Optimal Workflow Decisions for Investigators in Systems with Interruptions

Abstract

We model a system that 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 prioritize either seeing a new customer or completing 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 interested in the occupancy of the system (and thus the flow time of customers). We create a stylized queueing 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, 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. This paper was accepted by Assaf Zeevi, stochastic models and simulation.

Queueing Models of Case Managers

“…Models closest to our system are found in Saghafian et al (2014Saghafian et al ( , 2012, Dobson et al (2013), Tezcan and Zhang (2014), and Luo and Zhang (2013). Saghafian et al (2014) model an ED as a case-manager system, as we define it, and disaggregate the analysis to "Phase 1" (similar to our preassignment queue) and "Phase 2" (with repeated testing and interactions with a physician).…”

“…Saghafian et al (2012) use a model similar to that in Saghafian et al (2014) to examine how patients should be routed (or "streamed") through an ED, depending on whether the patient is likely to be discharged or admitted to the hospital. Dobson et al (2013) examine a case-manager system that is also motivated by an ED. Their model allows for limited capacity to serve customers in external delay, service interruptions from customers in external delay, and distinct service-time distributions for the initial versus subsequent encounters between a customer and a case manager.…”

“…Their model allows for limited capacity to serve customers in external delay, service interruptions from customers in external delay, and distinct service-time distributions for the initial versus subsequent encounters between a customer and a case manager. Both Dobson et al (2013) and this paper use simulation to analyze systems with separate (nonpooled) case managers. This paper differs from Dobson et al (2013) in terms of both methodology and focus.…”

“…Both Dobson et al (2013) and this paper use simulation to analyze systems with separate (nonpooled) case managers. This paper differs from Dobson et al (2013) in terms of both methodology and focus. This paper models the bounding systems as quasi-birth-death (QBD) processes and uses twotime-scale analysis to develop approximations, whereas Dobson et al (2013) use high-caseload asymptotic analysis to examine the performance of single-server and pooled systems.…”

Multitasking Scheduling Problems with Deterioration Effect

“…Let V ( ), 0 ≤ ≤ − 1, denote the remaining processing time of job after it has interrupted primary jobs. The multitasking function is defined as (| |)+ ∑ ∈ ( ) based on empirical evidence in the operations management literature [41,42]. Again, like Hall et al [14], we use (| |) and ∑ ∈ ( ) to denote, respectively, the switching time dependent only on the number of waiting jobs and the interruption time, which is the sum of the amount of time for all the waiting jobs ∈ interrupting job .…”