Optimal Workflow Decisions for Investigators in Systems with Interruptions

We model a system which consists of a stream of customers processed through three steps by two resources. The first resource, an investigator, handles the first step, in which she collects information from the customer and decides what work will be done in the second step by the second resource, the back office. In the third step the investigator returns to the customer armed with the additional information or analysis done by the back office and provides the customer with a conclusion, solution, or diagnosis.The investigator has to determine whether to prioritize seeing a new customer, or complete the work with a customer already in the system. While serving one customer, the investigator may be interrupted by requests from the other customers in the system. Our main objective is to understand the impact of the investigator's choices on system throughput. In addition we are also interested in the occupancy of the system (and thus on the flow time of customers). We create a stylized queuing model to examine the investigator's decisions and show that, when interruptions are not an issue, the investigator should prioritize new customers to maximize throughput, keeping the system as full as possible. If customers who have been in the system for a long time generate interruptions and thus additional work for the investigator, then we show that it is asymptotically optimal for the investigator to keep the system occupancy low and prioritize discharging customers. Our conclusions are based on a model of a re-entrant queue with dedicated servers serving multiple stations, with two novel features: a buffer that is shared between stations and jobs in the system generating additional work for the servers