Overall software management generally includes software testing as an important aspect. Defect prediction in software is an important activity for testing a software. Hybrid models which include statistical and machine learning techniques have become very popular in recent days for predicting existence of errors in a software. Till recently software reliability models were developed based on the number of undetected bugs. However, some recent works on software reliability drastically changed the idea of estimating software reliability. The newly developed concept of “bug size” in a software is used in this article along with a proven hybrid method to predict software reliability. We have used this new method on several NASA data sets. Several standard criteria have been used to examine the efficacy of the proposed method and we obtained much better results compared to the earlier results on similar data sets.

The critical nexus of sustainable manufacturing and logistics within the supply chain is pivotal for safeguarding the environment and navigating uncertain market landscapes. This study meticulously explores the intricate interplay between ecological commitments and the adaptability of risk coefficients, scrutinizing their impact on operational efficacy, production dynamics, and value chain optimization. Firstly, we have designed a dual-channel supply chain model that includes the supplier, green manufacturer, and sustainable retailer. Pricing and greening decisions across the multi-layered supply chain have been optimized meticulously by incorporating risk aversion effects into the utility function. Market demand is uncertain and highly sensitive to product price and level of green attributes. Secondly, in order to compare the optimal decision, the effectiveness of the supply chain has been analyzed under different business perspectives, which are centralized, decentralized, and rewards contracts with target green level with the help of the leader-follower Stackelberg game approach. The analytical results delve into the impact of supply chain contracts, revealing the way the retailer’s incentives shape manufacturer’s green initiatives and members’ risk aversion preferences. The numerical findings illustrate the manufacturer’s advancement in green manufacturing, achieving peak green product levels and higher profitability, contrasting centralized and decentralized marketing scenarios in the dual-channel model. Finally, some managerial insights with a sensitivity of major elasticity parameters have been addressed to achieve the performance of the supply chain.

Software reliability estimation is one of the most active areas of research in software testing. Since time between failures (TBF) has often been challenging to record, software testing data are commonly recorded as test-case-wise in a discrete set up. We have developed a Bayesian generalised linear mixed model (GLMM) based on software testing detection data and a size-biased strategy which not only estimates the software reliability, but also estimates the total number of bugs present in the software. Our approach provides a flexible, unified modelling framework and can be adopted to various real-life situations. We have assessed the performance of our model via simulation study and found that each of the key parameters could be estimated with a satisfactory level of accuracy. We have also applied our model to two empirical software testing data sets. While there can be other fields of study for application of our model (e.g., hydrocarbon exploration), we anticipate that our novel modelling approach to estimate software reliability could be very useful for the users and can potentially be a key tool in the field of software reliability estimation.

The demand for a product is influenced by a number of factors, including the selling price and the displayed stock level, among others. Considering this scenario, an EOQ inventory model is developed where demand is a function of both selling price and the inventory level which is one of the main contributions of this research work. Holding cost is assumed to be nonlinearly dependent on stock. Besides that, supplier grants a full trade credit policy to the retailer. This policy is very advantageous for both the counterpart—the supplier as well as the retailer. The supplier can attract more customers by offering a delay period whereas the latter enjoys the benefit of getting goods without instant payment. The proposed mathematical model aims to find out the optimal selling price and optimal length of the replenishment cycle so as to maximize the total profit of the retailer per unit time. Several theorems are well-established in order to reach to the optimal solution. A numerical example is also presented to demonstrate the suggested inventory model, and a sensitivity analysis is executed to highlight the findings of the inventory model and put forward valuable managerial insights. This research work can be helpful to the business communities facing nonlinear demand patterns. Businesses that want to offer trade credit policies but are dealing with nonlinear holding costs may also find it helpful. Sensitivity analysis can be useful in determining the impact of various cost parameters on the total generated profit.

Frequentist and Bayesian methods differ in many aspects but share some basic optimal properties. In real-life prediction problems, situations exist in which a model based on one of the above paradigms is preferable depending on some subjective criteria. Nonparametric classification and regression techniques, such as decision trees and neural networks, have both frequentist (classification and regression trees (CARTs) and artificial neural networks) as well as Bayesian counterparts (Bayesian CART and Bayesian neural networks) to learning from data. In this paper, we present two hybrid models combining the Bayesian and frequentist versions of CART and neural networks, which we call the Bayesian neural tree (BNT) models. BNT models can simultaneously perform feature selection and prediction, are highly flexible, and generalise well in settings with limited training observations. We study the statistical consistency of the proposed approaches and derive the optimal value of a vital model parameter. The excellent performance of the newly proposed BNT models is shown using simulation studies. We also provide some illustrative examples using a wide variety of standard regression datasets from a public available machine learning repository to show the superiority of the proposed models in comparison to popularly used Bayesian CART and Bayesian neural network models.

The efficacy of an integrated approach to supply chain decision-making has demonstrated cost-effectiveness in contrast to the traditional sequential decision-making strategy. This has inspired researchers to challenge conventional practices and emphasize the importance of integrated decision-making in the realm of supply chains. This article addresses a multi-period multi-echelon location-inventory-routing problem consisting of a single factory, multiple distribution centres, and multiple retailers where important managerial decisions such as the location of distribution centres, vehicle routing schedule, delivery quantity to the various retailers, and replenishment schedule of the distribution centres are determined in different time periods so as to minimize the total cost of the supply chain which is one of the significant contributions of this research work. To solve the mathematical model, a novel chromosome representation is designed, specifically tailored for genetic algorithm, adding an innovative dimension to this research. To ascertain the results, different selection mechanisms of the genetic algorithm have been employed. The determined results are also compared with particle swarm optimization. The study reveals that genetic algorithm with tournament selection criteria gives the best optimal solution compared to the other algorithms for the proposed mathematical model in all the numerical instances. Further, a sensitivity analysis is also carried out to highlight the impact of various input parameters and provide relevant managerial insights.

Hardware and software together are now part and parcel of almost all the modern devices. Hence, the study of both hardware reliability and software reliability has become very important in order to ensure availability of the devices. There are several distinct differences between hardware and software, and hence, even though the definition of reliability in both the cases remains the same, finding out reliability of a hardware may call for a different methodology than that for a software. Since a software cannot be seen, nor can it be touched, finding out reliability of a software becomes difficult as such. In this chapter we discuss in brief the concepts and methodologies adopted to find out reliabilities of software and hardware. We also discuss some basic differences between hardware and software. A few important methods used for estimating hardware and software reliability have been discussed in brief. A thorough bibliography has been provided for the readers to look into the details of the methodologies wherever required.

Traditional statistical learning algorithms perform poorly in case of learning from an imbalanced dataset. Software defect prediction (SDP) is a useful way to identify defects in the primary phases of the software development life cycle. This SDP methodology will help to remove software defects and induce to build a cost-effective and good quality of software products. Several statistical and machine learning models have been employed to predict defects in software modules. But the imbalanced nature of this type of datasets is one of the key characteristics, which needs to be exploited, for the successful development of a defect prediction model. Imbalanced software datasets contain non-uniform class distributions with most of the instances belonging to a specific class compared to that of the other class. We propose a novel hybrid model based on Hellinger distance-based decision tree (HDDT) and artificial neural network (ANN), which we call as hybrid HDDT-ANN model, for analysis of software defect prediction (SDP) data. This is a newly developed model which is found to be quite effective in predicting software bugs. A comparative study of several supervised machine learning models with our proposed model using different performance measures is also produced. Hybrid HDDT-ANN also takes care of the strength of a skew-insensitive distance measure, known as Hellinger distance, in handling class imbalance problems. A detailed experiment was performed over ten NASA SDP datasets to prove the superiority of the proposed method.

As global governments pay more attention to environmental issues, the idea of environmental protection has now been incorporated into the supply chain, and green supply chain management has become particularly significant. As such, this paper proposes a three-layer green supply chain model with a dual-channel structure consisting of a supplier, a manufacturer, and a retailer. The manufacturer sells the product through a (a) traditional retail-channel or (b) direct online-channel. The manufacturer sets a green product standard, while the government offers a subsidy to the manufacturer for green investment. We analyze the optimal decision under government subsidy and no government subsidy to maintain the profit maximization criteria of the supply chain. In addition, both the centralized and decentralized marketing strategies are evaluated using the Stackelberg game approach. To achieve the best pricing decisions for supply chain members, we compare the optimal pricing under consistent and inconsistent sales prices in both online and offline channels. The prime objective of the paper is to explore and compare the optimal pricing strategy with and without government subsidy pertaining to maximizing the overall profit of the supply chain. The numerical illustration and sensitivity analysis indicate that government subsidy can reduce the cost of green items and is beneficial to both manufacturer and supplier. Our research findings can lead to better decisions with and without government subsidy for members of the dual-channel green supply chain as well as enhance green product market competitiveness.

Academicians and practitioners have focused a lot of attention on the separate issues of pricing and inventory control in a competitive setting. However, integrating these choices in a competitive environment has received scant attention for deteriorating inventory systems from academics despite being crucial to practitioners. From this perspective, our research focuses on designing a supply chain model with inventory coordination to reflect time systems with improved accuracy and optimal control systems. In this research, we develop a two-layer supply chain model consisting of one manufacturer and one retailer incorporating the inventory classification of the retailer. Price-sensitive market demand and two-parameter time-varying Weibull distribution deterioration have been assumed to develop the mathematical model. First, a collective decision on price and inventory control of a deteriorating product has been evaluated in a duopoly environment. Secondly, to explore the decentralized scenario, we have proposed the NSGA-II algorithm to solve the bi-objective programming problem of the two-layer supply chain. The paper aims to explore product collaborative pricing policies and the inventory decision of the deteriorating item in two-layer supply chain coordination. Finally, numerical research is conducted to execute the centralized supply chain and NSGA-II application in a decentralized supply chain. The research findings can provide valuable insights for members of the two-layer supply chain to make optimal product pricing and inventory scheduling decisions.

Due to the advancement of online marketing, many manufacturers have started to provide a return policy with refund agreements. This paper concerns return policy in a dual-channel supply green chain, wherein customers can buy the products through a traditional retail channel or direct online channel. Under sustainable improvement, we have developed the dual-channel supply chain system with a return strategy including refund via direct online channel. Market demand is dependent on product sales price, green label, and refund amount. Firstly, the supply chain members target to optimize their decision variables under a centralized decision model. Secondly, the entire supply chain members make their decision individually to maximize the overall profit using the non-cooperative Stackelberg game approach. The prime objectives of the paper are to find out the optimal sales price, wholesale price, green label, and refund price so that the profit of the supply chain will be maximized. By solving the game model, we compare the optimal decision under both scenarios and implement sensitivity observation, which helps to reflect the influence of critical parameters.

Late blight of potato caused by Phytophthora infestans is one of the most destructive diseases of potato world over. The devastation of the disease is very much related with climatic factors like temperature, relative humidity, fog or dew deposition and also sunshine hours. An experiment was conducted in Indo-Gangetic plains of West Bengal to know the effect of weather parameters on initiation and severity of the disease as well as progress and pattern of development of disease which will ultimately help to develop the effective spray schedule to manage the disease. From the experiment it is observed that 7 days prior to first appearance of late blight disease of potato the average maximum and minimum temperature varied between 24-26˚C and 7-8˚C respectively; average maximum and minimum relative humidity varied between 90-93% and 41-44% respectively; average sunshine hours per day varied between 6-8 hours. Correlation study of late blight disease severity with different weather parameters were also carried out. Maximum and minimum temperature as well as maximum and minimum relative humidity found to be positively correlated with late blight disease build up. While sunshine hour found to be negatively correlated with the disease build up. But only minimum temperature was significant at 0.01 level in all the planting dates and maximum temperature was significant at 0.01 level in two dates of planting. Apparent rate of infection of the disease and area under disease progress curve were calculated for different planting dates of potato. From the results it is evident that late blight of potato progressed almost in an exponential fashion starting from its first appearance. As the crop approached towards maturity and weather became unfavourable for the pathogen the rate of progress declined. This may be due to non-availability of healthy tissue.

Recently, phoma blight disease is causing a huge loss in potato tuber production. Plant pathologists have assigned numbers to represent the intensities of diseases based on eye estimated severity of diseases. This manual estimation method takes a lot of effort and times, and it might not always give the desired results. One of the cutting-edge methods to solve the aforementioned issue is automatic deep learning-based method. In this paper, the actual affected area from each leaflet has been segmented by K-means clustering and the percentage of the affected area from each leaflet has been calculated. The grading on each leaflet has been assigned based on a common eye estimated disease rating scale based on the percentage of the affected area. Several leaflets have been graded based on the above techniques. The same numbers of affected leaflets have been sent to several pathologists for eye estimated grading based on a common grading scale. The maximum similar grading from plant pathologists has been calculated and modal value has also been calculated. The relationship has been computed between eye estimated grading by plant pathologists and grading assigned by k-means clustering. The matching percentage is found 61.67%. The existing disease rating scale has been modified and it has been observed that the modified scale has been given 94.44% accuracy concerning eye estimated scoring by plant pathologists. The potato leaflets with affected Phoma blight with different severity levels have been collected. The leaflets have been grouped based on a modified scale. Deep learning using a convolution neural network has been developed to predict the Phoma blight disease severity. The accuracies have been predicted based on different confidence levels. The developed deep learning model may be used as a Phoma blight disease intensity prediction tool using healthy and affected potato leaflets.

Finding out optimum maintenance crew strength in an organization is a common problem with many industries. In this article we tried to formulate the problem as a queuing theory problem. It was also noted that priority queues concepts are needed in order to formulate a real life problem. The model developed also took note of absenteeism pattern of the maintenance crew, so that the solution becomes more realistic. The model thus developed is then applied to the data obtained from a manufacturing organization. Interestingly, it was observed that the optimum solution obtained suggests that the maintenance department had sufficient number of people to handle even the most critical period of the year when maximum production is attempted.