First I have added the simple products and then a configurable product using the simple products.
Is it necessary to add both simple product and configurable product to the category where the product should be shown?
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It is indeed necessary to add associated simple products to the category of the parent configurable product only if you are going to define catalog price rules based on conditions around categories and are using the SCP extension.
This was at least one case where I found it necessary. If a price rule was configured on the basis of a category, then it would not apply to the associated simple products if they were not directly assigned to the category, notwithstanding that the configurable product was a category member.
However, if you are NEVER going to use the catalog price rules with category conditions and the SCP extension, then I did not find any other case which made this step seem necessary.
This is my experience based on Magento CE 1.9.2+