Mathematical Decision Model Research Articles

BUILDING AND DEVELOPING A PROJECT TEAM ON THE BASIS OF A MULTICRITERIA MODEL

The subject matter of the article is mathematical models for solving particular problems of selecting candidates for building a project team. The goal is to develop formalized models and methods for assessing the level of the generalized social and professional competence of each employee engaged at a specific type of work of an investment project while building and developing a project team. The objectives are: to formalize decision-making methods; to select the best option on the basis of multicriteria assessment and optimization methods; to analyze the peculiarities of multicriteria assessment tasks in the problems of human resource management; to apply mathematical models of decision making when selecting the most suitable candidates for the project on the basis of the general utility theory. The methods used are: multicriteria assessment and optimization methods, utility function. The following results are obtained. The general task of managing human resources and building a team for a new project was analyzed. The main criterion for involving candidates in the project team appeared to be the qualifications and experience of performing similar work accepted by the organization, but the impact of individual factors of a candidate should be also taken into account. Some methods for solving the task of multicriteria selection with the use of non-formalized experience applied to the tasks of managing the project labour resources are suggested. The suggested method of building a project team is based on the models of multicriteria optimization which, unlike available methods, enable taking into account not only professional competences of employees but also personal and psychological characteristics of candidates in various combinations, which contributes to qualitative performing project tasks depending on specifics requirements of the project. Conclusions. The task of selecting the most suitable candidates for the project on the basis of the general utility theory is considered. The competence approach to managing human resources is justified. The suggested model enables formalizing the preferences of decision-makers and obtaining objective numerical assessments of the competence of candidates. Thus, the task of building a project team is multicriteria and can be solved on the basis of multicriteria assessment and optimization methods. The questions of practical application of the proposed mathematical models and methods are considered. It is suggested to select candidates for a project team on the basis of their experience in solving similar tasks in previous projects.

Extending a pessimistic–optimistic fuzzy information axiom based approach considering acceptable risk: Application in the selection of maintenance strategy

Maintenance is considered as an important factor in the improvement of machine performance. Indeed, maintenance plays an important role in maintaining reliability, availability, quality of products, reducing risk, improving efficiency, and safety. In maintenance problems, the desired real data cannot easily be found, thus decision making by applying expert knowledge is the only way. However, due to the existence of uncertainties in these assessments, the accuracy of evaluations may be questioned. The aim of this study was to present an appropriate mathematical model for decision making in the assessment and selection of proper maintenance strategy in risky situations. For this purpose, a model based on fuzzy axiomatic design (FAD) is presented, wherein each evaluation has both optimistic and pessimistic fuzzy scores, as the fuzzy evaluations themselves have risks. In order to improve the accuracy of the presented method, a new concept called “acceptable risk” has been suggested. A real case study, to measure the effectiveness of the proposed model, is conducted in a rolling mill company and the obtained results are compared with other FAD concepts.

An iterative mathematical decision model for cloud migration: A cost and security risk approach

SummaryThis paper presents an iterative mathematical decision model for organizations to evaluate whether to invest in establishing information technology (IT) infrastructure on‐premises or outsourcing IT services on a multicloud environment. This is because a single cloud cannot cover all types of users’ functional/nonfunctional requirements, in addition to several drawbacks such as resource limitation, vendor lock‐in, and prone to failure. On the other hand, multicloud brings several merits such as vendor lock‐in avoidance, system fault tolerance, cost reduction, and better quality of service. The biggest challenge is in selecting an optimal web service composition in the ever increasing multicloud market in which each provider has its own pricing schemes and delivers variation in the service security level. In this regard, we embed a module in the cloud broker to log service downtime and different attacks to measure the security risk. If security tenets, namely, security service level agreement, such as availability, integrity, and confidentiality for mission‐critical applications, are targeted by cybersecurity attacks, it causes disruption in business continuity, leading to financial losses or even business failure. To address this issue, our decision model extends the cost model by using the cost present value concept and the risk model by using the advanced mean failure cost concept, which are derived from the embedded module to quantify cloud competencies. Then, the cloud economic problem is transformed into a bioptimization problem, which minimizes cost and security risks simultaneously. To deal with the combinatorial problem, we extended a genetic algorithm to find a Pareto set of optimal solutions. To reach a concrete result and to illustrate the effectiveness of the decision model, we conducted different scenarios and a small‐to‐medium business IT development for a 5‐year investment as a case study. The result of different implementation shows that multicloud is a promising and reliable solution against IT on‐premises deployment.

Development of mathematical model of decision making based on analysis of values of stakeholders

Определены ценности заинтересованной стороны проекта как набор а показателей оценки ее текущего состояния. Приведено математическое описание отношения заинтересованной стороны к ценностям. Основываясь на описании отношения к ценностям, предложена целевая функция максимизации степени обеспечения ценностей заинтересованной стороны. Предложены рекомендации для руководителей проектов по формированию ценностей.

Exploring the communication breakdown in global virtual teams

Virtual matrix-managed teams with geographically dispersed members are becoming increasingly common in the high-tech sector. These teams, referred to as global virtual teams (GVTs), are generally described as culturally diverse, geographically dispersed, electronicallycommunicating workgroups. They rapidly form, change, and dissolve due to dynamic changes in the market. In addition, most GVTs today have team members spread among several projects with competing priorities. Communication breakdown can wreak havoc on a project as team members struggle to effectively communicate and work with one another. As a result, project delivery risks with distributed teams tend to be greater when compared to co-located teams. To address this critical issue, this study investigates the types of factors that significantly contribute to communication breakdown by identifying five distinct areas through a series of interviews with project team members in high-tech companies. These areas are trust, interpersonal relations, cultural differences, leadership and technology. These criteria are analyzed using mathematical Decision Models taking expert opinions from professionals who worked in GVTs. © 2011 Elsevier Ltd. PMA and IPMA. All rights reserved.

Decision support system in an international-voice-services business company

We consider a problem facing by an international telecommunication services company in maximizing its profit. From voice services by controlling cost and business partnership. The competitiveness in this industry is very high, so that any efficiency from controlling cost and business partnership can help the company to survive in the very high competitiveness situation. The company trades voice traffic with a large number of business partners. There are four trading schemes that can be chosen by this company, namely, flat rate, class tiering, volume commitment, and revenue capped. Each scheme has a specific characteristic on the rate and volume deal, where the last three schemes are regarded as strategic schemes to be offered to business partner to ensure incoming traffic volume for both parties. This company and each business partner need to choose an optimal agreement in a certain period of time that can maximize the company’s profit. In this agreement, both parties agree to use a certain trading scheme, rate and rate/volume/revenue deal. A decision support system is then needed in order to give a comprehensive information to the sales officers to deal with the business partners. This paper discusses the mathematical model of the optimal decision for incoming traffic volume control, which is a part of the analysis needed to build the decision support system. The mathematical model is built by first performing data analysis to see how elastic the incoming traffic volume is. As the level of elasticity is obtained, we then derive a mathematical modelling that can simulate the impact of any decision on trading to the revenue of the company. The optimal decision can be obtained from these simulations results. To evaluate the performance of the proposed method we implement our decision model to the historical data. A software tool incorporating our methodology is currently in construction.

Development of Conceptual Model for Virtualization of Bulk Materials Dispensing Technological Process

The main objective of this research is the improvement of the effectiveness of implementation of the technological process for dispensing bulk materials by developing a conceptual model of the virtualization. The objectives of this research are: creating unified information space for managing the lifecycle of the dispensing bulk materials process; development of conceptual model of the virtualization of the technological process which includes visual, structural and object-oriented models; development of mathematical model for decision making process during virtualization of the technological process; developing the structure of the virtual company which implements the process for dispensing bulk materials.

Эволюционные игры в TCP сетях с политиками ограничения скорости

Competitive development of various versions of network protocols is an essential part of computer networks. The most-used protocol today is Transmission Control Protocol (TCP). There is a large number of implementations of the TCP protocol, which differ by mechanism of congestion control. TCP develops by improving its existent implementations, vanishing some of them and via creation of a new ones. The possibility of using new versions of the protocol allows the user to increase the data rate by selecting the appropriate implementation of TCP. It is difficult to predict consequences of computer network users’ interaction in situations when many users try to achieve higher data rate by applying different TCP implementation. The actual task is to develop a theoretical and program tools to model such competitive dynamic interactions. This is the goal of my scientific-research work. Game theory, which is the theory of mathematical models of optimal decision making in situations of conflicts of interest, is the best suited to solve a particular problem because it allows you to find a solution in terms of non-cooperative interaction, which usually happens between the networks TCP-connections. This paper examines the possibility of coexistence of different implementations of protocols that users can change to improve their own capacity. It also examines games between protocols in cases when users’ packets management policies are applied.

Identifying cost-effective dynamic policies to control epidemics.

We describe a mathematical decision model for identifying dynamic health policies for controlling epidemics. These dynamic policies aim to select the best current intervention based on accumulating epidemic data and the availability of resources at each decision point. We propose an algorithm to approximate dynamic policies that optimize the population's net health benefit, a performance measure which accounts for both health and monetary outcomes. We further illustrate how dynamic policies can be defined and optimized for the control of a novel viral pathogen, where a policy maker must decide (i) when to employ or lift a transmission-reducing intervention (e.g. school closure) and (ii) how to prioritize population members for vaccination when a limited quantity of vaccines first become available. Within the context of this application, we demonstrate that dynamic policies can produce higher net health benefit than more commonly described static policies that specify a pre-determined sequence of interventions to employ throughout epidemics. Copyright © 2016 John Wiley & Sons, Ltd.

Toward Simple Representative Mathematical Models of Naturalistic Decision Making Through Fast-and-Frugal Heuristics

Naturalistic decision making (NDM) describes how people make decisions with time pressure and other complexities in familiar and meaningful environments. The complexities of NDM, although essential for a thorough understanding of experts, have limited the use of NDM in decision support system (DSS) design and decision analysis. There have been attempts to computationally model NDM theories; however, to do so has required significant programming skill, resulting in opaque models while still leaving significant portions of the theories unrepresented. To provide a path toward simple, representative, mathematical models of NDM, we present a general mathematical form that can model most of the components of the judgment and decision-making strategies from the fast-and-frugal heuristics (FFH) program. As a case study, the NDM quick test process was transformed into representative FFH components and then into mathematical form. The results show that the quick test process is similar to the FFH strategy tallying, which itself is a type of fast-and-frugal tree. Although the mathematical form does not capture all the cognitive processes at work, it does provide a simple, representative form for use in DSS design and decision analysis. Moreover, the model’s basis in the extensive human-subjects, mathematical, and computational analyses completed by the FFH program provides another method for integrating FFH and NDM by providing (a) a framework for generating constructive questions about how NDM theories account for FFH components; (b) a basis for prescriptive NDM decision support tools that are easy to communicate, understand, and apply; and (c) a method for approximating experience, expertise, and time pressure.

Preemptive Bone Marrow Transplantation and Event-Free Survival in Fanconi Anemia

Fanconi anemia (FA) is a rare inherited bone marrow failure syndrome associated with high risks of severe bone marrow failure (BMF), acute myeloid leukemia (AML), and solid tumors (ST). Bone marrow transplantation (BMT) provides a theoretical cure for hematologic risks (BMF, AML), but it introduces uncertain risks of transplantation-related mortality (TRM) and carcinogenicity. We developed a mathematical (Markov) decision model to estimate event-free survival (EFS) conditional on age based on per-year cause-specific hazard rates. We assumed that preemptive (PE) BMT eliminates the risks of BMF and AML, but it may introduce independent risks of TRM or influence the trajectory to ST. Our model suggested that the expected mean EFS in FA is higher for PE-BMT at young ages, with minimal risk of TRM and with little carcinogenicity. PE-BMT in adults decreased expected EFS because of the greater competing risk of ST in adulthood. Estimates of EFS conditioned on attained age may be used in shared decision-making when clinicians must counsel patients using limited data. Our methods may be used to model early transplantation in other blood disorders for which hematopoietic stem cell transplantation mitigates some but not all of the risks.

Using the analytic hierarchy process to prioritize alternative medicine: selecting the most suitable medicine for patients with diabetes

<p>Diabetes mellitus (DM) is emerging as a major public health problem in Saudi Arabia and this disease affects the Middle East in general. The analytic hierarchy process (AHP) was performed to select the most appropriate oral hypoglycemic agent for use as a monotherapy among newly diagnosed patients with type 2 diabetes. Eight important criteria resulted from the hierarchy structure: side effects, chronic disease, background scientific evidence, age, weight, cost, education level, and gender. The involvement of these different factors reveals that treating diabetes is a multi-criteria decision making (MCDM) problem. Thus, AHP was used because it is one of the most common MCDM tools. This project developed a mathematical decision-making model that prioritizes the available medications for patients with diabetes in terms of the aforementioned criteria. Oral type 2 diabetes medications (metformin, pioglitazone, sitagliptin, and glimepiride) were ranked 1st, 2nd, 3rd and 4th, respectively; their weights were 48.42%, 24.47%, 13.61% and 13.50%, respectively. Thus, metformin is recommended because it has the highest weight. Side effects were the most important factor affecting drug selection. The AHP provides an overall ranking to aid with final decisions. Unquestionably, the results of this project, or at least the proposed methodology, facilitate the decision-making process, which is important because it assists the decision maker in determining which oral drug to choose for newly diagnosed patients with diabetes.</p>

Multi-criteria decision making method of minimal suitable values

This paper presents a conceptual and mathematical model of a multi-criteria decision making process in which the information about decision maker's preferences is expressed in the form of minimal suitable values.

MATHEMATICAL MODEL OF REIMBURSEMENT DECISION MAKING IN RUSSIA. RESULTS OF VIM LIST FOR 2016

Background: In 2014 we firstly analyzed the formalized system (points and expert opinions) of drug inclusion and exclusion into the reimbursement lists in Russian Federation. The liner mathematical model of decision making was developed and adopted. Aim. Update the existing model using the results of reimbursement procedures acting from 2106. Material and methods. The linear models developed and adopted in 2014 were used. In 2015 we included data on 141 drug dossiers. We analyzed the decision of the expert body, chief Ministry of Health expert and the final committee decision. Results. 43 new drugs were included into the reimbursement lists acting from 2016. The model of expert body decision had an error 7,09% (12,4% in 2014). The model of chief Ministry of Health expert decision had an error – 7% (10% in 2014). The above mentioned experts became more experienced in the formalized procedure of decision making. The model of final decision had an error about 42% (35% in 2014). Conclusion. Linear models are working tools for modelling reimbursement system decisions. At the mean time the existing system of decision making needs more formalization.

Preemptive Bone Marrow Transplantation and Event-Free Survival in Fanconi Anemia

Background: Fanconi anemia (FA) is a primarily autosomal recessive bone marrow failure and cancer predisposition syndrome associated with mutations in the FA/BRCA DNA damage response pathway. The median age at diagnosis of FA is 7 years; the diagnosis is often made due to recognition of characteristic birth defects. Over half of patients with FA develop severe bone marrow failure (BMF) by age 50 years, one in ten develop acute myeloid leukemia (AML), and one in four develop a solid tumor (ST) as their first event. Successful allogeneic bone marrow transplantation (BMT) is potentially curative of FA's hematologic manifestations but introduces risks of transplant-related mortality (TRM) and morbidity. We hypothesized that preemptive bone marrow transplantation (PE-BMT) for individuals diagnosed prior to the development of BMF, AML, or ST, would increase event-free survival (EFS) if the risks associated with transplantation were sufficiently low.Methods: We developed a mathematical decision model (Markov) of EFS with the assumption that successful PE-BMT would eliminate the risks of BMF and AML, but would introduce a procedural risk of TRM. We modeled the EFS of PE-BMT at variable ages at decision ranging from birth to 30 years, and without and with an increase in the rate of ST following BMT above the level in untransplanted patients with FA. We developed our model using empirical estimates of the age-specific conditional probabilities of BMF, AML, and ST (Alter et al, BJH, 2010), and a 4.4-fold estimated increased risk of ST following BMT (Rosenberg et al, Blood, 2005). We tested the sensitivity of the model over a range of values for TRM and an increased risk of ST following BMT, and evaluated the model using TreeAge Pro 2014 (TreeAge Software, Inc, Williamstown MA, http://www.treeage.com).Results: Children diagnosed at age 7 years receiving standard care could expect to live an additional 16 years before experiencing BMF, ST, or AML, and thus survive free of an event until an average age of 23 years. If those children instead received PE-BMT with a 10% risk of TRM, they could expect to survive an additional 29 years and be cancer-free until an average age of 36 years. However, if PE-BMT were to increase the rate of ST 4.4-fold, PE-BMT would only increase the mean EFS by 2 years over standard care, until an average age of 25 years. PE-BMT would increase the mean EFS at all ages if TRM was ≤10% and the risk of ST was the same as in untransplanted patients. PE-BMT would decrease the mean EFS when performed after age 9 years if there was 10% TRM and a 4.4-fold increased rate of ST. PE-BMT at age 18 years with 10% TRM would increase the mean EFS if it did not affect the trajectory to ST, but would decrease the mean EFS if it modestly increased the rate of ST (≥2.2-fold).Conclusions: PE-BMT in patients with FA may provide an event-free survival benefit so long as the risk of TRM appears to be low (≤10%) and the regimen has little or no impact on the development of ST. The decision was particularly sensitive to the increase in ST following BMT. Our model suggests that older ages at decision, higher risks of TRM, and greater relative risks of ST following transplant would lead to PE-BMT being a less desirable strategy. Our estimates of event-free survival may be used to inform shared decision making between providers and families, with attention paid to patient values and the morbidity associated with BMT. DisclosuresNo relevant conflicts of interest to declare.

Evaluating alternatives for decommissioning California's offshore oil and gas platforms.

This paper introduces a series of 6 additional papers in this issue that describe an in-depth analysis of options for decommissioning oil and gas platforms offshore southern California. Although current leases require lessees in both state and federal waters to completely remove all production facilities and restore the seafloor to its pre-platform condition, other options have emerged since these leases were signed. Laws and regulations in other jurisdictions (particularly in federal waters) have evolved to allow a number of other uses such as aquaculture, alternative energy production, and artificial reefing. In response, the California Natural Resources Agency initiated an effort to investigate the issues associated with these and other decommissioning alternatives. The papers in this series are the result of the second phase in this process, a broad investigation of the engineering, economic, and environmental costs and benefits of the most feasible and likely options. In addition to the project's final report, the authors produced an interactive mathematical decision model, PLATFORM, that enables users to explore the implications of different decommissioning projects and options, as well as the effects of different approaches to valuing the associated costs and benefits.

A costing model for offshore decommissioning in California.

California's 27 offshore oil and gas platforms will reach the end of their useful lifetimes sometime in the near future and will require decommissioning. Although existing leases require complete removal of all platforms and associated infrastructure, the underlying laws and regulations have changed in recent years to allow a number of alternative uses after decommissioning. In particular, AB 2503, signed into law in September 2010, provides for a rigs-to-reefs program that allows the state to accept ownership of decommissioned platforms in federal waters. Decisions about whether to remove platforms completely or leave them in place as artificial reefs will depend in part on the relative cost of the 2 options. In this study, we describe the design and use of a mathematical decision model that provides detailed cost estimates of complete and partial removal (to 85 feet below the water line) for California's offshore platforms. The model, PLATFORM, is loaded with Bureau of Safety and Environmental Enforcement (BSEE) and Bureau of Ocean Energy Management (BOEM) costs for complete removal, along with costs for partial removal calculated for this study and estimates of the uncertainty associated with decommissioning cost estimates. PLATFORM allows users to define a wide range of decommissioning and costing scenarios (e.g., number of platforms, choice of heavy lift vessel, shell mound removal, reef enhancement). As a benchmark cost, complete removal of all 27 offshore platforms, grouped into the 7 decommissioning projects defined by the most recent federal cost estimates produced in 2010, would cost an estimated $1.09 billion, whereas partial removal of these platforms, grouped into the same set of projects, would cost $478 million, with avoided costs of $616 million (with minor rounding).

Measuring Networkwide Traffic Delay in Schedule Optimization for Work-Zone Planning in Urban Networks

In this paper, we develop a mathematical decision model and a solution algorithm to prioritize and schedule work zones in the planning process. The model is designed to measure the mutually interacting traffic impact and delay as a result of work-zone disruptions in the network. Several construction strategies that interest stakeholders are discussed, including daytime and nighttime construction modes, sequencing precedence, and the seasonal variation effect of demand. The method evaluates networkwide traffic delay through a $k$-shortest path algorithm to analyze drivers' behavior of alternative-route selection. A numerical example is analyzed on a real-world network to demonstrate the applicability of the model for a road construction scheduling problem.

A business planning model to identify new safety net clinic locations.

Community health clinics serving the poor and underserved are geographically expanding due to changes in U.S. health care policy. This paper describes the experience of a collaborative alliance of health care providers in a large metropolitan area who develop a conceptual and mathematical decision model to guide decisions on expanding its network of community health clinics. Community stakeholders participated in a collaborative process that defined constructs they deemed important in guiding decisions on the location of community health clinics. This collaboration also defined key variables within each construct. Scores for variables within each construct were then totaled and weighted into a community-specific optimal space planning equation. This analysis relied entirely on secondary data available from published sources. The model built from this collaboration revolved around the constructs of demand, sustainability, and competition. It used publicly available data defining variables within each construct to arrive at an optimal location that maximized demand and sustainability and minimized competition. This is a model that safety net clinic planners and community stakeholders can use to analyze demographic and utilization data to optimize capacity expansion to serve uninsured and Medicaid populations. Communities can use this innovative model to develop a locally relevant clinic location-planning framework.

Multi-objective geometric programming problem with Karush−Kuhn−Tucker condition usingϵ-constraint method

Optimization is an important tool widely used in formulation of the mathematical model and design of various decision making problems related to the science and engineering. Generally, the real world problems are occurring in the form of multi-criteria and multi-choice with certain constraints. There is no such single optimal solution exist which could optimize all the objective functions simultaneously. In this paper, ϵ -constraint method along with Karush−Kuhn−Tucker (KKT) condition has been used to solve multi-objective Geometric programming problems(MOGPP) for searching a compromise solution. To find the suitable compromise solution for multi-objective Geometric programming problems, a brief solution procedure using ϵ -constraint method has been presented. The basic concept and classical principle of multi-objective optimization problems with KKT condition has been discussed. The result obtained by ϵ -constraint method with help of KKT condition has been compared with the result so obtained by Fuzzy programming method. Illustrative examples are presented to demonstrate the correctness of proposed model.