Machinery for sowing wheat directly into rice residues has become more common in the rice-wheat systems of the north-west Indo-Gangetic Plains of South Asia, with increasing numbers of farmers now potentially able to access the benefits of residue retention. However, surface residue retention affects soil water and temperature dynamics, thus the optimum sowing date and irrigation management for a mulched crop may vary from those of a traditional non-mulched crop. Furthermore, the effects of sowing date and irrigation management are likely to vary with soil type and seasonal conditions. Therefore, a simulation study was conducted using the APSIM model and 40 years of weather data to evaluate the effects of mulch, sowing date and irrigation management and their interactions on wheat grain yield, irrigation requirement (I) and water productivity with respect to irrigation (WPI) and evapotranspiration (WPET). The results suggest that the optimum wheat sowing date in central Punjab depends on both soil type and the presence or absence of mulch. On the sandy loam, with irrigation scheduled at 50% soil water deficit (SWD), the optimum sowing date was late October to early November for maximising yield, WPI and WPET. On the clay loam, the optimum date was about one week later. The effect of mulch on yield varied with seasonal conditions and sowing date. With irrigation at 50% SWD, mulching of wheat sown at the optimum time increased average yield by up to 0.5tha−1. The beneficial effect of mulch on yield increased to averages of 1.2–1.3tha−1 as sowing was advanced to 15 October. With irrigation at 50% SWD and 7 November sowing, mulch reduced the number of irrigations by one in almost 50% of years, a reduction of about 50mm on the sandy loam and 60mm on the clay loam. The reduction in irrigation amount was mainly due to reduced soil evaporation. Mulch reduced irrigation requirement by more as sowing was delayed, more so on the sandy loam than the clay loam soil. There was little effect of mulch on irrigation requirement for late October sowings.There were large trade-offs between irrigation input, yield, WPET and WPI on the sandy loam with regard to the optimum irrigation schedule. Maximum yield occurred with very frequent irrigation (10–20% SWD) which also had the greatest irrigation input, while WPI was highest with least frequent irrigation (70% SWD), and WPET was highest with irrigation at 40–50% SWD. This was the case with and without mulch. On the clay loam, the trade-offs were not so pronounced, as maximum yield was reached with irrigation at 50% SWD, with and without mulch. However, both WPET and WPI were maximum and irrigation input least at the lowest irrigation frequency (70% SWD). On both soils, maximum yield, WPET and WPI were higher with mulch, while irrigation input was slightly lower, but mulch had very little effect on the irrigation thresholds at which each parameter was maximised.