This paper considers a production lot sizing and scheduling problem with sequence-dependent setup times that are not triangular. Consider, for example, a product that contaminates some other product unless either a decontamination occurs as part of a substantial setup time or there is a third product that can absorb s contamination. When setup times are triangular then stpr ≤ stpq + stqr and there is always an optimal lot sequence with at most one lot per product per period (AM1L). However, product s ability to absorb s contamination presents a shortcut opportunity and could result in shorter non-triangular setup times such that stpr > stpq + stqr. This implies that it can sometimes be optimal for a shortcut product such as to be produced in more than one lot within the same period, breaking the AM1L assumption in much research. This paper formulates and explains a new optimal model that not only permits multiple setups and lots per product in a period (ML), but also prohibits subtours using a polynomial number of constraints rather than an exponential number. Computational tests demonstrate the effectiveness of the ML model, even in the presence of just one decontaminating shortcut product, and its fast speed of solution compared to the equivalent AM1L model. © 2014 Taylor & Francis.