An interactive decision support system for an aggregate production planning model based on multiple criteria mixed integer linear programming

In this paper, we present an aggregate production planning (APP) model applied to a Portuguese firm that produces construction materials. A multiple criteria mixed integer linear programming (MCMILP) model is developed with the following performance criteria: (1) maximize profit, (2) minimize late orders, and (3) minimize work force level changes. It includes certain operational features such as partial inflexibility of the work force, legal restrictions on workload, work force size (workers to be hired and downsized), workers in training, and production and inventory capacity. The purpose is to determine the number of workers for each worker type, the number of overtime hours, the inventory level for each product category, and the level of subcontracting in order to meet the forecasted demand for a planning period of 12 months. Additionally, a decision support system (DSS) based on the MCMILP model is proposed. It will help practitioners find the “best” solution for an APP problem without having to familiarize themselves with the mathematical complexities associated with the model. An example to illustrate the use of the DSS is also included.     

Hardness and algorithms for rainbow connection

An edge-colored graph G is rainbow connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection of a connected graph G, denoted rc(G), is the smallest number of colors that are needed in order to make G rainbow connected. In the first result of this paper we prove that computing rc(G) is NP-Hard solving an open problem from Caro et al. (Electron. J. Comb. 15, 2008, Paper R57). In fact, we prove that it is already NP-Complete to decide if rc(G)=2, and also that it is NP-Complete to decide whether a given edge-colored (with an unbounded number of colors) graph is rainbow connected. On the positive side, we prove that for every ε>0, a connected graph with minimum degree at least ε n has bounded rainbow connection, where the bound depends only on ε, and a corresponding coloring can be constructed in polynomial time. Additional non-trivial upper bounds, as well as open problems and conjectures are also presented.     

Response to the COVID-19: Understanding implications of government lockdown policies

The rising number of COVID-19 cases and economic implications of lockdown measures indicate the tricky balancing act policy makers face as they implement the subsequent phases of 'unlock'. We develop a model to examine how lockdown and social distancing measures have influenced the behavioral conduct of people. The current situation highlights that policy makers need to focus on bringing awareness and social restraint among people rather than going for stringent lockdown measures. We believe this work will help the policy makers gain insights into the troubled COVID-19 times ahead, and based on the estimates, they can frame policies to navigate these wild waves in the best possible way.     

A three-state continuous time Markov chain model for HIV disease burden

Plasma HIV viral load (VL) is the clinical indicator used to evaluate disease burden for HIV-infected patients. We developed a covariate-adjusted, three-state, homogenous continuous time Markov chain model for HIV/AIDS disease burden among subgroups. We defined Detectable and Undetectable HIV VL levels as two transient states and Death as the third absorbing state. We implemented the exact maximum likelihood method to estimate the parameters with related asymptotic distribution to conduct hypothesis testing. We evaluated the proposed model using HIV-infected individuals from South Carolina (SC) HIV surveillance data. Using the developed model, we estimated and compared the transition hazards, transition probabilities, and the state-specific duration for HIV-infected individuals. We examined gender, race/ethnicity, age, CD4 count, place of residence, and antiretroviral treatment regimen prescribed at the beginning of the study period. We found that patients with a higher CD4 count, increased age, heterosexual orientation, white, and single tablet regimen users were associated with reduced risk of transitioning to a Detectable VL from an Undetectable VL, whereas shorter time since diagnosis, being male, and injection drug use increased the risk of the same transition.     

Network design for reverse logistics

Collection and recycling of product returns is gaining interest in business and research worldwide. Growing green concerns and advancement of green supply chain management (GrSCM) concepts and practices make it all the more relevant. Inputs from literature and informal interviews with 84 stakeholders are used to develop a conceptual model for simultaneous location–allocation of facilities for a cost effective and efficient reverse logistics (RL) network. We cover costs and operations across a wide domain and our proposed RL network consists of collection centers and two types of rework facilities set up by original equipment manufacturers (OEMs) or their consortia for a few categories of product returns under various strategic, operational and customer service constraints in the Indian context.     

Using geographically weighted regression for environmental justice analysis: Cumulative cancer risks from air toxics in Florida

Previous quantitative research on environmental justice has been limited by simplistic assumptions used to measure health risks and traditional regression techniques that fail to discern spatial variations in statistical relationships. We address these gaps through a case study that examines: (a) whether potential health risks from exposure to hazardous air pollutants in Florida are related to race/ethnicity and socioeconomic status, and (b) how the significance of statistical associations between health risk and race/ethnicity or socioeconomic status vary across the state. This study integrates census tract level estimates of cumulative cancer risk compiled by the EPA with Census 2000 data and a spatial statistical technique known as geographically weighted regression that allows us to explore spatial variability in analytical results. Our findings indicate that while race and ethnicity are significantly related to cancer risks in Florida, conventional regression can hide important local variations in statistical relationships relevant to environmental justice analysis.     

On the one parameter unit-Lindley distribution and its associated regression model for proportion data

In this paper considering an appropriate transformation on the Lindley distribution, we propose the unit-Lindley distribution and investigate some of its statistical properties. An important fact associated with this new distribution is that it is possible to obtain the analytical expression for bias correction of the maximum likelihood estimator. Moreover, it belongs to the exponential family. This distribution allows us to incorporate covariates directly in the mean and consequently to quantify their influences on the average of the response variable. Finally, a practical application is presented to show that our model fits much better than the Beta regression.     

A modified Conway–Maxwell–Poisson type binomial distribution and its applications

This article proposes a generalized binomial distribution, which is derived from the finite capacity queueing system with state-dependent service and arrival rates. This distribution is also generated from the conditional Conway–Maxwell–Poisson (CMP) distribution given a sum of two CMP variables. In this article, we consider the properties of the probability mass function, indices of dispersion, skewness and kurtosis, and give applications of the proposed distribution. The estimation method and simulation study are also considered.     

Demographic scenarios by age,sex and education corresponding to the SSP narratives

In this paper, we translate the five narratives as defined by the Shared Socioeconomic Pathways (SSPs) research community into five alternative demographic scenarios using projections by age, sex and level of education for 171 countries up to 2100. The scenarios represent a significant step beyond past population scenarios used in the Intergovernmental Panel for Climate Change context, which considered only population size. The definitions of the medium assumptions about future fertility, mortality, migration and education trends are taken from a major new projections effort by the Wittgenstein Centre for Demography and Global Human Capital, while the assumptions for all the other scenarios were defined in interactions with other groups in the SSP community. Since a full data base with all country-specific results is available online, this paper can only highlight selected results.