But company chief executive Tony Gibson said Auckland's labour "utility" rate is only about 65 per cent compared with almost 90 per cent at Tauranga, a score he wants to improve by replacing the eight-hour roster with shifts varying from five to 12 hours.
He said workers would be able to "book" shifts four weeks ahead to give them, as well as him, greater flexibility to plan their lives.
The union fears the company will use such a system to "casualise" its workforce, which Mr Gibson denies.
His rostering offer is a relatively recent development in a long dispute in which the union initially refused a 2.5 per cent pay rise and the preservation of conditions unless the company "fixed" a festering sore left from its previous collective agreement.
The company says it was entitled within the two-and-a-half-year term of the agreement, which itself was reached only after 18 months of negotiation punctuated by strikes, to replace four unionised cargo shuttle drivers with contractors to a company in which it owns a majority stake.
But after being unable to strike during the previous agreement, the union is now making the issue a non-negotiable condition of restoring peace to the waterfront.
THE DISPUTE
What the company says it is offering
10 per cent rise on existing wage of about $27.40 an hour and extra bonuses in return for replacing eight-hour duties with shifts ranging from five to 12 hours.
What the union says it wants
An unquantified "realistic" increase on wages, the continuation of eight-hour rosters, and the reinstatement of four contracted-out union jobs.