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Global warming and climate change become a sensitive issue worldwide, and many countries try to control the CO2emissions by investigating in many projects. This study proposes a sustainable inventory model to reduce carbon emission. It is generally assumed that demand is increasing at starting of an inventory level and decreasing at ending for a particular newly launched product. In this situation, demand is usually represented by Normal distribution or imprecise fuzzy demand. However, in reality, those assumptions do not always hold. In most of the inventory models, it is seen that demand is a linearly increasing function of time before starting deterioration; then, the demand decreases inversely proportional to the deterioration rate after starting the deterioration. To describe the possible situations more clearly, we introduce here a new type of demand, called as composite demand. Most of the products have a fixed life span for maintaining the quality in original condition which is known as non-instantaneous deterioration. Therefore, we design an inventory model for non-instantaneous deteriorating items with composite demand function. The deterioration rate is assumed to follow an exponential distribution; the holding cost is considered as time dependent. The model is formulated based on retailer’s perspective and, thereafter, the total cost for the retailer is calculated. Numerical examples are provided for better understanding of this model. The results show that the total profit for non-instantaneous deteriorating items is higher than for instantaneously deteriorating items. A sensitivity analysis is conducted based on the important parameters. Finally, the paper ends with conclusions and an outlook to future research.

Discussions of the resiliency, sustainability, and agility of supply chains are important in the research and management of supply chains in these difficult times, considering the ongoing pandemic of COVID-19. A viable supply chain is often characterized by resiliency, sustainability, and agility in its network design. Resiliency is essential because disruption and demand fluctuations are forced upon SCs, and the effects of these for many managerial supply chains are unknown. In addition, applying novel technology in the supply chain, such as blockchain, Internet-of-Things (IoT), and artificial intelligence (AI) as agility tools can assist and enable the transition to lean production. This special issue of the Foundations of Computing and Decision Sciences is dedicated to advancements in this fields. Besides, the special issue covers instructional information about OR techniques which are useful for addressing real-world applications on such challenges.

Waste management involved in various fields of global ecosystem that provides several positive effects for green environment and sustainable development. We devise a multi-objective solid transportation model of waste management problem in agriculture field and forest department for urban or rural development. Starting to end point of the problem covered by considering the objective functions as transportation cost, job opportunity and carbon emission. Carbon emission is restricted by the combination of several policies of carbon mechanism (carbon tax, cap-and-trade and offset policy). Various critical sitchs appear in such realistic process and uncertainty attached with related data. Here we prefer Pythagorean hesitant fuzzy environment to overcome deep uncertainty rather than single uncertainty. After that, we initiate a ranking approach to convert uncertain data into crisp data. To justify the appropriateness of the formulated model and to select the best policy of carbon mechanism, we study two industrial applications with various cases of such mechanism. To derive the Pareto-optimal solution of the problems, two fuzzy techniques, namely, fuzzy programming and Pythagorean hesitant fuzzy programming, are utilized here. Comparative study, model validation, sensitivity analysis, managerial insights and conclusions with future research scopes are outlined at last.

This special issue of the Foundations of Computing and Decision Sciences, titled “Computational Performance Analysis based on Novel Intelligent Methods: Exploration and Future Directions in Production and Logistics”, is devoted to the application of Computational Performance Analysis (CPA) for real-life phenomena. The special issue and its editorial present novel intelligent methods as they meet with various research topics in production and logistics, especially in terms of challenges, limitations and future trends. This special issue aims to bring together current progress on the CPA, organization management, and novel models and solution techniques that can contribute to a better understanding of the CPA systems and delineate useful practical strategies. Methodologically interesting and well-documented case studies are highly recommended. Additionally, the special issue covers innovative cutting-edge research methodologies and applications in the related research field.

In this paper, we formulate and solve an economic order quantity model with default risk. Our main purpose is to investigate retailer’s optimal replenishment time and credit period for deteriorating items under selling price-dependent demand while maximizing profit per unit time. Here, shortages are allowed and items are partially backlogged for interested customers. We show that optimal replenishment time and credit period not only exist but they are also unique. We solve the proposed problem analytically. An algorithm is presented to derive the optimal solution of the model. The mathematical model is evaluated by numerical examples. We use Mathematica to obtain a global maximum solution to the optimal cycle time and the optimal credit period for the proposed model. A sensitivity analysis with respect to major parameters is performed in order to examine the stability of our model. At the end of the paper, conclusions are drawn and an outlook of possible future directions is depicted.

The special issue: “Numerical Techniques Meet with OR” of the Foundations of Computing and Decision Sciences consists of two parts which are of the main theme of numerical techniques and their applications in multi-disciplinary areas. The first part of this special issue was already collected in the FCDS Vol. 46, issue 1. In this second part of our special issue editorial, a description of the special issue presents numerical methods which can be used as alternative techniques for Scientific Computing and led Operational Research applications in many fields for further investigation.

This paper addresses Acoustic Emission (AE) from Computer Numerical Control (CNC) machining operations. Experimental measurements are performed on the CNC lathe sensors to provide the power consumption data. To this end, a hybrid methodology based on the integration of an Artificial Neural Network (ANN) and a Shuffled Frog-Leaping Algorithm (SFLA) is applied to the data resulting from these measurements for data fusion from the sensors which is called SFLA-ANN. The initial weights of ANN are selected using SFLA. The goal is to assess the potency of the signal periodic component among these sensors. The efficiency of the proposed SFLA-ANN method is analyzed compared to hybrid methodologies of Simulated Annealing (SA) algorithm and ANN (SA-ANN) and Genetic Algorithm (GA) and ANN (GA-ANN).

This special issue of the Foundations of Computing and Decision Sciences, titled ”Numerical Techniques Meet with OR”, is devoted to the numerical techniques and their applications in real-world phenomena. The special issue and its editorial present numerical algorithms as they meet with different research topics such as, e.g., from operational research, supply chain management, geometrical structures and Covid-19 effects on financial applications. Besides, the special issue covers instructional information about numerical techniques which are useful for OR research problems and real-world applications on such issues.

In today's worldwide markets, supply chain members have to control carbon emissions for a clean environment. This study addresses a dual-channel green supply chain model by contemplating dual selling channels, carbon diminution rate and online delivery lead-time as marketing efforts to fascinate customers to buy more products. Moreover, the carbon tax protocol, green technology, carbon cap-and-trade protocol are applied to the supply chain to save the environment by reducing carbon emissions. The customers' demands for both the direct and traditional retail channels are dependent on direct selling price, retail price, carbon reduction rate, and delivery lead-time of online products. The objective of this work is to maximise the supply chain profit by minimising the amount of carbon emissions. To determine optimal outcomes, a centralised system, manufacturer-leadership Stackelberg game and retailer-leadership Stackelberg game are employed. A comparison among the centralised system and the two Stackelberg games is also carried out. The results presented that to enhance the profits of the manufacturer as well as retailer and to decline carbon emissions, manufacturer-leadership Stackelberg game is the adequate game policy. Some managerial inspirations of this proposed work are listed. The paper ends with conclusions and possible future research directions.

Productivity, profitability and sustainability have become the essence of business survival; thus, modern industrial establishments are turning into frameworks consistent with environmental objectives by adopting cleaner technologies, green practices have ultimately resulting in generation of fewer pollutants. Urbanization and burgeoning technological advancement in different sector within India have brought the concept of green supply chain management, to highlight the importance of responsible consumption and production to maintain environmental quality, reduce wastage and bring out economic growth. This paper aims to segregate the sustainable and competitive performers from the average ones in the Indian manufacturing sector and to understand the degree of the impact of green practices of supply chain management based on their contribution towards sustainable environment. Using survey method, data are collected from 54 manufacturing organizations from Pune Nashik area, and a comprehensive framework of sustainability measurement is developed through successive applications of Chi-square Automatic Interaction Detector analysis, CHAID analysis. This paper is unique as it has applied the concept of CHAID analysis for first time to identify green logistics as main driver to achieve a reduction of ecological damage and improve business performance.

In recent years, the relationship between companies and suppliers has changed with the continuous rise in environmental awareness and customer expectations. In order to fulfill customers’ needs, the actors in a Supply Chain (SC) network sometimes compete and sometimes cooperate with each other. In SC management, both competitive and collaborative strategies have become important and have required different points of view. In a collaborative environment, companies should strive for common targets with mutual relationship. After managers decided to share their resources, some positive effects have appeared on the companies and suppliers’ performance such as profitability, flexibility and efficiency. Consequently, many companies are willing to cooperate with each other in a SC network because of these reasons. On the other hand, Closed-Loop Supply Chain (CLSC) management has been attracting a growing interest because of increased environmental issues, government regulations and customer pressures. Based on this initiative, our paper presents a novel allied CLSC network design model with two different SCs including common suppliers and common collection centers. First, a decentralized multi-level Mixed-Integer Linear Programming (MILP) model that consists of two different levels of Decision Makers (DMs) is developed. The plants of common SCs comprise the upper-level DMs, common suppliers, common collection centers, and the logistics firm comprises the lower-level DMs. A novel Interactive Fuzzy Programming (IFP) approach using Fuzzy Analytic Hierarchy Process (AHP) is proposed to obtain a preferred compromise solution for the developed model. Through use of Fuzzy AHP in the proposed IFP approach, the DMs can identify the importance of the lower-level DMs. In order to validate the developed model and the proposed IFP approach, a numerical example is implemented. According to the obtained results, our proposed IFP method outperforms Sakawa and Nishizaki’s1and Çalık et al.’s2approach with respect to the satisfaction degrees of upper-level DMs for the developed CLSC model.

Fractional-order proportional-integral-derivative (PIλDμ) controllers can provide better performance than conventional PID controllers because of two additional parameters, which makes the design more flexible. However, these additional parameters make the tuning of controllers harder. It needs additional attention/tools for a proper/desired performance. Therefore, in this study, tuning of fractional order PID controller is converted to an optimisation problem, and it is solved by using charged system search (CSS). Test plants are defined to compare the output response of the delayed system for different orders. In addition, the performance of the system is evaluated/compared by optimising with the CSS and particle swarm optimisation (PSO). The comparison between these two algorithms is performed based on the time response (transient response) properties of each system. The results show that the CCS optimised systems outperform against PSO optimised systems for non-delayed plants; in case of delay in the systems, the PSO presents better performance.

EUROPT, the Continuous Optimization working group of EURO, celebrated its 20 years of activity in 2020. We trace the history of this working group by presenting the major milestones that have led to its current structure and organization and its major trademarks, such as the annual EUROPT workshop and the EUROPT Fellow recognition.

This work addresses the cluster validation problem of determining the ‘right’ number of clusters. We consider a cluster stability property based on the k-nearest neighbour type coincidences model . Quality of a clustering is measured by the deviation from this model, where a small deviation indicates a good clustering. The true number of clusters corresponds to the empirical deviation distribution having the shortest right tail. Experiments carried out on synthetic and real data sets demonstrate the effectiveness of our method.

Abstract: Our recently developed CMARS is powerful in handling complex and heterogeneous data. We include into CMARS the existence of uncertainty about the scenarios. Indeed, data include noise in both output and input variables. Therefore, solutions of the optimization problem may reveal a remarkable sensitivity to perturbations in the parameters of the problem. The data uncertainty results in uncertain constraints and objective function. To overcome this difficulty, we refine our CMARS algorithm by a robust optimization technique proposed to cope with data uncertainty. In our previous study, we present the new robust CMARS (RCMARS) in theory and method and illustrate it with a numerical example. In this study, we present RCMARS results with different uncertainty scenarios for our numerical example. [Copyright &y& Elsevier]

Abstract: In this study, we discuss the models of genetic regulatory systems, so-called gene-environment networks. The dynamics of such kind of systems are described by a class of time-continuous ordinary differential equations having a general form , where is a vector of gene-expression levels and environmental factors and is the matrix having functional entries containing unknown parameters to be optimized. Accordingly, time-discrete versions of that model class are studied and improved by introducing 3rd-order Heun’s method and 4th-order classical Runge–Kutta method. The corresponding iteration formulas are derived and their matrix algebras are obtained. After that, we use nonlinear mixed-integer programming for the parameter estimation in the considered model and present the solution of a constrained and regularized given mixed-integer problem as an example. By using this solution and applying both the new and existing discretization schemes, we generate corresponding time-series of gene-expressions for each method. The comparison of the experimental data and the calculated approximate results is additionally done with the help of the figures to exercise the performance of the numerical schemes on this example. [Copyright &y& Elsevier]