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Time variant multi-objective linear fractional interval-valued transportation problem

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Applied Mathematics(A Journal of Chinese Universities) 2022年第1期37卷 111-130页

作者： dharmadas Mardanya sankar kumar Roy department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar UniversityMidnapore 721102West BengalIndia

This paper studies a time-variant multi-objective linear fractional transportation problem. In reality, transported goods should reach in destinations within a specific time. Considering the importance of time, a time-variant multi-objective linear fractional transportation problem is formulated here. We take into account the parameters as cost, supply and demand are interval valued that involved in the proposed model, so we treat the model as a multi-objective linear fractional interval transportation problem. To solve the formulated model, we first convert it into a deterministic form using a new transformation technique and then apply fuzzy programming to solve it. The applicability of our proposed method is shown by considering two numerical examples. At last, conclusions and future research directions regarding our study is included.

关键词： fractional transportation problem multi-objective optimization interval number time variant parameter fuzzy programming Pareto optimal solution

Bi-level Programming for Stackelberg Game with Intuitionistic Fuzzy Number: a Ranking Approach

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Journal of the Operations Research Society of China 2021年第1期9卷 131-149页

作者： Sumit kumar Maiti sankar kumar Roy School of Applied Sciences and Humanities Haldia Institute of TechnologyPurba MidnaporeWB 721657India department of Applied Mathematics with Oceanology and Computer ProgrammingVidyasagar UniversityMidnaporeWB 721102India

This paper introduces a ranking function procedure on a bi-level programming for Stackelberg game involving intuitionistic fuzzy *** fuzzy num-ber is considered in many real-life situations,so it makes perfect sense to address decision-making problem by using some specified intuitionistic fuzzy *** this paper,intuitionistic fuzziness is characterized by a normal generalized triangular intuitionistic fuzzy number.A defuzzification method is introduced based on the pro-portional probability density function associated with the corresponding membership function,as well as the complement of non-membership *** the proposed ranking technique,a methodology is presented for solving bi-level programming for Stackelberg *** application example is provided to demonstrate the applica-bility of the proposed methodology,and the achieved results are compared with the existing methods.

关键词： Bi-levelprogramming Triangular intuitionistic fuzz ynumber Ranking function Nonlinear programming Optimal solution

Transportation Problem with Multi-choice Cost and demand and Stochastic Supply

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Journal of the Operations Research Society of China 2016年第2期4卷 193-204页

作者： sankar kumar Roy department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar UniversityMidnaporeWest Bengal 721102India

This paper analyzes the multi-choice stochastic transportation problem where the cost coefficients of the objective function and the demand parameters of the constraints follow multi-choice *** that the supply parameters of the constraints in a transportation problem(TP)follow logistic *** main objective of this paper is to select an appropriate choice from the multi-choices for the cost coefficients of the objective function and the demand of the constraints in the TP by introducing Lagrange’s interpolating polynomial in such a way that the total cost is minimized and satisfies the required *** stochastic programming,the stochastic supply constraints of the TP are transformed into deterministic ***,a non-linear deterministic model is *** Lingo software,the optimal solution of the proposed problem is *** illustrate the methodology,a real-life problem on the TP is considered.

关键词： Transportation problem Multi-choice programming Lagrange’s interpolating polynomial Stochastic programming

Chromium-induced membrane damage: protective role of ascorbic acid

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Journal of Environmental Sciences 2001年第3期13卷 272-275页

作者： sankar kumar d.y Prasunpriya Nayak Somenath Roy department of Human Physiology with Community Health Vidyasagar UniversityMidnapore 721102West BengalIndia

Importance of chromium as environmental toxicant is largely due to impact on the body to produce cellular toxicity. The impact of chromium and their supplementation with ascorbic acid was studied on plasma membrane of liver and kidney in male Wistar rats (80-100g body weight). It has been observed that the intoxication with chromium (i.p.) at the dose of 0.8 mg/100g body weight per d.y for a period of 28 d.ys causes significant increase in the level of cholesterol and decrease in the level of phospholipid of both liver and kidney. The alkaline phosphatase, total ATPase and Na\++\|K\++\|ATPase activities were significantly decreased in both liver and kidney after chromium treatment, except total ATPase activity of kidney. It is suggested that chromium exposure at the present dose and duration induce for the alterations of structure and function of both liver and kidney plasma membrane. Ascorbic acid (i.p. at the dose of 0.5 mg/100g body weight per d.y for period of 28 d.ys) supplementation can reduce these structural changes in the plasma membrane of liver and kidney. But the functional changes can not be completely replenished by the ascorbic acid supplementation in response to chromium exposure. So it is also suggested that ascorbic acid (nutritional antioxidant) is useful free radical scavenger to restrain the chromium induced membrane damage.

关键词： chromium liver kidney membrane ascorbic acid

Alpha-tocopherol supplementation on chromium toxicity: a study on rat liver and kidney cell membrane

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Journal of Environmental Sciences 2003年第3期15卷 356-359页

作者： sankar kumar d.y Prasunpriya Nayak Somenath Roy department of Human Physiology with Community Health Vidyasagar UniversityDepartment of Human Physiology with Community Health Vidyasagar UniversityDepartment of Human Physiology with Community Health Vidyasagar University Midnapore-721 102 West Bengal IndiaMidnapore-721 102 West Bengal IndiaMidnapore-721 102 West Bengal India

Membrane damage is one of the important consequence of chromium, an environmental toxicant, to produce cytotoxicity. α-tocopherol, a membrane protectant can be used to reduce the chromium-induced membrane damage. In the present study, the impact of chromium in presence and absence of α-tocopherol was studied on plasma membrane of liver and kidney in male Wistar rats (80—100 g body weight). Significant increase in membrane cholesterol level as well as significant decrease in membrane phospholipid level in chromium exposed ( 0.8 mg /100 g body weight/d, i.p., for 4 weeks) animals suggest structural alteration of both liver and kidney plasma memebrane. The alkaline phosphatase, total ATPase and Na +-K +-ATPase activities of plasma membrane were significantly decreased in both liver and kidney after chromium treatment. However, α-tocopherol (30 mg/100 g diet) supplementation can restrict the changes in these membrane-bound enzyme activities. Thus, the usefulness of dietary supplementation of α-tocopherol to restrain the chromium-induced membrane damage is suggested.

关键词： chromium liver kidney membrane α-tocopherol

Two-layer supply chain model for Cauchy-type stochastic demand under fuzzy environment

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International Journal of Intelligent Computing and Cybernetics 2018年第2期11卷 285-308页

作者： Sujit kumar de Shib sankar Sana department of Mathematics Midnapore CollegeMidnaporeIndia department of Mathematics Bhangar MahavidyalayaKolkataIndia

Purpose–The purpose of this paper is to deal with profit maximization problem of two-layer supply chain(SC)under fuzzy stochastic demand having finite mean and unknown *** policy is employed from the retailer to *** profit of the supplier solely depends on the order size of the ***,the loss of shortage items is related to loss of profit and goodwill *** authors develop the profit function separately for both the retailer and supplier,first,for a decentralized system and,second,joining them,the authors get a centralized system(CS)of decision making,in which one is giving more profit to both of *** problem is solved analytically first,then the authors fuzzify the model and solve by fuzzy Hausdorff distance ***/methodology/approach–The analytical models are formed for both centralized and decentralized systems under non-cooperative and cooperative environment with suitable constraints.A significant assumption on density function,namely Cauchy-type density function,is introduced for demand rate because of its wider range of the retailers’*** Hausdorff metric is incorporated within the fuzzy components of the fuzzy sets *** this method,the authors find out closure values of both centralized and decentralized policies,which is an essential part of any cooperative and non-cooperative two-layer SC ***,the authors take care of the profit values with corresponding ambiguities for both the systems ***–It is found that the centralize policy of SC could only be able to maximize the profit of both the retailers and *** analytical results are illustrated numerically along with sensitivity analysis and side by side comparative studies between Hausdorff and Euclidean distance measure are done *** limitations/implications–The main focus of attention of the proposed model is given to usefulness of Hausdorff *** other distances,Hausdor

关键词： Supply chain Fuzziness Optimization

QoS aware routing and wavelength allocation in optical burst switching networks using differential evolution optimization

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digital Communications and Networks 2018年第1期4卷 3-12页

作者： Ravi sankar Barpanda Ashok kumar Turuk Bibhudatta Sahoo department of Computer Science & Engineering National Instiute of Technology Rourkela India 769008

The issue of burst losses imposes a constraint on the development of Optical Burst Switching （OBS） networks. Heavy burst losses strongly affect the Quality of Service （QoS） intended by end users. This article presents a QoS aware Routing and Wavelength Allocation （RWA） technique for burst switching in OBS networks. The RWA problem is modeled as a bi-objective Integer Linear Programming （ILP） problem, where objective functions are based on minimizing the number of wavelengths used and the number of hops traversed to fulfill the burst transmission requests for a given set of node pairs. The ILP model is solved using a novel approach based on a differential Evolution （dE） algorithm. Analytical results show that the dE algorithm provides a better performance compared to shortest path routing, which is a widely accepted routing strategy for OBS networks.

关键词： Burst loss Optical burst switching Quality of service Routing and wavelength assignmentInteger linear programmingdifferential evolution

Spatial variability of soil hydraulic and physical properties in erosive sloping agricultural fields

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Water Science and Engineering 2023年第1期16卷 57-66页

作者： deepak Singh Alok kumar Mishra Sridhar Patra sankar Mariappan Nisha Singh Saswat kumar Kar ICAR-Indian Institute of Soil and Water Conservation Dehradun 248195India Sam Higginbottom University of Agriculture Technology and SciencesPrayagraj 211007India Hemvati Nandan Bahuguna Garhwal University Srinagar(Garhwal)246174India

It is essential to minimize soil quality degradation in sloping agricultural fields through stabilization and improvement of soil hydraulic properties using sustainable soil *** study aimed to analyze the impact of different tillage practices,including conventional tillage(CT),minimum tillage(MT),and zero tillage(ZT),on soil hydraulic conductivity in a sloping agricultural field under maizeewheat *** results showed that the highest runoff volume(257.40 m3),runoff coefficient(42.84%),and soil loss(11.3 t)were observed when the CT treatment was *** contrast,the lowest runoff volume(67.95 m3),runoff coefficient(11.35%),and soil loss(1.05 t)were observed when the ZT treatment was *** soil organic carbon and aggregate mean weight diameter were found to be significantly greater(with mean values of 0.79%and 1.19 mm,respectively)with the ZT treatment than with the CT *** the tilled treatments(CT and MT),substantial changes in the saturated soil hydraulic conductivity(ks),near-saturated soil hydraulic conductivity(k),and water-conducting porosity(ε)were observed between two crop *** three soil parameters were significantly higher in the period after maize harvesting than in the wheat growing *** contrast,no significant difference in these soil parameters was found when the untilled treatment(ZT)was carried *** regard to the slope positions,ks,k,andεshowed different behaviors under different *** toe slope position showed significantly lower ks andεvalues than the summit and middle slope *** the evaluated tillage practices,ZT was found to be the most promising means to improve the soil hydro-physical properties and effectively reduce surface runoff and soil erosion.

关键词： Hydraulic conductivity Macropore Conservation tillage Spatiotemporal variability Soil erosion

Near-saturated soil hydraulic conductivity and pore characteristics as influenced by conventional and conservation tillage practices in North-West Himalayan region,India

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International Soil and Water Conservation Research 2021年第2期9卷 249-259页

作者： deepak Singh Alok kumar Mishra Sridhar Patra sankar Mariappan Nisha Singh ICAR-Indian Institute of Soil and Water Conservation Dehradun248195UttarakhandIndia Sam Higginbottom University of Agriculture Technology and SciencesPrayagraj211007U.PIndia Hemvati Nandan Bahuguna Garhwal University(A Central University) Srinagar(Garhwal)246174UttarakhandIndia

Tillage plays an important role in modifying soil hydraulic *** objective of the present study was to evaluate the effect of conservation tillage practices in a maize-wheat cropping system on nearsaturated soil hydraulic properties and pore characteristics in the North-West Himalayan region,*** treatments *** tillage(CT),minimum tillage(MT),and zero tillage(ZT)were evaluated in terms of field saturated hydraulic conductivity(ks),unsaturated hydraulic conductivity k(h),the inverse of capillary length(a),flow-weighted mean pore radius(r0),numbers of pores per square meter(n0)and water-conducting macroporosity(Ɛ).The above hydraulic conductivity and pore characteristics were derived from steady-state water flux(q)measured using hood infiltrometer at 0,1,and3 cm pressure head for each treatment after seven years of establishment of this tillage *** revealed significantly(pdƐin ZT as compared with *** had intermediate *** a values suggested a greater gravity-dominated flow under ZT and MT as compared with *** of r0 values indicated better connectivity of pores in ZT and MT as compared with *** flow suggested that on average pore radii,>0.50 mm conducted about 63.60,68.01,and 75.97%of total flow(at 0 cm pressure head)in the corresponding water-conducting macroporosity of 0.00030,0.00044,and 0.00069%of soil volume under CT,MT,and ZT,***,zero-tillage based agriculture system was found to improve near-saturated soil hydraulic properties.

关键词： Near-saturated hydraulic conductivity Macropores Tillage Flow weighted mean pore radius Water-conducting macroporosity