A mixed integer linear program to compress transition probability matrices in Markov chain bootstrapping

Cerqueti, Roy; Falbo, Paolo; Pelizzari, Cristian; Ricca, Federica; Scozzari, Andrea

doi:10.1007/s10479-016-2181-9

Cited by 4 publications

(3 citation statements)

References 31 publications

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“…For instance, [33] used MDP to solve inventory control of perishable goods for long-term humanitarian operations. [34] use a mixed-integer linear programming problem to solve the Markov Decision Process by reducing the number of states using bootstrapping methods. [35] modeled the spare parts supply chain problem using random lead times and disruption risks.…”

Section: Markov Decision Processmentioning

confidence: 99%

An Integrated Supply Chain Risk Mitigation tool - Model, Analysis, and Insights

Balan,

Handfield

2024

Preprint

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In this paper, we propose a two-phase approach that seeks to create insights into disruptions, allowing managers to mitigate supply chain risks using an integrated risk-mitigation tool. In the first phase, the problem is formulated as a Markov Decision Process (MDP) that maximizes the expected long-run revenue induced by supply chain risks, given the current state of the risk score. We map four decision states to four specific managerial actions: "do nothing," "track the supplier," "monitor the supplier," and "change the supplier." If the optimal policy is "do nothing", then the supply chain risk scores are continued to be monitored. In the case of "track the supplier", the firm will track the supplier’s performance internally, however, in the case of "monitor the supplier", the firm will hire an external contractor to monitor the external supply chain risks in the supplier’s country and macroeconomic factors. Lastly, if the optimal policy from phase 1 is to ’change the supplier,’ the best-performing supplier is identified using an integrated best-worst goal programming (BWGP) method as a multi-criteria decision-making (MCDM) method. This second phase of decision support can help allocate supply contracts to the least risky supplier. We demonstrate the integrated risk-based model and the proposed best-worst goal programming (BWGP) method on a global automation technologies company and share the risk-mitigating capability as a case study. Results based on consistency ratio, conformity, and total deviation show that the BWGP performs better than the other MCDM methods and can be used effectively in the integrated two-phase approach with MDP as a supply chain risk mitigation tool.

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Section: Markov Decision Processmentioning

confidence: 99%

An Integrated Supply Chain Risk Mitigation tool - Model, Analysis, and Insights

Balan,

Handfield

2024

Preprint

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“…where P r defines the transition probability and a is the action performed by the decision maker. Similarly, the mathematical equation that expresses the system is termed as Transition Probability Matrix P [11], which represents various transition rates from one state to other state. Similarly, the mathematical equation that is 158 U. Pervez, A. Mahmood, O. Hasan, K. Latif and A. Gawanmeh used to calculate the probability of next state is given below…”

Section: Markov Decision Process (Mdp)mentioning

confidence: 99%

Improvement Strategies for Device Interoperability Middleware using Formal Reliability Analysis

Pervez¹,

Mahmood²,

Hasan³

et al. 2016

SCPE

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Ensuring the correctness of middleware that ensures interoperability of various medical devices is one of the biggest challenges in the e-health domain. Traditionally, these Device Interoperability Middleware (DIM) are analyzed using software testing. However, given the inherent incompleteness of testing and the randomness of the user behaviours, the analysis results are not guaranteed to be accurate. Some of these inaccuracies in analysis results could even put human life at risk. In order to overcome these limitations, we propose to use a probabilistic model checker PRISM for analyzing DIM. The proposed approach allows us to rigorously verify reliability properties of the given DIM and thus allows the designers to make appropriate measures to design more reliable systems. For illustration, we formally analyze a middleware that uses the HL7 FHIR and ontology-based description of the devices and a communication protocol to bridge the gap in heterogeneity for dealing with different vendors and incompatible data formats.

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“…Seasonal time series of a regular nature are encountered in many fields, such as soil dryness index (Li et al, 2003), tourism demand (Huang and Min, 2002), municipal solid waste management (Navarro-Esbrí et al, 2002) and electricity prices (Cerqueti et al, 2017). The seasonal autoregressive integrated moving average (SARIMA) model is the best-known approach and was introduced by Box and Jenkins (1976).…”

Section: Introductionmentioning

confidence: 99%

Developing intuitionistic fuzzy seasonality regression with particle swarm optimization for air pollution forecasting

Chang

Hung

et al. 2019

IMDS

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Purpose The purpose of this paper is to develop a novel intuitionistic fuzzy seasonality regression (IFSR) with particle swarm optimization (PSO) algorithms to accurately forecast air pollutions, which are typical seasonal time series data. Seasonal time series prediction is a critical topic, and some time series data contain uncertain or unpredictable factors. To handle such seasonal factors and uncertain forecasting seasonal time series data, the proposed IFSR with the PSO method effectively extends the intuitionistic fuzzy linear regression (IFLR). Design/methodology/approach The prediction model sets up IFLR with spreads unrestricted so as to correctly approach the trend of seasonal time series data when the decomposition method is used. PSO algorithms were simultaneously employed to select the parameters of the IFSR model. In this study, IFSR with the PSO method was first compared with fuzzy seasonality regression, providing evidence that the concept of the intuitionistic fuzzy set can improve performance in forecasting the daily concentration of carbon monoxide (CO). Furthermore, the risk management system also implemented is based on the forecasting results for decision-maker. Findings Seasonal autoregressive integrated moving average and deep belief network were then employed as comparative models for forecasting the daily concentration of CO. The empirical results of the proposed IFSR with PSO model revealed improved performance regarding forecasting accuracy, compared with the other methods. Originality/value This study presents IFSR with PSO to accurately forecast air pollutions. The proposed IFSR with PSO model can efficiently provide credible values of prediction for seasonal time series data in uncertain environments.

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A mixed integer linear program to compress transition probability matrices in Markov chain bootstrapping

Cited by 4 publications

References 31 publications

An Integrated Supply Chain Risk Mitigation tool - Model, Analysis, and Insights

An Integrated Supply Chain Risk Mitigation tool - Model, Analysis, and Insights

Improvement Strategies for Device Interoperability Middleware using Formal Reliability Analysis

Developing intuitionistic fuzzy seasonality regression with particle swarm optimization for air pollution forecasting

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