Dynamic overbooking scheduling system to improve patient access

Patient no-show has long been a recognized problem in modern outpatient health-care delivery systems. The common impacts are reduced clinic efficiency and provider productivity, wasted medical resources, increased health-care cost and limited patient access to care. The main goal of this research is to develop an effective dynamic overbooking policy into any scheduling system that accounts for the predictive probability of no-shows for any given patient. This policy increases the quality of patient care in terms of wait time and access to care while minimizing the clinic's costs. This proposed model is also illustrated to be more cost-effective than overbooking patients evenly throughout a clinic session. This paper also suggests that overbooking should be performed at better patient flow and higher no-show rate so that the costs are minimized. Consequently, this research improves the outpatient experience for both patients and medical providers.     

Coordinating a supply chain with green innovation in a dynamic setting

This paper addresses the channel coordination problem in a green supply chain consisting of a manufacturer and a retailer, in which the manufacturer controls green innovation and wholes price, while the retailer controls sales price. Pricing and green innovation strategies in integrated and decentralized channels are computed and compared, and a two-part tariff contract is designed to coordinate the decentralized supply chain. A Nash bargaining model is further developed to distribute the extra-profit between channel members. A numerical example is conducted to explore the impacts of green effectiveness and operational inefficiency effect on optimal/equilibrium solutions and coordination. The main results show that the green innovation investment, energy efficiency level and channel profit of integrated channel are larger than those of decentralized one, but the relationship of sales prices under two channel structures depends on system parameters. Green effectiveness exerts a positive effect on optimal/equilibrium solutions. The coordinator’s coordination capability is improved by green effectiveness, but weakened by operational inefficiency effect.     

The complexity of partial match retrieval in a dynamic setting

The partial match retrieval problem analyzed in this paper is described as follows. Given a positive integer d, a record having d binary attributes consists of a d dimensional binary vector, referred to as the record's key, and a quantity which lies in a commutative semigroup, referred to as the value of the record. Given a set of such records having distinct keys, a partial match query is a request for the sum of the values of all records in the set whose keys lie in a hyperrectangle specified by the query. We consider the problem of designing data structures which permit insertions and deletions of records, and partial match queries. Among our results is the following. There exist data structures which accommodate arbitrary sequences of N manipulations (insertions, deletions, and queries) in (worst case) time approximately (1.226)^dN. Moreover, relative to an appropriate model of computation, this complexity is best possible.     

A stochastic appointment scheduling system on multiple resources with dynamic call-in sequence and patient no-shows for an outpatient clinic

This research focuses on the stochastic assignment system motivated by outpatient clinics, especially the physical therapy in rehabilitation service. The aim of this research is to develop a stochastic overbooking model to enhance the service quality as well as to increase the utilization of multiple resources, like therapy equipment in a physical therapy room, with the consideration of patients’ call-in sequence. The schedule for a single-service period includes a fixed number of blocks of equal length. When patients call, they are assigned to an appointment time for that block, and an existing appointment is not allowed to be changed. In each visit, a patient might require more than one resource and a probability of no-show. Two estimation methods were proposed for the expected waiting and overtime cost with multiple resources: Convolution Estimation Method and Joint Cumulative Estimation Method for the upper and lower bound value; respectively. A numerical example based on a physical therapy room was used to show that this stochastic model was able to schedule patients for better profitability compared with traditional appointment systems based on four prioritization rules. The workload in each appointment slot was more balanced albeit more patients were assigned to the first slot to fill up the empty room.     

Optimizing strategic behaviour in a dynamic setting in professional team sports

This article develops a dynamic game-theoretic model of optimizing strategic behaviour by football (soccer) teams. Teams choose between defensive and attacking formations and between a non-violent and a violent playing style, and can vary these choices continuously throughout each match. Starting from the end of the match and working backwards, the teams’ optimal strategies conditional on the current state of the match are determined by solving a series of two-player non-cooperative subgames. Numerical simulations are used to explore the sensitivity of strategic behaviour to variations in the structural parameters. The analysis demonstrates that the strategic behaviour of football teams can be rationalized in accordance with game-theoretic principles of optimizing strategic behaviour by agents when payoffs are uncertain and interdependent.     

A dynamic analysis of protection and environmental policy in a small trading developing country

We analyze a dynamic model of protection and environmental policy in a small trading developing country (DC). The DC government protects the import competing (and the polluting) sector of the economy with a tariff. The employment and output effects of three different pollution taxes are analyzed. These taxes incorporate different assumptions about the DC government's ability to commit to its announced policy. First, we describe the taxes, we study the dependence of these taxes on the tariff, and we show that in general an activist environmental policy is called for, irrespective of the length of time to which the government can commit to its announced policy. Second, we identify a situation in which the conduct of environmental policy raises welfare unambiguously, and the situations in which it does not do so. Finally, we show that the time inconsistency of certain optimal programs can prevent the DC government from achieving its environmental and employment objectives.     

A story-based dynamic geometry approach to improve attitudes toward geometry and geometric proof

This work is a part of a larger study, which presents geometry through a daily life story using dynamic geometry software. It aimed in particular to enable students to feel the importance of geometry in daily life, to share in the process of formulating geometric statements and conjectures, to experience the geometric proof more than validating the correctness of geometric statements and to start with a real-life situation and go through seven steps to geometric proof. The content of the suggested approach was organized so that every activity was a prerequisite for entering the next one, either in the structure of geometric concepts or in the geometric story context. Some indications will be presented according to three Likert-type questionnaires, which were prepared by the researcher with the purpose of assessing students?? attitudes toward geometry and geometric proof, using computers in mathematics learning and the suggested approach. The analysis of single responses to questionnaire items showed significant changes in students?? beliefs about geometry, importance and functions of geometric proof and toward using the suggested approach.     

A performance analysis of channel fragmentation in dynamic spectrum access systems

Dynamic Spectrum Access systems offer temporarily available spectrum to opportunistic users capable of spreading transmissions over a number of non-contiguous subchannels. Such methods can be highly beneficial in terms of spectrum utilization, but excessive fragmentation degrades performance and hence off-sets the benefits. To get some insight into acceptable levels of fragmentation, we present experimental and analytical results derived from a mathematical model. According to the model, a system operates at capacity serving requests for bandwidth by assigning a collection of one or more gaps of unused bandwidth to each request as bandwidth becomes available. Our main result is a proof that, even if fragments can be arbitrarily small, the system remains stable in the sense that the average total number of fragments remains bounded. Within the class of dynamic fragmentation models, including models of dynamic storage allocation that have been around for many decades, this result appears to be the first of its kind. In addition, we provide extensive experimental results that describe behavior, at times unexpected, of fragmentation as parameter values are varied. Different scanning rules for searching gaps of available spectrum, all covered by the above stability result, are also studied. Our model applies to dynamic linked-list storage allocation, and provides a novel analysis in that domain. We prove that, interestingly, a version of the 50?% rule of the classical, non-fragmented allocation model holds for the new model as well. Overall, the paper provides insights into the behavior of practical fragmentation algorithms.     

Simulation-based framework to improve patient experience in an emergency department

The global economic crisis has a significant impact on healthcare resource provision worldwide. The management of limited healthcare resources is further challenged by the high level of uncertainty in demand, which can lead to unbalanced utilization of the available resources and a potential deterioration of patient satisfaction in terms of longer waiting times and perceived reduced quality of services. Therefore, healthcare managers require timely and accurate tools to optimize resource utility in a complex and ever-changing patient care process. An interactive simulation-based decision support framework is presented in this paper for healthcare process improvement. Complexity and different levels of variability within the process are incorporated into the process modeling phase, followed by developing a simulation model to examine the impact of potential alternatives. As a performance management tool, balanced scorecard (BSC) is incorporated within the framework to support continual and sustainable improvement by using strategic-linked performance measures and actions. These actions are evaluated by the simulation model developed, whilst the trade-off between objectives, though somewhat conflicting, is analysed by a preference model. The preference model is designed in an interactive and iterative process considering decision makers preferences regarding the selected key performance indicators (KPIs). A detailed implementation of the framework is demonstrated on an emergency department (ED) of an adult teaching hospital in north Dublin, Ireland. The results show that the unblocking of ED outflows by in-patient bed management is more effective than increasing only the ED physical capacity or the ED workforce.     

Determination of optimal penalties for antitrust violations in a dynamic setting

We analyze a differential game describing the interactions between a firm that might be violating competition law and the antitrust authority. The objective of the authority is to minimize social costs (loss in consumer surplus) induced by an increase in prices above marginal costs. It turns out that the penalty schemes which are used now in EU and US legislation appear not to be as efficient as desired from the point of view of minimization of consumer loss from price-fixing activities of the firm. In particular, we prove that full compliance behavior is not sustainable as a Nash Equilibrium in Markovian strategies over the whole planning period, and, moreover, that it will never arise as the long-run steady-state equilibrium of the model. We also investigate the question which penalty system enables us to completely deter cartel formation in a dynamic setting. We found that this socially desirable outcome can be achieved in case the penalty is an increasing function of the degree of offence and is negatively related to the probability of law enforcement.     

A green policy to schedule tasks in a distributed cloud

In the last years, demand and availability of computational capabilities experienced radical changes. Desktops and laptops increased their processing resources, exceeding users’ demand for large part of the day. On the other hand, computational methods are more and more frequently adopted by scientific communities, which often experience difficulties in obtaining access to the required resources. Consequently, data centers for outsourcing use, relying on the cloud computing paradigm, are proliferating. Notwithstanding the effort to build energy-efficient data centers, their energy footprint is still considerable, since cooling a large number of machines situated in the same room or container requires a significant amount of power. The volunteer cloud, exploiting the users’ willingness to share a quote of their underused machine resources, can constitute an effective solution to have the required computational resources when needed. In this paper, we foster the adoption of the volunteer cloud computing as a green (i.e., energy efficient) solution even able to outperform existing data centers in specific tasks. To manage the complexity of such a large scale heterogeneous system, we propose a distributed optimization policy to task scheduling with the aim of reducing the overall energy consumption executing a given workload. To this end, we consider an integer programming problem relying on the Alternating Direction Method of Multipliers (ADMM) for its solution. Our approach is compared with a centralized one and other non-green targeting solutions. Results show that the distributed solution found by the ADMM constitutes a good suboptimal solution, worth to be applied in a real environment.     

Pricing policy in dynamic markets and a generalization of the Ramsey rule

Pricing policy in a regulated monopoly industry is usually based on maximizing welfare or some other measure of utility level of return on investment. Previously, the Ramsey pricing policy which states that the percentage deviation of quasi-optimal price from marginal cost for each product must be inversely proportional to its price elasticity of demand, has been developed for a static market. The Ramsey framework assumes instantaneous demand response to price changes; empirical evidence suggests demand changes occur dynamically through time.In this paper an optimum pricing rule for a profit maximizing firm based on a general time varying demand model in a dynamic market is obtained assuming a single price change at the beginning of the planning period. A dynamic market equivalent of the well known inverse elasticity law of the static market is developed. Defining the concept of average price elasticity for dynamic markets we show that the inverse elasticity law of static markets takes an inequality form in dynamic markets. For demand functions which decrease, increase or are constant with time the optimum price markups are greater than, less than, or equal to the inverse of the average price elasticity, respectively.The results are then generalized to the case of a constrained welfare maximizing firm. This leads to the development of a dynamic market generalization of the well known Ramsey pricing rule. A simple rule for making quantitative arguments about the relative size of the optimum price in static and dynamic markets is also derived.This work was completed when the author was with Bell Laboratories, USA.     

A band method approach to a positive expansion problem in a unitary dilation setting

In this paper a positive commuting expansion problem is presented and solved. The problem is set up in the framework of a minimal unitary dilation of a contraction acting on a Hilbert space and includes the Carathéodory and other classical interpolation problems. By combining the geometry of the minimal unitary dilation with state space techniques from system theory, a special solution is constructed. Next using the band method approach and spectral factorizations of this special solution a linear fractional parameterization of all solutions is obtained. Explicit state space formulas and applications to some classical interpolation problems are given.     

A planning and routing model for patient transportation in health care

In this paper, a problem concerning both the planning of health care services and the routing of vehicles, for patients transportation is addressed. An integrated approach, based on the column generation technique, is proposed to solve the planning and routing problem. Preliminary results on real data show the effectiveness of the proposed approach.     

A new contribution to a dynamic competitive equilibrium problem

The aim of this paper is to study the Walrasian equilibrium problem when the data are time dependent. For this model an existence result is provided using the variational inequality theory in infinite dimensional spaces. Our results are the generalization of some of the results obtained by several authors in the static case (see e.g. Donato et al. (2008) [5], Donato et al. (2008) [4] and Mordukhovich (2006) [11], Nagurney (1993) [2] and the references therein).     

When to refinance a mortgage: A dynamic programming approach

When should one refinance a mortgage loan? It is one of the most common finance questions in today's world. There have been surprisingly few attempts to answer this question in a structured manner, however. Moreover, the existing guidelines for refinancing consist of a short list of very simple rules that have a limited application. This article addresses the question through a dynamic programming model coupled with an analysis of historical interest rates. The analysis reveals a more complex set of rules for an optional refinance decision––oftentimes conflicting with the conventionally accepted idea that rate differences must be greater than two percent.     

A simple approach to dynamic stabilization of a rotating body-beam

In this paper, we use the frequency multiplier method to provide a simple proof of an exponential stabilization result, obtained in [B. Chentouf. Dynamic boundary controls of a rotating body-beam system with time-varying angular velocity, J. Appl. Math. 2 (2004) 107–126], for a rotating body-beam system with a control torque applied on the rigid body and either a dynamic boundary control moment or a dynamic boundary control force or both of them applied at the free end of the beam.     

Matching patient and physician preferences in designing a primary care facility network

This paper introduces an integer programming model for planning primary care facility networks, which accounts for the interests of different stakeholders while maximizing access to health care. Physician allocation to health-care facilities is explicitly modelled, which allows consideration of physician incentives in the planning phase. An illustrative case study in the Turkish primary care system is presented to show the implications of focusing on patient or physician preferences in the planning phase. A discussion of trade-offs between the different stakeholder preferences and some recommendations for modelling choices to match these preferences are provided. In the context of this case, we found that using an access measure that decays with distance, and incorporating nearest allocation constraints improves performance for all stakeholders. We also show that increasing the number of physicians may have adverse affects on access measures when physician preferences are addressed.