To keep a sentence parallel, each item in a list needs to be in the same verb format. Here you have "checking, initialing, and to call." Mixing up the gerund (ing) verb and the preposition (to) verb form is the most common parallelism mistake. It happens because some words work better in "ing" and others usually are used with the "to." However, there are several possible ways to correct this. The first thing to try is to switch all of the items to one form:
1. My job includes to check the inventory, to initial the orders and to call the suppliers.
2. My job includes checking the inventory, initialing the orders and calling the suppliers.
Usually, you can do this in your head (or you can write it out as I did here) and it is frequently easy to see that one of these sounds better than the other. In this case, the second sentence sounds more natural because "includes to check" doesn't sound correct. There is another way to fix this sort of error, and that is to put one of the items in front of the verb in an introductory phrase. Here's a sample:
Along with checking the inventory, my job includes initialing the orders and calling suppliers.
Along with checking the inventory, my job is to initial the orders and call the suppliers.
Notice that in the second example, I did not repeat the "to." If the same preposition (or verb) could be used in front of each item in the list, you don't have to repeat it. Here are some examples:
1. Before we go to the movies, I need to walk the dog, take out the trash, reply to Grandma's email, make my lunch for tomorrow, and water my plants.
2. Before our trip abroad, I am planning on: packing my bags, finding someone to take care of the pets, locating my passport, buying my tickets and making sure we have enough cash for the trip.
Notice that in the last example I used a colon to tell the reader that I was going to write a list. A colon is especially useful if you have a longer list.