K. Maity

A two warehouse supply-chain model under possibility/ necessity/credibility measures

This article presents a joint performance of a supply chain (SC) with two warehouse facilities. A realistic two warehouse multi-collection-production-inventory model with constant/stock dependent demand, defective production system and fuzzy budget constraint has been formulated in an SC context. Here rate of defectiveness follows a probability distribution and fuzzy constraint is imposed in a necessity/possibility/credibility sense and defuzzied following fuzzy relations. The rates of collection for each raw material and production are assumed as control variables. Also the defective units are screened along with production and reworked with a known rework rate. The model is reduced to the equivalent deterministic one of minimizing the expected total cost with imprecise demand through possibility, necessity or convex combination of them (credibility). All these formulations are solved using Generalized Reduced Gradient (GRG) technique. The model is illustrated numerically for different types of demands and with respect to those demands, the optimal production and stock level are presented in both tabular and graphical forms. The sensitivity of the total operating cost on the variation of capacity of the market warehouse is also presented to illustrate the advantage of a two warehouse system in SC.

Structural characterization of an immunoenhancing heteroglycan isolated from an aqueous extract of an edible mushroom, Lentinus squarrosulus (Mont.) Singer.

A water-soluble polysaccharide, isolated from the hot water extract of the fruiting bodies of an edible mushroom, Lentinus squarrosulus (Mont.) Singer was found to contain d-galactose, l-fucose, and d-glucose in a molar ratio of nearly 1:1:5. Structural investigation of the polysaccharide was carried out using acid hydrolysis, methylation analysis, periodate oxidation study, and NMR experiments ((1)H, (13)C, DQF-COSY, TOCSY, NOESY, ROESY, HMQC, and HMBC). On the basis of above-mentioned experiments, the structure of the repeating unit of the polysaccharide was established as: This polysaccharide showed macrophage as well as splenocyte and thymocyte activation.

A single period inventory model with imperfect production and stochastic demand under chance and imprecise constraints

Abstract This paper develops a mathematical model for a single period multi-product manufacturing system of stochastically imperfect items with continuous stochastic demand under budget and shortage constraints. After calculating expected profit in general form in terms of density functions of the demand and percentage of imperfectness, particular expressions for those density functions are considered. Here the constraints are of three types: (i) both are stochastic, (ii) one stochastic and other one imprecise (fuzzy) and (iii) both imprecise. The stochastic constraints have been represented by chance constraints and fuzzy constraints in the form of possibility/necessity constraints. Stochastic and fuzzy constraints are transformed to equivalent deterministic ones using ‘here and now’ approach and fuzzy relations respectively. The deterministic problems are solved using a non-linear optimization technique-Generalized Reduced Gradient Method. The model is illustrated through numerical examples. Sensitivity analyses on profit functions due to different permitted ‘aspiration’ and ‘confidence’ levels are presented.

Possibility and necessity constraints and their defuzzification—A multi-item production-inventory scenario via optimal control theory

Abstract In this paper, analogous to chance constraints, real-life necessity and possibility constraints in the context of a multi-item dynamic production-inventory control system are defined and defuzzified following fuzzy relations. Hence, a realistic multi-item production-inventory model with shortages and fuzzy constraints has been formulated and solved for optimal production with the objective of having minimum cost. Here, the rate of production is assumed to be a function of time and considered as a control variable. Also the present system produces some defective units along with the perfect ones and the rate of produced defective units is constant. Here demand of the good units is time dependent and known and the defective units are of no use. The space required per unit item, available storage space and investment capital are assumed to be imprecise. The space and budget constraints are of necessity and/or possibility types. The model is formulated as an optimal control problem and solved for optimum production function using Pontryagin’s optimal control policy, the Kuhn–Tucker conditions and generalized reduced gradient (GRG) technique. The model is illustrated numerically and values of demand, optimal production function and stock level are presented in both tabular and graphical forms. The sensitivity of the cost functional due to the changes in confidence level of imprecise constraints is also presented.

A heteroglycan from the mycelia of Pleurotus ostreatus: structure determination and study of antioxidant properties

A heteroglycan (PS) isolated from the mycelia of Pleurotus ostreatus was found to consist of l-fucose, d-mannose, and d-glucose in a molar ratio of nearly 1:2:3. On the basis of acid hydrolysis, methylation analysis, periodate oxidation, and NMR studies (1H, 13C, TOCSY, DQF-COSY, NOESY, ROESY, HSQC, HMBC, and DEPT), the structure of the repeating unit of the PS was determined. The repeating unit had a branched backbone composed of (1→6)-linked α and βd-glucose and (1→2)-linked α-l-fucose. Branching occurred at C-4 position of (1→6)-linked α-d-glucopyranosyl residue with terminal β-d-mannose and C-3 position of (1→6)-linked β-d-glucopyranosyl residue with (1→6)-α-d-mannopyranosyl moiety terminated by α-d-glucose. The structure of the repeating unit of the PS was proposed as: [formula: see text]. The antioxidant properties of the PS were studied. The scavenging activity of hydroxyl free radicals whose EC50 value of PS at 943 μg/mL was determined. Further, EC50 value of the PS at 53 μg/mL was observed for scavenging activity of superoxide free radicals. Chelating effects (54.82%) of ferrous ions were observed at 1mg/mL of the PS.

Chemical analysis of an immunoenhancing water-soluble polysaccharide of an edible mushroom, Pleurotus florida blue variant

An immunoenhancing polysaccharide isolated from the aqueous extract of the fruit bodies of the mushroom, Pleurotus florida blue variant, was found to consist of d-glucose and d-galactose in a molar ratio of nearly 5:1. On the basis of sugar analysis, methylation analysis, periodate oxidation, Smith degradation, and NMR studies ((1)H, (13)C, DEPT-135, DQF-COSY, TOCSY, NOESY, ROESY, HMQC, and HMBC), the structure of the repeating unit of the polysaccharide was established as: →6)-β-D-Glcp-(1→3)-α-D-glcp-(1→[6)-β-D-Glcp-(1]3→ α-D=Glcp. The molecule activated macrophages, splenocytes, and thymocytes.

A heteropolysaccharide from aqueous extract of an edible mushroom, Pleurotus ostreatus cultivar: structural and biological studies.

A water soluble polysaccharide isolated from the hot aqueous extract of Pleurotusostreatus cultivar was found to contain d-glucose and d-galactose in a molar ratio of nearly 7:1. Structural investigation was carried out using acid hydrolysis, methylation analysis, periodate oxidation, Smith degradation, and NMR studies ((1)H, (13)C, DEPT-135, TOCSY, DQF-COSY, NOESY, ROESY, HMQC, and HMBC). On the basis of the above mentioned experiments the structure of the repeating unit of the polysaccharide was established as: This heteroglycan stimulates macrophages, splenocytes, and thymocytes.

Chemical analysis of new water-soluble (1→6)-, (1→4)-α, β-glucan and water-insoluble (1→3)-, (1→4)-β-glucan (Calocyban) from alkaline extract of an edible mushroom, Calocybe indica (Dudh Chattu)

Two different glucans (PS-I, water-soluble; and PS-II, water-insoluble) were isolated from the alkaline extract of fruit bodies of an edible mushroom Calocybe indica. On the basis of acid hydrolysis, methylation analysis, periodate oxidation, and NMR analysis ((1)H, (13)C, DEPT-135, TOCSY, DQF-COSY, NOESY, ROESY, HMQC, and HMBC), the structure of the repeating unit of these polysaccharides were established as: PS-I: →6)-β-D-Glcp-(1→6)-β-D-glcp-(1→6)-)-β-D-Glcp-(1→ α-D=Glcp (Water-soluble glucan). PS-II: →3)-β-D-Glcp-(1→3)-β-D-glcp-(1→3)-)-β-D-Glcp-(1→3)-β-D-Glcp-(1→ β-D-Glcp (Water-insoluble glucan, Calocyban).

A Chebyshev approximation for solving the optimal production inventory problem of deteriorating multi-item

In this paper, some realistic multi-period production-inventory models are formulated for deteriorating items with known dynamic demands for optimal productions. Here, the rates of production are time dependent (quadratic/linear) or constant expressed by a Chebyshev polynomial and considered as a control variable. The models are solved using Chebyshev spectral approximations, the El-Hawary technique and a genetic algorithm (GA). The models have been illustrated by numerical data. The optimum results for different production functions are presented in both tabular and graphical forms.

Optimal inventory policies for deteriorating complementary and substitute items

The optimal production for an inventory control system of deteriorating multi-items where items are either complementary and/or substitute is formulated with a resource constraint. Here, the production function is unknown and considered as a control variable. Also, the deterioration rates of the items are either stock dependent or constant. The demand is stock dependent, shortages are not allowed and deteriorated items are salvaged. The total profit, which consists of the sales proceeds, production cost, inventory holding cost, salvage value, is formulated as a Pontryagins Optimal Control problem for both steady and transient states and evaluated using Taylors theorem, generalised reduced gradient technique and optimal control theory satisfying the Generalised Legendre conditions. The model is formulated in general form for n-items, and in particular, is illustrated with three items for some numerical data. The optimum results are presented both in tabular form and graphically.