In this paper, an exact geometric algorithm is presented for solving two-job sequencing and scheduling problems in flexible flow shop and job shop environments while the resources are (un)available in some time periods and processors (un) Availability is the same in all work centers. This study seems utterly new and it is applicable to any performance measure based on the completion time. The investigated models are very close to the actual scheduling problems, because they envisage the flexible job shop environments, heads, set-up times, arbitrary number of unAvailability periods on all resources, arbitrary number of work-centers, any kind of cross-ability, any kind of resume-ability and several types of performance measures. The proposed model is presented to solve two-job problems because it is a graphical approach. However, it is concluded that the idea can be extended to n-dimensional problems as well.

Background: Hispanics comprise 17% of the total U.S. population, surpassing African-Americans as the largest minority group. Linguistically, almost 60 million people speak a language other than English. This language diversity can create barriers and additional burden and risk when seeking health services. Patients with Limited English Proficiency (LEP) for example, have been shown to experience a disproportionate risk of poor health outcomes, making the provision of Language Services (LS) in healthcare facilities critical. Research on the determinants of LS adoption has focused more on overall cultural competence and internal managerial decision-making than on measuring LS adoption as a process outcome influenced by contextual or external factors. The current investigation examines the relationship between state policy, service area factors, and hospital characteristics on hospital LS adoption.Methods: We employ a cross-sectional analysis of survey data from a national sample of hospitals in the American Hospital Association (AHA) database for 2011 (N= 4876) to analyze hospital characteristics and outcomes, augmented with additional population data from the American Community Survey (ACS) to estimate language diversity in the hospital service area. Additional data from the National Health Law Program (NHeLP) facilitated the state level Medicaid reimbursement factor.Results: Only 64% of hospitals offered LS. Hospitals that adopted LS were more likely to be not-for-profit, in areas with higher than average language diversity, larger, and urban. Hospitals in above average language diverse counties had more than 2-fold greater odds of adopting LS than less language diverse areas [Adjusted Odds Ratio (AOR): 2.26, P<0.01]. Further, hospitals with a strategic orientation toward diversity had nearly 2-fold greater odds of adopting LS (AOR: 1.90, P<0.001).Conclusion: Our findings support the importance of structural and contextual factors as they relate to healthcare delivery. Healthcare organizations must address the needs of the population they serve and align their efforts internally. Current financial incentives do not appear to influence adoption of LS, nor do Medicaid reimbursement funds, thus suggesting that further alignment of incentives. Organizational and system level factors have a place in disparities research and warrant further analysis; additional spatial methods could enhance our understanding of population factors critical to system-level health services research.

In real world scheduling applications, machines might not be available during certain time periods due to deterministic or stochastic causes. In this article, the machine scheduling with Availability constraints for both deterministic and stochastic cases with different environments, constraints and performance measures will be discussed. The existing body of research work in the literature will be completely reviewed and the NP-complete models will be identified.