According to Craig L Good, Pixar Camera Artist, human characters were too expensive to design back then. So since a dad was not necessary for the story, Andy didn't get one.
I did want the backstory, though: Is dad dead? A deadbeat? So I posed
the question to Lee Unkrich, who directed solo on this film after
co-directing with Ash Brannon and John Lasseter on "Toy Story 2"
(Lasseter directed the original "Toy Story").
"It's an oft asked question, but there is no concrete answer," Unkrich
said. "We don't mean to be mysterious about it; it's just never been
relevant to the story."
It's just always been that way, Unkrich said. "The decision was made
really early on in 'Toy Story' to have Andy's dad not be around," he
said. "We've never addressed it directly, nor have we given any
explanation for where he is or why he's absent."