Shortest Expected Processing Time Research Articles

Discretionary Task Ordering: Queue Management in Radiological Services

Work scheduling research typically prescribes task sequences implemented by managers. Yet employees often have discretion to deviate from their prescribed sequence. Using data from 2.4 million radiological diagnoses, we find that doctors prioritize similar tasks (batching) and those tasks they expect to complete faster (shortest expected processing time). Moreover, they exercise more discretion as they accumulate experience. Exploiting random assignment of tasks to doctors’ queues, instrumental variable models reveal that these deviations erode productivity. This productivity decline lessens as doctors learn from experience. Prioritizing the shortest tasks is particularly detrimental to productivity. Actively grouping similar tasks also reduces productivity, in stark contrast to productivity gains from exogenous grouping, indicating deviation costs outweigh benefits from repetition. By analyzing task completion times, our work highlights the trade-offs between the time required to exercise discretion and the potential gains from doing so, which has implications for how discretion over scheduling should be delegated. The online appendix is available at https://doi.org/10.1287/mnsc.2017.2810 . This paper was accepted by Serguei Netessine, operations management.

Stochastic Single-Machine Scheduling With Learning Effect

Learning is ubiquitous in the modern scheduling environment. While the deterministic scheduling problems with known processing time and learning rate have been extensively studied, limited work exists to address the problems with both learning effect and uncertainty. In this paper, the single-machine scheduling problem with random nominal processing time and/or random job-based learning rate is studied, with the objective of minimizing the expected total flow time and expected makespan. Several optimal policies are obtained: first, the shortest expected processing time is optimal when only the nominal processing time is random; second, when the job-based learning rate is random, the optimal policy can be obtained by solving an assignment problem with random assignment cost. Computational study is conducted to offer insights on the behavior of optimal policy. The expected value of perfect information (EVPI) is calculated as the difference between the expected objective value found by the optimal policy, and the expected objective value with perfect information. EVPI offers a practical way for decision makers to quantify the incentive and benefit of reducing uncertainty for the addressed problem. The results show that the performance of optimal policy will be negatively impacted by high variation of random parameters.

Discretionary Task Ordering: Queue Management in Radiological Services

A long line of research examines how best to schedule work to improve operational performance. This literature typically takes the perspective of a central planner who directs individuals to execute tasks in a prescribed order. In many settings, however, workers have discretion to deviate from the assigned order. This paper considers the operational implications of “discretionary task ordering,” defined as the task sequence resulting from an individual’s ability to select which task to complete next from a work queue. Using data from more than 2.4 million radiological studies read by 91 physicians over a period of two and a half years, we examine the conditions under which discretion is exercised to deviate from the assigned First-In-First-Out scheduling policy, and the performance effects of those choices. Exploiting random assignment of tasks (cases) to doctors’ queues, together with variation in queue characteristics, we find that, on average, deviations lead to slower completion times, providing evidence of the costs of exercising discretion. Doctors tend to deviate more and deviations tend to be less detrimental with experience, yet deviations remain harmful even for high levels of experience. Moreover, doctors tend to deviate to follow two common ordering strategies: shortest expected processing time and batching similar cases. Choosing the shortest tasks first is particularly detrimental for speed. Batching is associated with better performance when it occurs naturally, but not when it results from using discretion, suggesting that the benefit of repetition does not compensate for the cost of exercising discretion in this setting. Our research offers a behavioral perspective on queue management and highlights that discretion may have unintended negative costs.

Decision support for hospital bed management using adaptable individual length of stay estimations and shared resources

BackgroundElective patient admission and assignment planning is an important task of the strategic and operational management of a hospital and early on became a central topic of clinical operations research. The management of hospital beds is an important subtask. Various approaches have been proposed, involving the computation of efficient assignments with regard to the patients’ condition, the necessity of the treatment, and the patients’ preferences. However, these approaches are mostly based on static, unadaptable estimates of the length of stay and, thus, do not take into account the uncertainty of the patient’s recovery. Furthermore, the effect of aggregated bed capacities have not been investigated in this context. Computer supported bed management, combining an adaptable length of stay estimation with the treatment of shared resources (aggregated bed capacities) has not yet been sufficiently investigated. The aim of our work is: 1) to define a cost function for patient admission taking into account adaptable length of stay estimations and aggregated resources, 2) to define a mathematical program formally modeling the assignment problem and an architecture for decision support, 3) to investigate four algorithmic methodologies addressing the assignment problem and one base-line approach, and 4) to evaluate these methodologies w.r.t. cost outcome, performance, and dismissal ratio.MethodsThe expected free ward capacity is calculated based on individual length of stay estimates, introducing Bernoulli distributed random variables for the ward occupation states and approximating the probability densities. The assignment problem is represented as a binary integer program. Four strategies for solving the problem are applied and compared: an exact approach, using the mixed integer programming solver SCIP; and three heuristic strategies, namely the longest expected processing time, the shortest expected processing time, and random choice. A baseline approach serves to compare these optimization strategies with a simple model of the status quo. All the approaches are evaluated by a realistic discrete event simulation: the outcomes are the ratio of successful assignments and dismissals, the computation time, and the model’s cost factors.ResultsA discrete event simulation of 226,000 cases shows a reduction of the dismissal rate compared to the baseline by more than 30 percentage points (from a mean dismissal ratio of 74.7% to 40.06% comparing the status quo with the optimization strategies). Each of the optimization strategies leads to an improved assignment. The exact approach has only a marginal advantage over the heuristic strategies in the model’s cost factors (≤3%). Moreover,this marginal advantage was only achieved at the price of a computational time fifty times that of the heuristic models (an average computing time of 141 s using the exact method, vs. 2.6 s for the heuristic strategy).ConclusionsIn terms of its performance and the quality of its solution, the heuristic strategy RAND is the preferred method for bed assignment in the case of shared resources. Future research is needed to investigate whether an equally marked improvement can be achieved in a large scale clinical application study, ideally one comprising all the departments involved in admission and assignment planning.

Dynamic state-dependent dispatching for wafer fabrication

A dynamic state-dependent dispatching (DSDD) heuristic for a wafer fabrication plant is presented. The DSDD heuristic dynamically uses different dispatching rules according to the state of a production system. Rather than developing new rules, the DSDD heuristic combines and modifies existing rules. This heuristic first classifies workstations into dynamic bottlenecks and non-dynamic bottlenecks. Dynamic bottleneck workstations apply a revised two-boundary dispatching rule when their queue length exceeds the average obtained from simulation using constant lot-release policy and first-in, first-out dispatching rule. Otherwise, the shortest expected processing time until next visit dispatching rule is used. A revised FGCA (FGCA+) dispatching rule is used for all non-dynamic bottlenecks workstations. Simulation results demonstrate that the DSDD heuristic obtains the best performance among the compared six dispatching rules in terms of average and standard deviation of cycle time and work-in-process.

Extremal properties of the FIFO discipline in queueing networks

We show that using the FIFO service discipline at single server stations with ILR (increasing likelihood ratio) service time distributions in networks of monotone queues results in stochastically earlier departures throughout the network. The converse is true at stations with DLR (decreasing likelihood ratio) service time distributions. We use these results to establish the validity of the following comparisons:(i) The throughput of a closed network of FIFO single-server queues will be larger (smaller) when the service times are ILR (DLR) rather than exponential with the same means.(ii) The total stationary number of customers in an open network of FIFO single-server queues with Poisson external arrivals will be stochastically smaller (larger) when the service times are ILR (DLR) rather than exponential with the same means.We also give a surprising counterexample to show that although FIFO stochastically maximizes the number of departures by any time t from an isolated single-server queue with IHR (increasing hazard rate, which is weaker than ILR) service times, this is no longer true for networks of more than one queue. Thus the ILR assumption cannot be relaxed to IHR.Finally, we consider multiclass networks of exponential single-server queues, where the class of a customer at a particular station determines its service rate at that station, and show that serving the customer with the highest service rate (which is SEPT — shortest expected processing time first) results in stochastically earlier departures throughout the network, among all preemptive work-conserving policies. We also show that a cµ rule stochastically maximizes the number of non-defective service completions by any time t when there are random, agreeable, yields.

Extremal properties of the FIFO discipline in queueing networks

We show that using the FIFO service discipline at single server stations with ILR (increasing likelihood ratio) service time distributions in networks of monotone queues results in stochastically earlier departures throughout the network. The converse is true at stations with DLR (decreasing likelihood ratio) service time distributions. We use these results to establish the validity of the following comparisons: (i) The throughput of a closed network of FIFO single-server queues will be larger (smaller) when the service times are ILR (DLR) rather than exponential with the same means. (ii) The total stationary number of customers in an open network of FIFO single-server queues with Poisson external arrivals will be stochastically smaller (larger) when the service times are ILR (DLR) rather than exponential with the same means. We also give a surprising counterexample to show that although FIFO stochastically maximizes the number of departures by any time t from an isolated single-server queue with IHR (increasing hazard rate, which is weaker than ILR) service times, this is no longer true for networks of more than one queue. Thus the ILR assumption cannot be relaxed to IHR. Finally, we consider multiclass networks of exponential single-server queues, where the class of a customer at a particular station determines its service rate at that station, and show that serving the customer with the highest service rate (which is SEPT — shortest expected processing time first) results in stochastically earlier departures throughout the network, among all preemptive work-conserving policies. We also show that a cµ rule stochastically maximizes the number of non-defective service completions by any time t when there are random, agreeable, yields.

Scheduling stochastic jobs with increasing hazard rate on identical parallel machines

We consider a discrete time model of m identical machines operating in parallel to complete a collection of jobs. The processing times of the jobs are independent, identically distributed discrete random variables having increasing hazard rate. The jobs may have received different amounts of prior processing. A reward β t , 0 < β < 1, is acquired when a job is finished at time t. We show that a non-preemptive SEPT (Shortest Expected Processing Time) strategy maximizes the expected total reward among all possible policies. We show that SEPT strategy is still optimal for several generalizations of this problem scenario.

The Impact of Processing Time Knowledge on Dynamic Job-Shop Scheduling

The goal of this paper is to determine if the results for dynamic job-shop scheduling problems are affected by the assumptions made with regard to the processing time distributions and the scheduler's knowledge of the processing times. Three dynamic job-shop scheduling problems (including a two-station version of Conway et al.'s 1967 nine-station symmetric shop) are tested under seven different scenarios, one deterministic and six stochastic, using computer simulation. The deterministic scenario, where the processing times are exponential and observed by the scheduler, has been considered in many simulation studies, including Conway et al.'s. The six stochastic scenarios include the case where the processing times are exponential and only the mean is known by the scheduler, and five different cases where the machines are subject to unpredictable failures. Two policies were tested, the shortest expected processing time (SEPT) rule, and a rule derived from a Brownian analysis of the corresponding queueing network scheduling problem. Although the SEPT rule performed well in the deterministic scenario, it was easily outperformed by the Brownian policies in the six stochastic scenarios for all three problems. Thus, the results from simulation studies of dynamic, deterministic job-shop scheduling problems may not carry over to the more realistic setting where there is unpredictable variability.

Optimal Scheduling of Jobs with Exponential Service Times on Identical Parallel Processors

The scheduling of jobs with stochastically independent, exponentially distributed service times on identical parallel processors is considered. General sufficient conditions for optimality in expectation of priority policies for certain cost functions are given, including cases of the weighted flow time. The priority policies under consideration may be more general than the longest expected processing time (LEPT) or the shortest expected processing time (SEPT) policy. We deal with a fixed number of processors as well as certain more general resource constraints. Finally, precedence relations between jobs given by strict interval orders are admitted and an optimality result for LEPT is stated for this situation.

Scheduling jobs with stochastically ordered processing times on parallel machines to minimize expected flowtime

A number of jobs are to be processed using a number of identical machines which operate in parallel. The processing times of the jobs are stochastic, but have known distributions which are stochastically ordered. A reward r(t) is acquired when a job is completed at time t. The function r(t) is assumed to be convex and decreasing in t. It is shown that within the class of non-preemptive scheduling strategies the strategy SEPT maximizes the expected total reward. This strategy is one which whenever a machine becomes available starts processing the remaining job with the shortest expected processing time. In particular, for r(t) = – t, this strategy minimizes the expected flowtime.

Scheduling jobs with stochastically ordered processing times on parallel machines to minimize expected flowtime

A number of jobs are to be processed using a number of identical machines which operate in parallel. The processing times of the jobs are stochastic, but have known distributions which are stochastically ordered. A reward r(t) is acquired when a job is completed at time t. The function r(t) is assumed to be convex and decreasing in t. It is shown that within the class of non-preemptive scheduling strategies the strategy SEPT maximizes the expected total reward. This strategy is one which whenever a machine becomes available starts processing the remaining job with the shortest expected processing time. In particular, for r(t) = – t, this strategy minimizes the expected flowtime.

Scheduling of stochastic tasks on two parallel processors

AbstractWe consider the problem of scheduling n tasks on two identical parallel processors. We show both in the case when the processing times for the n tasks are independent exponential random variables, and when they are independent hyperexponentials which are mixtures of two fixed exponentials, that the policy of performing tasks with longest expected processing time (LEPT) first minimizes the expected makespan, and that in the hyperexponential case the policy of performing tasks with shortest expected processing time (SEPT) first minimizes the expected flow time. The approach is simpler than the dynamic programming approach recently employed by Bruno and Downey.