The durability issues, which have hit airlines all around the world, have resulted in an increased number and frequency of engineering checks required.
"This has meant that at any time up to five of our 13 787 Dreamliners must be grounded while the engines are serviced in Singapore," Luxon wrote.
"This has placed significant pressure on our whole interconnected network of over 3,500 weekly flights."
During the last ten months, tens of thousands of passengers have had flights cancelled, rescheduled or faced flying in different planes.
Luxon said that he would be meeting with Rolls Royce management in London in a few weeks to "further seek personal reassurance that all is being done to get our affected engines back in service as soon as possible."
To cope with the reduced fleet, Luxon said Air New Zealand has had to lease three other aircraft from two of the world's top airlines as well as cut back on some of its services – such as stopping flying to Vietnam next year – and service frequencies – including reduced number of flights to Argentina and Taipei.
Luxon labelled the moves as vital in freeing up capacity and allowing the carrier to concentrate on delivering a better experience.
Another major issue that hit the airline was the rupture of the fuel pipeline at Ruakaka, north of Auckland.
The incident, which took place in September last year, forced the shutdown of fuel supplies, which caused international flights to be cancelled and petrol shortages around the top of the North Island.
Luxon wrote, "while these are not in our direct control, how we choose to respond certainly is."
Luxon also highlighted how a significant increase in people passing through airports in New Zealand had disrupted their operations due to under investment of our airports.
"Simply put, some airport facilities, especially in Auckland, are struggling to keep up with the surge in demand for air travel due to under investment by the airport companies," Luxon wrote.
During the past year, the total number of passengers using Auckland Airport increased by 5.7 per cent to 20.5 million.
The Air New Zealand boss said he was working with the chief executives of several airports to do whatever they could to "accelerate improvements".
Luxon said they were also in the process of hiring a further 80 Contact Centre employees after strong feedback from customers about frustration over call wait times into the Contact Centre.
While Luxon commended the agility and resilience of Air New Zealand's staff in responding to the recent challenges it's faced, he said they now need to implement more assertive actions in order to deliver a more reliable schedule for customers.
"I really do apologise and thank you for your patience and support of the airline at this time," Luxon wrote.
