Guolin Lai

DSC8240 Course Web

Background
Objective Hierarchies
Variables and Attributes
Influence Diagram
Mathematical Representation
Testing and Validation
Implementation and Use

Background

The Great Threads Company sells hand-knit sweaters. It is planning to print a brochure of its products and undertake a direct mail campaign.

The cost of printing the brochure is $20,000 plus $0.10 a catalog. The cost of mailing each catalog is $0.15. In addition, the company will include direct reply envelopes in it’s mailings. It incurs $0.20 in extra cost for each direct mail envelope that is used by a respondent. The average size of a customer order is $40, and the company’s variable cost per order averages around 80% of the order’s value. The company plans to mail 100,000 catalogs.

Objective Hierarchies

The company plans to mail 100,000 catalogs. It wants to develop a spreadsheet model to answer the following questions:

1. How does a change in the response rate affect profit?
2. For what response rate does a company break even?
3. If the company estimates a response rate of 3%, should it proceed with the mailing?
4. How does the presence of uncertainty affect the usefulness of the model?

Influence Diagram

Mathematical Representation

Number of Responses = Number Mailed * Response Rate;
Revenue = Number of Responses * Average Order;
Variable Cost from Mailing = SUM(Variable Cost of Mailing) * Number Mailed;
Variable Cost from Ordering = Number of Responses * (Average Order * Variable Cost % of Order + Variable Cost of Envelopes);
Total Cost = Fixed Cost of Printing + Variable Cost from Mailing + Variable Cost from Ordering
Profit = Revenue - Total Cost.

Testing and Validation

How does a change in the response rate affect profit?

Clearly, profit increases in a linear manner as response rate varies. More specifically, a 1% increase in the response rate always increased profit by $7800. Here is the reasoning. Each 1% in response rate results in 100,000 x 0.01=1000 more orders. Each order yields an average revenue of $40 but incurs a variable cost of $40 x 80% = $32 and a $0.20 envelope cost. The net gain is $7.80 per order, or $7800 for 1000 orders. From the data table, we see that profit goes from negative to positive when the response rate is somewhere between 4% and 5%.

For what response rate does a company break even?

This could be found with trial and error but is easy with Excel’s Goal Seek tool. If the response rate is 5.77% Great Threads breaks even. If the response rate is greater then 5.77%, the company makes money; otherwise, it loses money.

If the company estimates a response rate of 3%, should it proceed with the mailing?

From the data table, the apparent answer is " no" because profit is negative, a loss. However, if we look at long-term impact of the decision, the answer will be " yes " --- if customers who respond to direct mail will reorder in the future and thus the company will achieve a positive profit. If we want to incorporate the long term explicitly into the model, we must build a more complex model.

How does the presence of uncertainty affect the usefulness of the model?

When there is a high degree of uncertainty about model inputs, it makes little sense to talk about the profit level or the breakeven response rate. It makes more sense to talk about the probability that profit will have a certain value or the probability that the company will break even.

Implementation and Use

The model can be manipulated in Microsoft Excel.