, B, C, D and E with 6, 2, 3, 2 and 3 package and size varieties, resp. As prices were fixed, MXD - Maximum Difference Scaling was used as the test exercise. This example is concerned with modern trade only.

The results from the view of the brand A producer when all other brands are set as competing are shown in the picture below. Since research data are never without error it is always useful to look at several best portfolios. The first 10 of them are usually sufficient to form an opinion.

It is clear the products A2, A3 and A5 are the golden eggs with their presence in 9 of 10 best portfolios. The presence of the  extra small package A6 (50 ml) is surprising as it was intended namely for other sales points such as filling stations or restaurants. The products A1 and A4 are partly interchangeable and of smaller size than expected to be sold in malls. The recommendation would be to keep all the 6 products in portfolio as they make the 5-th best portfolio and their number is not excessive. 

The choice sets for a modern trade sales point that tends to minimize the portfolio size and still have a satisfactory offer for majority of customers are in the picture below.

The most persuasive portfolio is composed of 9 products from the total of 16 tested products. The 3 varieties of the brand A mentioned above appear in nearly all successful portfolios for a modern trade sales point. Adding the product A4 would make the second best portfolio. Each of the other brands is represented by a lower number of varieties. Namely the products A1, B1, C2 and D1 are losers in the competitive environment and can be recommended for exclusion from a modern trade portfolio.