Small deviations, JIT sequencing and symmetric case of Fraenkel's conjecture

We prove Fraenkel's conjecture for the special case of symmetric words, and show that this proof implies the conjecture of Brauner and Crama [Facts and questions about the maximum deviation just-in-time scheduling problem, Discrete Appl. Math. 134 (2004) 25–50] concerning instances of the just-in-time sequencing problem with maximum deviation B*<12.