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Journal Home > Volume 12, Issue 4 - December 30, 2017

JAQM Volume 12, Issue 4 - December 30, 2017


A Mathematical Optimization Model of the Magliozzi Brothers’ Revolt of the Lab Rats Puzzle

Car Talk is a popular radio program that aired for many years on National Public the United States. It is still on the air today and airs re-runs as the “Best of Car Talk.” One regular segment of the program is called “The Puzzler”. The optimization model discussed in this paper is based on the puzzler which aired the week of February 15, 2010 (The Puzzler: Revolt of the Lab Rats). The puzzle proved to be a classic binary programming puzzle. Microsoft Excel Solver was used to model and solve this puzzle.

Estimating the Cure Fraction among Cancer Patients by using Promotional Time Cure Rate Model with Negative Binomial Distribution
Gurprit GROVER, Komal GOEL

Modern cancer treatments have substantially improved cure rates and have generated a great interest and need for proper statistical tools to analyze survival data with non-negligible cure fractions. However, the patient's death, which is the event of interest, might happen due to different latent competing causes which can develop cancer. In this paper, a flexible cure rate survival model (Promotional time cure model) has been proposed by assuming that the number of competing causes follows the Negative Binomial distribution and the time to event follows Exponential distribution. Parameter estimation has been done by Bayesian approach to a real dataset of melanoma clinical trial using MCMC technique. Model comparison has been accessed using Deviance information Criterion.

Fuzzy Inventory Model Incorporating Advance Payment without Shortages having Constant and Time Dependent Demand

In this paper, an inventory model with advance payment for a single item has been developed in which the lead time is taken to be fixed and there is no shortage. The crisp model has been developed under two different circumstances, with constant demand and with linear time dependent demand. Then the corresponding fuzzy models are formulated in which several parameters involved are taken as hexagonal fuzzy numbers. The very effective signed-distance method has been used to convert the fuzzy numbers into the crisp numbers. Then the fuzzy model has been solved using LINGO12.0. Finally, some numerical examples are presented to illustrate the model and solution methodology. The effects of change of different inventory parameters has been studied and are presented.

Is Economic Development the Determining Factor of Social Progress?
Mihaela MIHAI

The Social Progress Imperative initiative argues that traditional indicators of economic growth do not fully reflect the progress of a country. There is a general tendency to measure development and to understand the influence of related components on economic or social phenomena. Let's not forget that both GDP and its derivatives are often used to describe and substantiate changes in development. However, when considering non-economic components, traditional economic indicators may not fully explain development. This highlights that an economic growth does not always mean an increase in the quality of life standards or opportunities for any citizen. Most of the time, GDP points to the concerns of developing social, environmental and personal nature. This could also be valid for aspects of the development and performance of society and the economy, such as social progress. Defined by the ability of a society to meet the fundamental needs of its citizens and to provide them with the essential elements of improving life, social progress can be made possible even at relatively modest income levels. Practically, the Social Progress Index measures the results of the development and performance of society and the economy in practical terms. Similarly, we can say that the development of a high-income society may regress over time. The empirical analysis of data shows that there is a strong correlation between GDP per capita and the Social Progress Index both in the countries for which it was calculated and in the analysis targeting only the countries of the European Union. This result is also relevant in case of a causality inverse correlation. However, if we are just talking about economic development, it means we are talking about an incomplete development strategy.