Armann Ingolfsson

Run by run process control: combining SPC and feedback control

The run by run controller provides a framework for controlling a process which is subject to disturbances such as shifts and drifts as a normal part of its operation. The run by run controller combines the advantages of both statistical process control (SPC) and feedback control. It has three components: rapid mode, gradual mode, and generalized SPC. Rapid mode adapts to sudden shifts in the process such as those caused by maintenance operations. Gradual mode adapts to gradual drifts in the process such as those caused by build-up of deposition inside a reactor. The choice between the two modes is determined by the outcome from generalized SPC which allows SPC to be applied to a process while it is being tuned. The run by run controller has been applied to the control of a silicon epitaxy process in a barrel reactor. Rapid mode recovered the process within 3 runs after a disturbance. Gradual mode reduced the variation of the process by a factor of 2.7 as compared to historical data. >

Stability and Sensitivity of an EWMA Controller

The performance of a process control algorithm based on EWMA statistic is analyzed. A simple condition relating the EWMA weight and the estimated process gain is shown to ensure that the control strategy is stable for a first-order multiple-input, singl..

Catastrophe Avoidance Models for Hazardous Materials Route Planning

The most-widely used definition of risk in the hazardous materials transportation literature is the expected consequence of an incident (accident resulting in a release), which, for each edge of the network, is equal to the product of the incident probability and a quantifiable consequence (such as number of people evacuated). This definition ignores the risk-averse attitudes of many decision-makers when dealing with low probability/high consequence events. We suggest that avoiding a catastrophe (an incident with a very large consequence) may be a relevant issue in routing hazardous materials, and we introduce three different catastrophe-avoidance models. In the first model, catastrophe avoidance is achieved by minimizing the maximum population exposure. In the second model, the variance of the route consequence is incorporated into the decision. In the third model, an explicit disutility function is used. We show that all three models reduce to a standard shortest path problem. Each model avoids high-population areas of the transport network. We give numerical examples and discuss the similarities and the differences among the three models. The first of the three models suggested may be the most intuitive, and is the most tractable computationally. Implementation of the other two models may be difficult due to scaling issues. Nevertheless, these models offer theoretical insight that may be valuable to researchers.

Transport risk models for hazardous materials: revisited

Several proposed path evaluation functions for hazardous materials transport use an approximation. Modified functions that avoid the approximation violate two reasonable axioms. We present new models by redefining the decision problem as one of satisfying demand at the destination. The new models satisfy the axioms and are relatively tractable.

Combining Integer Programming and the Randomization Method to Schedule Employees

We describe a method to find low cost shift schedules with a time-varying service level that is always above a specified minimum. Most previous approaches used a two-step procedure: (1) determine staffing requirements and (2) find a minimum cost schedule that provides the required staffing in every period. Approximations in the first step sometimes cause the two-step approach to find infeasible or suboptimal solutions. Our method iterates between a schedule evaluator and a schedule generator. The schedule evaluator calculates transient service levels using the randomization method and identifies infeasible intervals, where the service level is lower than desired. The schedule generator solves a series of integer programs to produce improved schedules, by adding constraints for every infeasible interval, in an attempt to eliminate infeasibility without eliminating the optimal solution. We present computational results for several test problems and discuss factors that make our approach more likely to outperform previous approaches.

Empirical Analysis of Ambulance Travel Times: The Case of Calgary Emergency Medical Services

Using administrative data for high-priority calls in Calgary, Alberta, we estimate how ambulance travel times depend on distance. We find that a logarithmic transformation produces symmetric travel-time distributions with heavier tails than those of a normal distribution. Guided by nonparametric estimates of the median and coefficient of variation, we demonstrate that a previously proposed model for mean fire engine travel times is a valid and useful description of median ambulance travel times. We propose a new specification for the coefficient of variation, which decreases with distance. We illustrate how the resulting travel-time distribution model can be used to create probability-of-coverage maps for diagnosis and improvement of system performance.

A Survey and Experimental Comparison of Service-Level-Approximation Methods for Nonstationary M(t)/M/s(t) Queueing Systems with Exhaustive Discipline

We compare the performance of seven methods in computing or approximating service levels for nonstationary M(t)/M/s(t) queueing systems: an exact method (a Runge-Kutta ordinary-differential-equation solver), the randomization method, a closure (or surrogate-distribution) approximation, a direct infinite-server approximation, a modified-offered-load infinite-server approximation, an effective-arrival-rate approximation, and a lagged stationary approximation. We assume an exhaustive service discipline, where service in progress when a server is scheduled to leave is completed before the server leaves. We used all of the methods to solve the same set of 640 test problems. The randomization method was almost as accurate as the exact method and used about half the computational time. The closure approximation was less accurate, and usually slower, than the randomization method. The two infinite-server-based approximations, the effective-arrival-rate approximation, and the lagged stationary approximation were less accurate but had computation times that were far shorter and less problem-dependent than the other three methods.

Markov chain models of a telephone call center with call blending

Motivated by a Bell Canada call center operating in blend mode, we consider a system with two types of traffic and two types of agents. Outbound calls are served only by blend agents, whereas inbound calls can be served by either inbound-only or blend agents. Inbound callers may balk or abandon. There are several performance measures of interest, including the rate of outbound calls and the proportion of inbound calls waiting more than some fixed number of seconds. We present a collection of continuous-time Markov chain (CTMC) models which capture many real-world characteristics while maintaining parsimony that results in fast computation. We discuss and explore the tradeoffs between model fidelity and efficacy and compare our different CTMC models with a realistic simulation model of a Bell Canada call center, used as a benchmark.

Simulation of single start station for Edmonton EMS

The City of Edmontons Emergency Medical Services (EMS) department proposed to move to a ‘single start station system’ (SS system) in which all ambulances would begin and end their shifts at the same location. We developed a discrete event simulation model to estimate the impact of this change and subsequently used this model to explore other changes to Edmonton EMS operations, including the addition of stations, the addition of ambulances, different shifts, and a different redeployment system. We found that a SS system increased average unit availability and the fraction of calls reached within the departments response time standard, particularly during the current shift changeover periods. The paper describes the development and validation of the simulation model and summarizes the results of its application.

Technical Note---Approximating Vehicle Dispatch Probabilities for Emergency Service Systems with Location-Specific Service Times and Multiple Units per Location

To calculate many of the important performance measures for an emergency response system, one requires knowledge of the probability that a particular server will respond to an incoming call at a particular location. Estimating these “dispatch probabilities” is complicated by four important characteristics of emergency service systems. We discuss these characteristics and extend previous approximation methods for calculating dispatch probabilities to account for the possibilities of workload variation by station, multiple vehicles per station, call-and station-dependent service times, and server cooperation and dependence.