A multi-objective wholesaler–retailers inventory-distribution model with controllable lead-time based on probabilistic fuzzy set and triangular fuzzy number

This paper develops a single wholesaler and multi retailers mixture inventory distribution model for a single item involving controllable lead-time with backorder and lost sales. The retailers purchase their items from the wholesaler in lots at some intervals throughout the year to meet the customers’ demand. Not to loose the demands, the retailers offer a price discount to the customers on the stock-out items. Here, it is assumed that the lead-time demands of retailers are uncertain in both stochastic and fuzzy sense, i.e., these are simultaneously random and imprecise. To implement this behavior of the lead-time demands, at first, these demands are assumed to be random, say following a normal distribution. With these random demands, the expected total cost for each retailer is obtained. Now, the mean lead-time demands (which are crisp ones) of the retailers are fuzzified. This fuzzy nature of the lead-time demands implies that the annual average demands of the retailers must be fuzzy numbers, suppose these are triangular fuzzy numbers. Using signed distance technique for defuzzification, the estimate of total costs for each retailer is derived. Therefore, the problem is reduced to optimize the crisp annual costs of wholesaler and retailers separately. The multi-objective model is solved using Global Criteria method. Numerical illustrations have been made with the help of an example taking two retailers into consideration. Mathematical analyses have been made for global pareto-optimal solutions of the multi-objective optimization problem. Sensitivity analyses have been made on backorder ratio and pareto-optimal solutions for wholesaler and different retailers are compared graphically.     

Synthesis,characterization, and in vitro biological evaluation of highly stable diversely functionalized superparamagnetic iron oxide nanoparticles

In this article, we report the design and synthesis of a series of well-dispersed superparamagnetic iron oxide nanoparticles (SPIONs) using chitosan as a surface modifying agent to develop a potential T ₂ contrast probe for magnetic resonance imaging (MRI). The amine, carboxyl, hydroxyl, and thiol functionalities were introduced on chitosan-coated magnetic probe via simple reactions with small reactive organic molecules to afford a series of biofunctionalized nanoparticles. Physico-chemical characterizations of these functionalized nanoparticles were performed by TEM, XRD, DLS, FTIR, and VSM. The colloidal stability of these functionalized iron oxide nanoparticles was investigated in presence of phosphate buffer saline, high salt concentrations and different cell media for 1 week. MRI analysis of human cervical carcinoma (HeLa) cell lines treated with nanoparticles elucidated that the amine-functionalized nanoparticles exhibited higher amount of signal darkening and lower T ₂ relaxation in comparison to the others. The cellular internalization efficacy of these functionalized SPIONs was also investigated with HeLa cancer cell line by magnetically activated cell sorting (MACS) and fluorescence microscopy and results established selectively higher internalization efficacy of amine-functionalized nanoparticles to cancer cells. These positive attributes demonstrated that these nanoconjugates can be used as a promising platform for further in vitro and in vivo biological evaluations.     

Generation and characterization of stable, highly concentrated titanium dioxide nanoparticle aerosols for rodent inhalation studies

The intensive use of nano-sized titanium dioxide (TiO₂) particles in many different applications necessitates studies on their risk assessment as there are still open questions on their safe handling and utilization. For reliable risk assessment, the interaction of TiO₂ nanoparticles (NP) with biological systems ideally needs to be investigated using physico-chemically uniform and well-characterized NP. In this article, we describe the reproducible production of TiO₂ NP aerosols using spark ignition technology. Because currently no data are available on inhaled NP in the 10?C50 nm diameter range, the emphasis was to generate NP as small as 20 nm for inhalation studies in rodents. For anticipated in vivo dosimetry analyses, TiO₂ NP were radiolabeled with ⁴⁸V by proton irradiation of the titanium electrodes of the spark generator. The dissolution rate of the ⁴⁸V label was about 1% within the first day. The highly concentrated, polydisperse TiO₂ NP aerosol (3?C6 × 10⁶ cm^?3) proved to be constant over several hours in terms of its count median mobility diameter, its geometric standard deviation, and number concentration. Extensive characterization of NP chemical composition, physical structure, morphology, and specific surface area was performed. The originally generated amorphous TiO₂ NP were converted into crystalline anatase TiO₂ NP by thermal annealing at 950 °C. Both crystalline and amorphous 20-nm TiO₂ NP were chain agglomerated/aggregated, consisting of primary particles in the range of 5 nm. Disintegration of the deposited TiO₂ NP in lung tissue was not detectable within 24 h.     

A facile strategy for the fabrication of uniform CdS nanowires with high yield and its controlled morphological growth with the assistance of PEG in hydrothermal route

A series of novel wurtzite cadmium sulphide (CdS) nanowires with uniform diameter were synthesized by using a rapid and simple solvothermal route. CdS nano structures with certain morphology could be selectively produced by only varying the concentration of poly ethylene glycol (PEG) as a surfactant in the reaction system with cadmium acetate, sulphur powder and ethelynediamine (EDA). We extensively studied UV-vis absorption spectra, photoluminescence spectra after confirming CdS nanowires with diameter 24-25 nm and length ranging up to several nano meters by field emission scanning electron microscopy (FE-SEM). Therefore we may definitely propose a new formation mechanism of CdS nanowires assisted by PEG with its illustrating optical properties.     

A transportation problem with fuzzy-stochastic cost

In this paper, we consider some transportation problems (TPs) with different types of fuzzy-stochastic unit transportation costs and budget constraints. These fuzzy stochastic costs are reduced to corresponding crisp ones in two different ways. For the first method, using the definition of α$\alpha$-cut of the fuzzy numbers, expectation is taken separately on both lower and upper α$\alpha$-cuts and then mean expectation is calculated with the help of signed distance. In the second procedure, we realize fuzzy random events (ξ?r)$(\xi ?r)$ and (ξ?r)$(\xi ?r)$ for the fuzzy random variable (ξ)$(\xi )$. Using credibility measure of these events, mean chances for the above fuzzy random events are calculated and then expectation is taken to get the crisp expressions. The reduced deterministic problems of the fuzzy stochastic TP are solved using a real coded genetic algorithm with Roulette wheel selection, arithmetic crossover and random mutation. Few numerical examples are demonstrated to find the optimal solutions of the proposed models.     

Two storage inventory model with fuzzy deterioration over a random planning horizon

An inventory model for a deteriorating item with stock dependent demand is developed under two storage facilities over a random planning horizon, which is assumed to follow exponential distribution with known parameter. For crisp deterioration rate, the expected profit is derived and maximized via genetic algorithm (GA). On the other hand, when deterioration rate is imprecise then optimistic/pessimistic equivalent of fuzzy objective function is obtained using possibility/necessity measure of fuzzy event. Fuzzy simulation process is proposed to maximize the optimistic/pessimistic return and finally fuzzy simulation-based GA is developed to solve the model. The models are illustrated with some numerical data. Sensitivity analyses on expected profit function with respect to distribution parameter λ and confidence levels α₁ and α₂ are also presented.     

Small-angle neutron scattering studies on water soluble complexes of poly(ethylene glycol)-based cationic random copolymer and SDS

The interaction of cationic random copolymers of methoxy poly(ethylene glycol) monomethacrylate and (3-(methacryloylamino)propyl) trimethylammonium chloride with oppositely charged surfactant, sodium dodecyl sulphate, and the influence of surfactant association on the polymer conformation have been investigated by small-angle neutron scattering. SANS data showed a positive indication of the formation of RCPSDS complexes. Even though the complete structure of the polyion complexes could not be ascertained, the results obtained give us the information on the local structure in these polymer-surfactant systems. The data were analysed using the log-normal distribution of the polydispersed spherical aggregate model for the local structure in these complexes. For all the systems the median radius and the polydispersity were found to be in the range of 20 ± 2 Å and 0.6 ± 0.05, respectively.     

Two-storage inventory model with lot-size dependent fuzzy lead-time under possibility constraints via genetic algorithm

Multi-item inventory models with stock dependent demand and two storage facilities are developed in a fuzzy environment where processing time of each unit is fuzzy and the processing time of a lot is correlated with its size. These are order-quantity reorder-point models with back-ordering if required. Here possibility and crisp constraints on investment and capacity of the small storehouse respectively are considered. The models are formulated as fuzzy chance constrained programming problem and is solved via generalized reduced gradient (GRG) technique when crisp equivalent of the constraints are available. A genetic algorithm (GA) is developed based on fuzzy simulation and entropy where region of search space gradually decreases to a small neighborhood of the optima and it is used to solve the models whenever the equivalent crisp form of the constraint is not available. The models are illustrated with some numerical examples and some sensitivity analyses have been done. For some particular cases results observed via GRG and GA are compared.