Journal of Graphic Era University

A Heuristic for Solving the M-salesmen (M > 1) Travelling Salesmen Tour Problem with Different Home Stations

Santosh Kumar OAM — 2026-05-25

This paper presents a heuristic for solving a M-salesmen problem, when M>1, and these M-salesmen have different home stations, from where their tour will begin and end. Once again, the index restricted shortest connected tree approach has been applied to identify two independent index restricted connected paths, which have been interpreted as equivalent to the required tours for M-salesmen. Situation of more than one salesman is a natural extension that can arise in all industrial and commercial situations where the salesman tours have applications.

A Comprehensive Overview of Sentiment Analysis: Evolution, Approaches, and Applications

Muskan Mahato — 2026-06-09

Sentiment analysis (SA) also known as opinion mining is a tool to determine the sentiments associated with linguistic data and is used by a variety of organisations over various domain. SA analysis has proved to be an effective tool at various business levels, organisational levels etc. Big companies, organisations, governments use social media platforms to identify the sentiments of the target audience in order to enhance their services and products. Current study is a chronological survey of SA, its applications and various approaches that were developed over the time for SA. This paper focuses on various SA techniques developed and their real-world applications. Details of SA, types of SA, terminology and approaches related and developed overtime are discussed at length. Applications and works related SA in domains related to social media, big business, and political campaigns are also discussed.

Fuzzy Bounded Separation Method for Solving Fully Fuzzy Interval Integer Transportation Problems: A New Approach

Govind Pathak — 2026-06-17

To solve fully fuzzy interval integer transportation problems, a new approach, known as the fuzzy bounded separation method, is proposed. This approach is based on the maximum modulus zero suffix method. The given problem is split into two fuzzy transportation problems, the fuzzy upper bounded interval transportation problem (FUBITP) and fuzzy lower bounded interval transportation problem (FLBITP), and the maximum modulus zero suffix approach is used to get the best solution. Without using any ranking approaches, the suggested strategy applies to a very similar situation. Numerical examples are used to demonstrate the solution process. When treating different types of logistic problems with fully fuzzy integer interval problems, decision makers may find the fuzzy bounded separation method to be extremely useful. This method follows a methodical process and is simple to use and comprehend.

Artificial Intelligence (AI) Monitored EOQ Model for Deteriorating Items under Limited Storage Facility, Partial Backlogging and Time Dependent Demand

Sanjay Sharma — 2026-08-06

In today’s highly competitive markets, the rising cost of warehouse space has become a critical challenge for effective inventory management. This necessitates inventory replenishment policies that explicitly account for limited storage capacity. In this study, we develop an inventory model designed to optimize inventory levels and improve ordering decisions under storage-space constraints. Motivated by the growing influence of Artificial Intelligence (AI) and Machine Learning (ML) in supply chain management implementing AI in this domain requires a structured approach beginning with the collection of high-quality data from diverse sources such as sales records, customer interactions, production logs, and real-time inventory levels. This data must undergo rigorous pre-processing and cleaning to remove inconsistencies and ensure reliability for subsequent analysis. Based on operational needs, suitable AI models – such as machine learning algorithms for demand forecasting, natural language processing for customer inquiries, and computer vision for product identification – can then be selected and trained on historical datasets to identify actionable patterns The data collected support more accurate and timely reorder point decisions. Demand is assumed to be time-dependent, while deterioration is also considered as a time-varying phenomenon. The production rate is finite, shortages are permitted with partial backlogging and the backlogging rate is inversely related to customer waiting time. The objective of the model is to minimize the total inventory cost by jointly determining the optimal cycle length, production rate and order quantity. The effectiveness of the proposed model is demonstrated through a numerical example and a comprehensive sensitivity analysis is conducted to examine the impact of key parameters. The results indicate that incorporating storage constraints and AI-supported reorder decisions can significantly enhance inventory performance and cost efficiency.

A Comparative Analysis of Generalized Thermoelastic Theories in Seismic Wave Propagation

Sumit Mahiya — 2026-08-06

Seismic wave propagation is defined as the framework of classical elasticity in which thermal effects are neglected. Although, under high frequency dynamic loading and deep Earth conditions mechanical deformation and temperature variations become strongly coupled for advanced thermoelastic formulation. The development of thermoelastic theories applied to seismic wave propagation beginning with classical thermoelasticity and extending through generalized models includes the Lord-Shulman (LS), Green-Lindsay (GL) and Green-Naghdi (GN) theories. The emphasis is placed on the finite speed of thermal wave propagation, thermal relaxation mechanism and their influence on dispersion, attenuation and wave characteristics. The behavior of body and surface waves is analyzed within homogeneous, layered, anisotropic and pre-stressed media. This study suggests that thermoelastic coupling may contribute intrinsic seismic attenuation significantly with high-frequency and high-temperature geological environment. This provides a unified theoretical basis for improved seismic modeling, deep Earth investigation and hazard assessment.