Mathematical and Statistical Analysis of Farm Level Agricultural Sector in Bangladesh under Uncertainty (Published)
This study presents three different mathematical models for profit optimization of agricultural products in Bangladesh. To develop a Mixed Integer Linear Programming (MILP) model and analyze this model for two situation of demand uncertainty. Considering demand will be known before production and demand will be known after production. For the mentions of two cases, we investigate the change of solution applying least demand, maximum perhaps demand and extreme demand scenarios. I think this is real life problem and this analysis will be helpful for all types of agricultural producers. The proposed MILP model is to maximize the total profit and also to estimate the profitable production locations. The formulated MILP model were solved by A Mathematical Programming Language (AMPL) and results obtained by appropriate solver MINOS. Numerical example with the sensitivity of several parameters has been deployed to validate the models. Results show that maximum perhaps demand scenario gets better solution according to our expected value compare of other two scenarios.
Keywords: Agricultural products, Demand, Mixed integer linear program, Uncertainty, optimization
MODE BEHAVIOUR IN RELATION TO BIN SIZE AND DATA DISTRIBUTION (Published)
The “mode” has been proposed as an appropriate statistic to improve estimate especially in situations when data distributions are skewed or contain outliers such as activity duration in project scheduling. Since the underlying distribution of activity duration may be unknown and different modes can be obtained using different bin sizes of the histogram method, this paper,investigates the effect of varying histogram bin width and data distribution on the behaviour of the mode. Random numbers were generated from five distributions commonly used to model project activity duration at five different levels and varying sample sizes. Each set of sample is then binned using varying histogram bin width, Sturges’rule and Scott’s rule. The grand mode for all levels per classification is recorded and analyzed. It was found that bin width does not significantly affect the behaviour of the mode but the value of the mode is significantly dependent on the data distribution and sample size.
Keywords: : Statistical mode, Bin size, Estimate, Statistical distribution, Uncertainty