Dispatching is well matched to fuzzy logic, whether the item being dispatched is an elevator car or a police cruiser. The handling of limited resources in dispatching scenarios is within the realm of what fuzzy logic systems have been doing well in building systems and aeronautics for two decades.
This question require more than that, specifically bidirectional natural language handling along with some level of customer service via phone lines. Although that is more difficult than a web based request system, there is no requirement in the question that the caller be fooled into thinking the computer is a person, as in Turing's imitation game thought experiment.
One attractive approach is to collect dispatch calling data, time span labeled to identify customers and dispatchers.
Very little plumbing advice is customarily given over the phone, other than to shut off the water main if a significant leak exists. Contracts with plumbing vendors can include an emergency response system that allows plumbers to contact the customer, upon verbal agreement to pay for such an emergency call, to instruct them how to shut off the main valve. Clogged lines on the drain side of a plumbing system can be an emergency of a health risk type, but does not require water main manipulation. The usual recommendation is not to run additional wastewater into the clogged drain.
Consequently, this system may be feasible without waiting for more advanced semantic processing systems and frameworks to become generally available.
Although a reasonable level of voice recognition is necessary in this system, there is likely to be only a limited number of voice responses. Recent advancements in voice synthesis may make it possible to train voices rather than prerecord. This allows parameterized responses both human sounding and flexible.
With the current state of technology, both the customer and the plumbing vendor will have to accept that they are talking to a computer. Simulating human cognition such that conversation would be indistinguishable with human dispatchers is still out of reach. Some callers will be unaware of the computer nature of the dispatcher simply because they are used to automated callers, don't know about Turing's thought experiment, and don't really care. Their focus will be on getting the problem solved. As long as the computer facilitates that effectively, they will not likely negatively react to the missing extensiveness of human cognition.
The requirement, "Includes conflicts between the operators and contrasting point of views," is probably infeasible at this time. Mediation is has not yet been successfully engineered into any voice centered or even text centered products.
Regarding multi-level call center design, such is not a customer service driven feature of a call center. It is done only to reduce the cost of the call center. If a low level caller can satisfy the customer, the more expensive human resources don't need to connect to those calls that require their higher expertise.
The question mention repeating what a human speaker says back to them in the form of a query for more detail, as in early natural language speaking experiments where the computer played the counselor. That worked only marginally well for short periods of time for counselling and wouldn't work at all in this case. The caller wants to know when the plumber will arrive, which cannot be derived from the caller's speech, and needs to know what to do in the interim, which is domain knowledge. A chatbot without domain knowledge will annoy the customer.
The collected real dispatch conversation with appropriate labels as mentioned above can be used to train a response system that provides one of a few hundred known domain related speech components, parameterized by the person's name and the way they phrase the issue, so that responses back are clear and reasonably personalized. The statements to the caller must also be parameterized by the output of the dispatching system.
The reason it is difficult to find a paper on this problem is because of the profitability involved. The solutions that exist are company confidential and under heavy guard from a corporate integrity point of view.