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Need help with approach to gift card optimization

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@feldozz wrote:

Apologies in advance, statistics and data analysis isn’t my speciality. Currently doing commercial strategy with a small, private retailer to expand the business and looking at gift cards as one of those levers. My challenge is I’m trying to determine the optimal discount % to offer on the gift card depending both the overall value of the card and how many are purchased. I can offer gift cards at any value (i.e. $100, $200, $500, $1000) and as the value gets higher, there will obviously be fewer that get purchased. In theory the discount % on the lower value cards would be less than the higher value cards but I’m not sure that’s true (i.e. would I rather have 1,000 cards worth $100 purchased at 30% off or 10 cards for $1,000 at 50% off). The inverse is true for volume as the discount % goes up (for any value card) the number of cards purchased would increase. There really isn’t any constraint on the overall number of gift cards I can offer. So I’m trying to determine a relatively simple way of proposing the optimal discount % for each value to help the sales agents use as a guideline with the overall objective being maximized profit. I’m not even sure there is an easy way to model this out since there is no constraint on the number of gift cards I can offer? Really appreciate any help, suggestions or guidance…so out of my depths!!!

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