This paper deals with the degree constrained k-cardinality minimum spanning tree (k-MSTPD) problem defined on a connected, edge weighted and undirected graph. The aim of this problem is to determine the least weighted spanning tree with exactly k vertices such that except the root vertex, no other vertex in the resultant spanning tree exceeds the specified degree limit. The k-MSTPD problem has many practical applications for the design of electric, communication, and transportation networks. The problem is then formulated as a zero-one programming. In this paper, an exact algorithm known as Lexi-search algorithm (LSA) is developed to tackle the k-MSTPD problem. Furthermore, the developed LSA is programmed in Matlab and tested on some benchmark instances as well as on random instances and the respective results are reported. The obtained experimental results showed that the developed LSA takes significantly less time to find the optimal solutions.

In this paper, the ranking performance of six most popular and easily comprehensive multi-criteria decision-making (MCDM) methods, i.e. weighted sum method (WSM), weighted product method (WPM), weighted aggregated sum product assessment (WASPAS) method, multi-objective optimization on the basis of ratio analysis and reference point approach (MOORA) method, and multiplicative form of MOORA method (MULTIMOORA) is investigated using two real time industrial robot selection problems. Both single dimensional and high dimensional weight sensitivity analyses are performed to study the effects of weight variations of the most important as well as the most critical criterion on the ranking stability of all the six considered MCDM methods. The identified local weight stability interval indicates the range of weights within which the rank of the best alternative remains unaltered, whereas, the global weight stability interval determines the range of weights within which the overall rank order of all the alternatives remains unaffected. It is observed that for both the problems, multiplicative form of MOORA is the most robust method being least affected by the changing weights of the most important and the most critical criteria.

When a supplier announces a price increase at a certain time in the future, for each retailer it is important to choose whether to purchase supplementary stock to take benefit of the current lower price or procure at a new price. This article focuses on the possible effects of price increase on a retailer’s replenishment strategy for constant deterioration of items. Here, quadratic demand is debated; which is appropriate for the products for which demand increases initially and subsequently it starts to decrease with the new version of the substitute. We discuss two scenarios in this study: (I) when the special order time coincides with the retailer’s replenishment time and (II) when the special order time falls during the retailer’s sales period. We determine an optimal ordering policy for each case by maximizing total cost savings between special and regular orders during the depletion time of the special order quantity. Scenarios are established and illustrated with numerical examples. Through, sensitivity analysis important inventory parameters are classified. Graphical results, in two and three dimensions, are exhibited with supervisory decision.

Trade credit mainly signifies increase in order quantity when retailer offers a trade credit to the customer. From the customer’s view, granting trade credit not only increases sales and revenue but also increases opportunity cost. So, the choice to offer trade credit is an important managerial consideration. Moreover another significant decision on purchasing is to include (or not to include) cash discount benefits and the motivations behind it. Therefore, the major objective of this article is to derive the inventory models for deteriorating items by maximizing the total profit of the retailer. The models includes the cash discount for the retailer depending on ordering quantity and also cash discount for the customer depending on the time. The customer’s demand is expressed as a function of time and price, which is appropriate for the products for which demand increases initially and after sometime it starts to decrease. Lastly, numerical examples along with sensitivity analysis are done, which extracts some fruitful managerial insights.

The present study investigates an inventory model for non-instantaneous deteriorating items under inflationary conditions with partially backlogged shortages. In today’s market structure consumers are looking for goods for which there is a delay in deterioration. At the same time, the consumers’ willingness to wait has been decreased over time, which leads to lost sales. Moreover in financial decision-making, the effects of inflation and time value of money cannot be oblivious to an inventory system. In this scenario, managing inventory of goods remains a challenging task for the decision makers, who may also have to rent warehouse under different prevailing factors such as, bulk discount, limited space in the retail outlet, or increasing inflation rates. With a focus on reduction of costs and increasing customer service, warehouse decision models are crucial for an organization’s profitability. Hence a mathematical model has been developed in the view of above scenario, in order to determine the optimal policy for the decision maker, by minimizing the present worth of total cost. The optimization procedure has been illustrated by a numerical example and detailed sensitivity analysis of the optimal solution has been performed to showcase the effect of various parameters. Managerial implications has also been presented to aid the decision making process.

A clean and efficient, mediated in water and assisted by ultrasound method for the synthesis of a series of N-substituted 1-amino-3-ferrocenyl-3-oxoprop-1-enes starting from acetyl ferrocene was developed. Our approach offers shortening of the reaction time under the mild reaction conditions and easy work up procedure.

Pioglitazone hydrochloride (PGH) is an oral anti-hyperglycemic agent used in the treatment of type-2 diabetes mellitus. Potassium permanganate was found to oxidize PGH both in acidic and basic conditions, based on which two simple and sensitive methods were developed for its determination in bulk sample and tablets, and validated. In the first method (indirect method), PGH was reacted with a measured excess of standard permanganate in H₂SO₄ medium, and the residual oxidant was determined by measuring its absorbance at 550 nm. The second method (Direct method) entails treating PGH with permanganate in NaOH medium, followed by the measurement of the resulting bluish-green manganite at 610 nm. Experimental variables affecting the reactions were studied and optimized. Under optimum conditions, linear relationships with good correlation coefficients were found between absorbance and concentration in the ranges, 1.25 – 25 µg mL^-1 (Indirect method) and 1-12 µg mL^-1 (Direct method) with respective molar absorptivity values of 1.10 × 10⁴ and 2.77 × 10⁴ l mol^-1 cm^-1. The limits of detection (LOD) and quantification (LOQ) were 0.36 and 1.08 (Indirect method) and 0.23 and 0.69 µg mL^-1 (Direct method). Intra-day and inter-day precisions were satisfactory, with %RSD values of ≤2.11, and the respective accuracies were excellent with %RE values of ≤2. The methods were also validated for robustness, ruggedness and selectivity. The methods were applied to the determination of PGH in its tablets with good accuracy and precision, and no interference from the tablet additives was encountered. The results were also compared with those obtained by a reference method.

An ecofriendly methods for the synthesis of medicinally important class of heterocyclic scaffold, pyrazole 4-carbonitrile derivatives by one pot three component reaction of malononitrile, phenyl hydrazine and aromatic aldehyde has been achieved at room temperature. Greener protocols of reaction are followed by using sodium chloride to accelerate the reaction in aqueous media. Present methodology is a condition based divergence on synthesis of pyrazole by using simple salts, which offers several advantages like use of aqueous media and high yield of product along with short reaction time, simple work up procedure, no waste or by products, avoid the use of heavy metals or nanoparticles are the fascinating characteristics of reaction.

An ecofriendly methods for the synthesis of medicinally important class of heterocyclic scaffold, pyrazole 4-carbonitrile derivatives by one pot three component reaction of malononitrile, phenyl hydrazine and aromatic aldehyde has been achieved at room temperature. Greener protocols of reaction are followed by using sodium chloride to accelerate the reaction in aqueous media. Present methodology is a condition based divergence on synthesis of pyrazole by using simple salts, which offers several advantages like use of aqueous media and high yield of product along with short reaction time, simple work up procedure, no waste or by products, avoid the use of heavy metals or nanoparticles are the fascinating characteristics of reaction.