I am an Inspector and do not have a duty roster published. Is this right?

Yes. Police Regulations do not require rosters to be published for Inspectors or Chief Inspectors but Home Office Circular 21/97 states that inspectors and chief inspectors, no less than other members need to be able to plan for work, personal and family commitments. Therefore, it is important that you should be given reasonable notice of when you will be required to be on duty.