Optimizing flowering time is crucial for maximizing crop productivity, but gaps remain in the knowledge of the mechanisms underpinning temperate legume flowering. Medicago, like winter annual Arabidopsis, accelerates flowering after exposure to extended cold (vernalization, V) followed by long-day (LD) photoperiods. In Arabidopsis, photoperiodic flowering is triggered through CO, a photoperiodic switch that directly activates the FT gene encoding a mobile florigen and potent activator of flowering. In Arabidopsis, several CYCLING DOF FACTORs (CDFs), including AtCDF1, act redundantly to repress CO and thus FT expression, until their removal in LD by a blue-light-induced F-BOX1/GIGANTEA (FKF1/GI) complex. Medicago possesses a homolog of FT, MtFTa1, which acts as a strong activator of flowering. However, the regulation of MtFTa1 does not appear to involve a CO-like gene. Nevertheless, work in pea suggests that CDFs may still regulate flowering time in temperate legumes. Here, we analyze the function of Medicago MtCDF genes with a focus on MtCDFd1_1 in flowering time and development. MtCDFd1_1 causes strong delays to flowering when overexpressed in Arabidopsis and shows a cyclical diurnal expression in Medicago with peak expression at dawn, consistent with AtCDF genes like AtCDF1. However, MtCDFd1_1 lacks predicted GI or FKF1 binding domains, indicating possible differences in its regulation from AtCDF1. In Arabidopsis, CDFs act in a redundant manner, and the same is likely true of temperate legumes as no flowering time phenotypes were observed when MtCDFd1_1 or other MtCDFs were knocked out in Medicago Tnt1 lines. Nevertheless, overexpression of MtCDFd1_1 in Medicago plants resulted in late flowering relative to wild type in inductive vernalized long-day (VLD) conditions, but not in vernalized short days (VSDs), rendering them day neutral. Expression of MtCO-like genes was not affected in the transgenic lines, but LD-induced genes MtFTa1, MtFTb1, MtFTb2, and MtSOC1a showed reduced expression. Plants carrying both the Mtfta1 mutation and 35S:MtCDFd1_1 flowered no later than the Mtfta1 plants. This indicates that 35S:MtCDFd1_1 likely influences flowering in VLD via repressive effects on MtFTa1 expression. Overall, our study implicates MtCDF genes in photoperiodic regulation in Medicago by working redundantly to repress FT-like genes, particularly MtFTa1, but in a CO-independent manner, indicating differences from the Arabidopsis model.

In this paper, we propose a new linear programming-based approach that enables the consideration of technical car sequencing rules in the master production scheduling of mixed-model assembly lines at a much higher level of detail than previous approaches. To this end, we investigate certain interdependencies of car sequencing rules, which have largely been neglected, both in practice and in the research literature. We illustrate the existence and impact of these interdependencies and show that they induce additional implicit constraints, which can be represented by linear inequalities and incorporated into linear optimization models for master production scheduling. In a numerical study, we evaluate the approach and show, that it can significantly reduce sequencing violations compared to existing approaches.