The company is also doing battle with fellow up-and-coming fast casual pizza companies such as MOD Pizza and PieFive. Blaze Pizza estimates there are about 75 players in the relatively new fast casual pizza space.

Nevertheless, the privately held Blaze Pizza has another busy year ahead.

The company plans to open 70 to 80 new restaurants in 2016. Two of those locations will be high-profile flagships inside of Disney World and Universal Studios.

This month the company will unveil its first mobile ordering app, which will include a loyalty program that gives customers a free pizza after ten trips to the restaurant.

Loyalty programs have proven very popular in the fast food pizza industry. Papa John's launched its "Papa Rewards" platform in 2010, with users scoring a free large pizza after they spend $100. The program has helped Papa John's sales that are made online or on a mobile device to reach a whopping 50% of its business.

In September, Domino's Pizza launched its "Piece of the Pie" rewards program. For every digital order of $10 or more, a user is given 10 points. After amassing 60 points, the points can be redeemed for a free medium pizza.

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