On Solving Bi-level Multi-Objective Fully Quadratic Fractional Optimization Model with Fuzzy Demands

This paper has been designed to introduce the method for solving the Bi-level Multi-objective (BL-MO) Fully Quadratic Fractional Optimization Model through Fuzzy Goal Programming (FGP) approach by utilising non-linear programming. In Fully Quadratic Fractional Optimization Model, the objective functions are in fractional form, having quadratic functions in both numerator and denominator subject to quadratic constraints set. The motive behind this paper is to provide a solution to solve the BL-MO optimization model in which number of decision-makers (DM) exists at two levels in the hierarchy. First, the fractional functions with fuzzy demand, which are in the form of fuzzy numbers, are converted into crisp models by applying the concept of α-cuts. After that, membership functions are developed which are corresponding to each decision-maker’s objective and converted into simpler form to avoid complications due to calculations. Finally, the model is simplified by applying FGP approach, and a compromised solution to the initial model is obtained. An algorithm, flowchart and example are also given at the end to explain the study of the proposed model.

The Post-Covid-19 Era Requires Maximum Urban Resilience

This paper reviews the low-resilience problem in many cities, poor designs of cities to cope with disasters, and the need for tolerance of urban constructions. It explores answers concerning the question of how shall we build cities resiliently? The method of this applied research is a multiphase process that considers all physical and socioeconomic elements of a city. It introduces six indicator groups of urban management (M), economy (E), built environments (U), Infrastructures (I), natural environments (N), and health protection (H). The groups include 55 indicators as variables in the mathematical calculations in this paper. This paper builds a mathematical model to maximize the profitability of resilient buildings by optimizing investments in the required projects. The projects will upgrade the firmness and tolerance of cities against nature-based and human-made dangers and risks. There is a linear programming in 55 variables to select optimal solutions from fifty-five factorial alternatives. Then, the programming will develop into non-linear programming. The unique innovation of this paper is its linear programming interpretation by non-linear to give optimal solutions for the problem. Applying the Lagrange function in the Kuhn-Tucker conditions proves the accuracy of the hypothesis that post-COVID urbanization requires maximum resilience. Only in this way, the urban economies will be free of risks. Outcomes in this paper will assist in the pre-planning, design, and building of built environments everywhere resilient and sustainable.

Robust optimal classification trees under noisy labels

In this paper we propose a novel methodology to construct Optimal Classification Trees that takes into account that noisy labels may occur in the training sample. The motivation of this new methodology is based on the superaditive effect of combining together margin based classifiers and outlier detection techniques. Our approach rests on two main elements: (1) the splitting rules for the classification trees are designed to maximize the separation margin between classes applying the paradigm of SVM; and (2) some of the labels of the training sample are allowed to be changed during the construction of the tree trying to detect the label noise. Both features are considered and integrated together to design the resulting Optimal Classification Tree. We present a Mixed Integer Non Linear Programming formulation for the problem, suitable to be solved using any of the available off-the-shelf solvers. The model is analyzed and tested on a battery of standard datasets taken from UCI Machine Learning repository, showing the effectiveness of our approach. Our computational results show that in most cases the new methodology outperforms both in accuracy and AUC the results of the benchmarks provided by OCT and OCT-H.

Multi-Product Multi Echelon Measurements of Perishable Supply Chain: Fuzzy Non-Linear Programming Approach

The perishable milk products industry has to deal with multiple pressures such as demand forecasting, price fluctuations, lead time, order batching, and inflated orders along with difficulties of climatic and traffic conditions, storage areas and shipment in unfavorable circumstances. The Indian dairy industry faces immense wattage issue due to improper infrastructure for the cold chain storage facilities, resulting in unsatisfied customers. A study is undertaken to comprehend the supply chain framework that handles perishability issues in production and distribution. Researchers propose a multi-objective mixed-integer non-linear supply chain coordination model under uncertain environments to minimize the cost of transportation, offset wastage of products and neutralize the losses due to insufficiencies of transit and storage amenities. The proposed model is meant for managing the delivery with lesser deterioration losses for producers, warehouses, and retailers. The model considers various costs for holding, halting, discounts on purchased cost, transportation cost for truckload policy under regular and unforeseen circumstances of curfew, and identify the rate of deterioration to know the impact on the cost for all players involved in the SCM framework. To handle uncertainty of objective functions, fuzzy set concepts and the defuzzification method are imposed, and fuzzy non-linear programming algorithms are used to get the single objective function from the defuzzified multi-objective functions. Data analysis is done on Lingo 18.0 software. Rate of deterioration is highest for the warehouse, which indicates that efforts should be made to augment warehouse facilities for less spoilage to reduce losses in cost. Finally, the study ends with main findings, conclusions, limitations and future scopes.