What can managers do to improve inter-departments communication?

make the department work on some task as workshop together, in each meeting try to make them do the brainstorming and discuss between them even it will kill some minute from the meeting but it will improve them communication, and maybe you can meet them at dinner or arrange a party for them or any other activite you can do it to let them meet each other out of the working hours

Every manager should be a people's person. Managers should build a mutual understanding of each other first. All managers must work for the betterment of the company.

As per the question raised, initially, all departments need to have a general meeting or discussion to highlight the communication gaps in between or any misunderstandings or confusions. These should be noted and then corrective action must be planned and implemented. All the communication between departments should be integrated so that the work is always streamlined.  If any department manager observes a flaw they can immediately discuss that and solve it then and there. 

By building a team based reward and benefits systems. We win together.

HAVE GOOD RELATIONSHIP WITH THE BOSS OF EACH DEPARTMENT AND ATLEAST ONE FROM JUNIOR CADER.