Derek Atkins

Joint optimization of maintenance and inventory policies for a simple system

We examine age replacement and ordering decisions for a system with only one component subject to random failure and with room for only one spare in stock. The system incurs costs for replacement, shortage, holding, and breakage; the lead time for receipt of an ordered spare is constant. We consider the solvability and desirability of jointly optimizing these two traditionally separate decisions. We show that the problem has some convexity properties that make it amenable to minimization. For our data set, we find that using separate optimization gives an average loss of 3% relative to the joint minimum; about a tenth of die time the difference was more than 10%, but in general this loss can vary from zero to arbitrarily large.

A Simulation Optimization Approach to Long-Term Care Capacity Planning

This paper describes a methodology for setting long-term care capacity levels over a multiyear planning horizon to achieve target wait time service levels. Our approach integrates demographic and survival analysis, discrete event simulation, and optimization. Based on this methodology, we developed a decision support system for use in practice. We illustrate this approach through two case studies: one for a regional health authority in British Columbia, Canada, and the other for a long-term care facility. We also compare our approach to the fixed ratio approach used in practice and the SIPP (stationary, independent, period by period) and MOL (modified offered load) approaches developed in the call center literature. Our results suggest that our approach is preferable. The fixed ratio approach lacks a rigorous foundation, and the SIPP and MOL approaches do not perform reliably mainly because of long service times. We conclude the paper with policy recommendations.

Modeling the Patient Journey from Injury to Community Reintegration for Persons with Acute Traumatic Spinal Cord Injury in a Canadian Centre

Background A patient’s journey through the health care system is influenced by clinical and system processes across the continuum of care. Methods To inform optimized access to care and patient flow for individuals with traumatic spinal cord injury (tSCI), we developed a simulation model that can examine the full impact of therapeutic or systems interventions across the care continuum for patients with traumatic spinal cord injuries. The objective of this paper is to describe the detailed development of this simulation model for a major trauma and a rehabilitation centre in British Columbia (BC), Canada, as part of the Access to Care and Timing (ACT) project and is referred to as the BC ACT Model V1.0. Findings To demonstrate the utility of the simulation model in clinical and administrative decision-making we present three typical scenarios that illustrate how an investigator can track the indirect impact(s) of medical and administrative interventions, both upstream and downstream along the continuum of care. For example, the model was used to estimate the theoretical impact of a practice that reduced the incidence of pressure ulcers by 70%. This led to a decrease in acute and rehabilitation length of stay of 4 and 2 days, respectively and a decrease in bed utilization of 9% and 3% in acute and rehabilitation. Conclusion The scenario analysis using the BC ACT Model V1.0 demonstrates the flexibility and value of the simulation model as a decision-making tool by providing estimates of the effects of different interventions and allowing them to be objectively compared. Future work will involve developing a generalizable national Canadian ACT Model to examine differences in care delivery and identify the ideal attributes of SCI care delivery.

Performance evaluation of scheduling control of queueing networks : Fluid model heuristics

Motivated by dynamic scheduling control for queueing networks, Chen and Yao [8] developed a systematic method to generate dynamic scheduling control policies for a fluid network, a simple and highly aggregated model that approximates the queueing network. This study addresses the question of how good these fluid policies are as heuristic scheduling policies for queueing networks. Using simulation on some examples these heuristic policies are compared with traditional simple scheduling rules. The results show that the heuristic policies perform at least comparably to classical priority rules, regardless of the assumptions made about the traffic intensities and the arrival and service time distributions. However, they are certainly not always the best and, even when they are, the improvement is seldom dramatic. The comparative advantage of these policies may lie in their application to nonstationary situations such as might occur with unreliable machines or nonstationary demand patterns.

Secondary Complications in SCI Across the Continuum: Using Operations Research to Predict the Impact and Optimize Management Strategies

Secondary complications following traumatic spinal cord injury (tSCI) have a tremendous impact on quality of life and health care costs. Although some complications result from the injury itself, many originate from the care provided; complications arising early in the tSCI journey can predispose an individual to recurrence later. To measure the total impact of secondary complications on patient outcomes and health care costs, all the stages of care, from first response to life in the community, must be spanned. Interventions to ameliorate secondary complications need to consider the effects on the whole system and not just individual phases of care; however, such an approach is not common in the literature. To measure the impact of complications as well as the effect of proposed interventions, a partnership between clinical researchers and operations research professionals was formed to develop a discrete-event simulation model of the entire continuum of tSCI care. In this article, we focus on the part of the model concerning common secondary complications (eg, pressure ulcers, pneumonia). We first describe early results from the model, discuss how the effects from the complications impact care throughout the tSCI continuum, and review assumptions of the model. The article concludes with a discussion as to the possible uses of the model, their strengths/limitations, and future directions.

A note on competitive supply chains with generalised supply costs

This note generalises models from two influential papers in the theory of supply chain outsourcing under competition: (McGuire and Staelin, 1983) and (Cachon and Harker, 2002). The first paper studies the impact of competitive intensity on the outsourcing decision from the suppliers point of view for linear supply cost; the second paper examines the impact of supply economies of scale from the retailers point of view when selling perfectly substitutable products. By considering competitive intensity and supply economies of scale simultaneously, we find that equilibrium channel structures are primarily determined by the competitive intensity, which is true even under supply diseconomies of scale; the key message in the second paper of scale economies driving retailers outsourcing supply decision is highly dependent on the assumption of perfect substitutes. Our finding has no qualitative difference when either the suppliers or the retailers are modeled as the channel leader and make the outsourcing decisions.

Patient choice analysis and demand prediction for a health care diagnostics company

This paper describes a case study for a medical diagnostic laboratory service provider to model the behavior of patients when choosing a patient service centre for their medical tests and to estimate future demand volume. A tool developed based on our methodology allows the management of the diagnostic services to experiment with locations and capacities for locating or relocating service centres. In addition to the focal firm, the methodology considers the impact of decisions on another service provider and hospital laboratories located in the same area. The methodology identifies the most significant service centre attractiveness factors. Our models are validated from different perspectives and show good predictive capability. This case study is used to draw a number of lessons for applying these types of models to other similar services in order to assist other applications.

Revenue management under joint pricing and capacity allocation competition

We investigate joint pricing and capacity allocation decisions of a duopoly, each of which competes in selling a fixed amount of substitutable perishable goods in both early discount and regular full-fare markets with demand uncertainty. Upon a firm’s stockout, unsatisfied demand spillovers to the competitor, depending on the substitutability of products offered by the two firms. We first show that there exists a pure-strategy Nash equilibrium. For identical firms, there exists a unique pure-strategy Nash equilibrium that is symmetric. Then we study how firms’ pricing and capacity allocation decisions depend on operational and market conditions. In particular, we show that more cut-throat competition in the full-fare market never leads to a rise in the price and a fall in the protection level simultaneously in the full-fare market. We demonstrate a similar result of comparative statics for the competition intensity in the discount market. In comparison with a monopolist’s optimal decision, a duopoly equilibrium never results in a situation that definitely benefits the full-fare consumers in both dimensions of price and availability. Finally, we examine how the adoption of early discount, as practiced in the airline industry, may benefit competing firms. When one of the two firms first introduces early discount sales, we find that there is a “free-ride” effect for the other firm. Interestingly, the “free-rider” can benefit more than the adopter, especially with stronger competition.

Medical facility network design: User-choice and system-optimal models

Abstract Motivated by a real-life project, this paper presents several models for designing a network of “walk-in” medical facilities that provide a homogeneous service in competitive and centralized environments. The problem in a competitive environment is to optimize the location and capacity of each open facility for a focal firm so as to maximize its total demand volume, subject to a total capacity limit. We assume that travel time to a facility and expected waiting time at a facility are the two main determinants for clients to choose where to receive the service. We consider two alternative “user-choice” models, one “probabilistic-choice” and the other “deterministic-choice”. In a centralized environment, a central decision maker determines the optimal location and capacity of each open facility, to maximize overall social welfare. We consider a “system-optimal” model and two user-choice models. All the models follow a bilevel structure, i.e., the location-allocation framework. The user-choice models are formulated as mathematical programs with equilibrium constraints. To solve the problems efficiently, we propose a common solution methodology in line with the location-allocation framework. Through a real-life case study, we discuss several interesting managerial insights about model selection and facility network design strategies.