Template-Type: ReDIF-Article 1.0 Author-Name: G. Ayyappan Author-X-Name-First: G. Author-X-Name-Last: Ayyappan Author-Name: S. Sankeetha Author-X-Name-First: S. Author-X-Name-Last: Sankeetha Title: Dynamic service management and priority handling in dual server queuing systems with breakdowns Abstract: This paper examines a dual-server system comprising server 1 and server 2, each with its dedicated queue (queue 1 and queue 2). Queue 1, with lower priority, can handle an unlimited number of tasks, while queue 2, with higher priority, has a maximum capacity of N tasks. Task arrivals follow a Markovian process, and their service times adhere to a phase-type distribution. In the event of server 2's breakdown, server 1 seamlessly takes over, minimising service disruptions. To address customer dissatisfaction, server 1 provides prompt feedback during these transitions. The study employs the quasi-birth-death (QBD) process, utilising matrix analytic methods with finite-dimensional block matrices to analyse steady-state behaviour. Performance metrics like busy periods, costs, and other relevant measures are assessed, yielding insights into system efficiency. Numerical computations and graphical representations showcase the system's performance across various scenarios, providing a comprehensive understanding of its operation. Journal: Int. J. of Mathematics in Operational Research Pages: 43-72 Issue: 1 Volume: 33 Year: 2026 Keywords: Markovian arrival process; phase type service; vacation; priority queues; breakdown; repair. File-URL: http://www.inderscience.com/link.php?id=151172 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:ids:ijmore:v:33:y:2026:i:1:p:43-72 Template-Type: ReDIF-Article 1.0 Author-Name: Sandeep Kumar Author-X-Name-First: Sandeep Author-X-Name-Last: Kumar Author-Name: Robin Singh Author-X-Name-First: Robin Author-X-Name-Last: Singh Author-Name: Manoj Kumar Author-X-Name-First: Manoj Author-X-Name-Last: Kumar Author-Name: Mukesh Kumar Author-X-Name-First: Mukesh Author-X-Name-Last: Kumar Author-Name: Prachi Fartyal Author-X-Name-First: Prachi Author-X-Name-Last: Fartyal Title: An inventory system for imperfect products with the effect of carbon emission and with free transportation on a prepaid basis Abstract: The EPQ model is a mathematical model used for inventory management in shop floor systems. However, it assumes manufacturers pay upfront costs and may have low-grade items. The classical inventory model assumes no imperfect items are manufactured, but the production process may shift from controlled to uncontrolled states due to various causes. To make the current study more realistic, we represent a model with imperfect production that accounts for random carbon emissions under continuous prepayment. We also assumed that the production process was imperfect, so we got some defective items, and out of these, some were reworked. Further, it is assumed that the producer provides free shipping to the retailers on a prepaid basis. The concept of carbon emissions is related to transportation and production decisions. Due to environment-saving rules, a tax on carbon emissions is required to be paid by the manufacturer. The model is validated using a numerical example and sensitivity analysis. Journal: Int. J. of Mathematics in Operational Research Pages: 73-87 Issue: 1 Volume: 33 Year: 2026 Keywords: inventory; carbon emission; imperfect products; transportation cost; prepayment. File-URL: http://www.inderscience.com/link.php?id=151173 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:ids:ijmore:v:33:y:2026:i:1:p:73-87 Template-Type: ReDIF-Article 1.0 Author-Name: Neha Rani Author-X-Name-First: Neha Author-X-Name-Last: Rani Author-Name: Manoj Kumar Sharma Author-X-Name-First: Manoj Kumar Author-X-Name-Last: Sharma Title: Towards sustainable two-warehouse inventory management: flexible payments and demand-driven optimisation with preservation technology and carbon emission considerations Abstract: This study explores the transformative impact of conservation and eco-friendly technologies on two warehouse inventory, aiming to prevent product degradation and substantially reduce carbon emissions in greenhouse operations. The research underscores the urgent need for government-led carbon emission laws to address environmental and economic repercussions. With a focus on the proposed model, two key contributions emerge: 1) strategic investments in eco-friendly technologies and conservation methods for minimising carbon emissions and product degradation; 2) the application of preservation technology to curtail product deterioration. The comprehensive model integrates factors such as demand dynamics, pricing, stock, expiry dates, payment delays, and inflation, seeking optimal order quantities, cycle durations, and selling prices for profit maximisation. Validated and exemplified quantitatively, the model's efficacy is demonstrated, complemented by a thorough sensitivity analysis. This research not only advances inventory management practices but also advocates for environmentally sustainable strategies with direct financial implications. Journal: Int. J. of Mathematics in Operational Research Pages: 1-42 Issue: 1 Volume: 33 Year: 2026 Keywords: two warehouses inventory; price-stock and lifetime dependent demand; inflation; preservation technology; carbon emission. File-URL: http://www.inderscience.com/link.php?id=151174 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:ids:ijmore:v:33:y:2026:i:1:p:1-42 Template-Type: ReDIF-Article 1.0 Author-Name: Varuna Bhardwaj Author-X-Name-First: Varuna Author-X-Name-Last: Bhardwaj Author-Name: Sunil Kumar Author-X-Name-First: Sunil Author-X-Name-Last: Kumar Author-Name: Vipin Kumar Tyagi Author-X-Name-First: Vipin Kumar Author-X-Name-Last: Tyagi Title: A two-tier sustainable supply chain model with the influence of carbon release under a fuzzy environment Abstract: Environmental sustainability is a worldwide issue in the present-day business management environment, and scholars have been concentrating broadly on this subject. It is difficult to run an organisation efficiently while ensuring the environment, and lots of companies have understood that they have to prioritise production with minimum waste and carbon emissions. Government measures to promote sustainability have also led corporations to emphasise minimising their carbon footprints across the supply chain by utilising green supply chain strategies. Green inventories contribute significantly to system design by minimising unfavourable environmental effects while enhancing positive economic and social consequences. In the course of production, keeping inventory, depreciation, shipping, and scrap management, the investigation evaluates concerns related to carbon emissions in both developer and vendor channels. In order to reduce total average expenses, a crisp model has been developed. Using the signed distance approach, the total average expenditure is defuzzified and proven to be convex with a unique approach. Both crisp and fuzzy scenarios undergo numerical analysis. Sensitivity analysis and visual representations are used to demonstrate how innovative the suggested technique is. Journal: Int. J. of Mathematics in Operational Research Pages: 113-131 Issue: 1 Volume: 33 Year: 2026 Keywords: sustainable; degradation; carbon emission; developer; vendor. File-URL: http://www.inderscience.com/link.php?id=151175 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:ids:ijmore:v:33:y:2026:i:1:p:113-131 Template-Type: ReDIF-Article 1.0 Author-Name: Yang Huang Author-X-Name-First: Yang Author-X-Name-Last: Huang Author-Name: Wenxuan Wang Author-X-Name-First: Wenxuan Author-X-Name-Last: Wang Author-Name: Qiangqiang Wang Author-X-Name-First: Qiangqiang Author-X-Name-Last: Wang Title: The strategic value of seller's option in buyback guarantee financing Abstract: This paper extends traditional bank credit (BC) and buyback guarantee (BG) financing models by considering uncertain salvage value, and proposes a novel buyback guarantee financing with seller's option (SBG). We derive the optimal decisions for the bank, retailer, and manufacturer under each financing scheme. Additionally, we compare the optimal decisions for the retailer and manufacturer when the BC contract, BG contract, and SBG contract are feasible. The results reveal that the optimal financing schemes for the manufacturer and retailer are not always aligned. Both parties stand to increase profits with the SBG contract compared to other contracts when the salvage value is high. Furthermore, there is a significant range where the supply chain could generate greater profits with the SBG contract compared to other contracts. Journal: Int. J. of Mathematics in Operational Research Pages: 88-112 Issue: 1 Volume: 33 Year: 2026 Keywords: seller's option; buyback guarantee financing; bank credit financing; supply chain management. File-URL: http://www.inderscience.com/link.php?id=151176 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:ids:ijmore:v:33:y:2026:i:1:p:88-112 Template-Type: ReDIF-Article 1.0 Author-Name: G. Ayyappan Author-X-Name-First: G. Author-X-Name-Last: Ayyappan Author-Name: N. Arulmozhi Author-X-Name-First: N. Author-X-Name-Last: Arulmozhi Title: Investigation on inventory replenishment policy for a queueing system with catastrophic failure, negative arrival and discouragement customers Abstract: The single queues of inventory systems (<i>IS</i>) with warehouse catastrophes and negative arrivals (<i>NA</i>) occur in the service area were examined in this work. Arriving positive customers (<i>PC</i>) can queue up infinitely to make purchases. Customers in the system are still waiting for stock replenishment after catastrophes even when all of the system's commodities are destroyed. The positive customer that is now getting service from the server is disrupted and removed as a result of the negative arrival. The server is instantly impacted by the breakdown as a result of the negative customer's arrival. After examining queueing inventory system's stability conditions, busy period, and the transition probability vector was calculated using the matrix-analytic method. The results of numerical assessments have been presented together with formulas for performance measures. Journal: Int. J. of Mathematics in Operational Research Pages: 133-167 Issue: 2 Volume: 33 Year: 2026 Keywords: Markovian arrival process; MAP; phase-type service; negative arrival; catastrophic failure; (s, S) and (s, Q) policies; repair. File-URL: http://www.inderscience.com/link.php?id=152302 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:ids:ijmore:v:33:y:2026:i:2:p:133-167 Template-Type: ReDIF-Article 1.0 Author-Name: S. Meena Author-X-Name-First: S. Author-X-Name-Last: Meena Author-Name: G. Ayyappan Author-X-Name-First: G. Author-X-Name-Last: Ayyappan Title: Analysis of MAP/PH1, PH2/1 retrial inventory queueing system with phase type vacation, working breakdown, repair, essential and optional inventories Abstract: This research analyses an inventory retrial queueing system with a constant retrial rate, working breakdown, repair, single vacation and inventory items that are essential and optional. We assume that an arrival follows the Markovian arrival process and that the server will provide them with phase-type services. The (<i>s</i><SUB align="right"><SMALL>1</SMALL></SUB>, <i>S</i><SUB align="right"><SMALL>1</SMALL></SUB>) and (<i>s</i><SUB align="right"><SMALL>2</SMALL></SUB>, <i>S</i><SUB align="right"><SMALL>2</SMALL></SUB>) policies are used to replenish the essential and optional inventory items, respectively, and there will be an exponential distribution in the replenishment time. The server takes a single vacation if there are no orbital customers, no essential inventory, or both. The server provides an optional item, if there exists a positive inventory level, otherwise the customer gets only the essential item and then leaves the system. When a server breaks down, the server provides the slow mode service for the current customer and then starts the repair process. The number of consumers in orbit, inventory level, and server status may all be determined in the steady state. Numerous key performance indicators are defined, and a cost analysis is obtained. In order to make our mathematical concept clearer, a few numerical examples are provided. Journal: Int. J. of Mathematics in Operational Research Pages: 287-326 Issue: 3 Volume: 33 Year: 2026 Keywords: queueing-inventory; (s, S) policy; retrial; essential and optional item; single vacation; working breakdown; repair; Markovian arrival process; MAP; phase-type distribution; matrix analytic method. File-URL: http://www.inderscience.com/link.php?id=152307 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:ids:ijmore:v:33:y:2026:i:3:p:287-326 Template-Type: ReDIF-Article 1.0 Author-Name: Le Duc Dao Author-X-Name-First: Le Duc Author-X-Name-Last: Dao Author-Name: Huynh Nhat Huy Author-X-Name-First: Huynh Nhat Author-X-Name-Last: Huy Title: Optimising inventory replenishment system - a case in multi-product multi-retailer Abstract: Inventory management and replenishment are considered as important process in supply chain, especially in the retail industry. The replenishment process requires businesses to consider a large amount of information to support the decisions related to the appropriate quantity and timing of replenishment. The goal is to minimise costs associated with inventory including purchasing, holding and shortage costs at retail stores and maintain a high customer service level. The problem of the paper is formulated with mixed integer linear programming and to be solved by genetic algorithm to achieve optimal distribution cost for firm. The results of the paper will support businesses in providing product replenishment strategies while considering related constraints on demand, budget, thereby providing businesses with the lowest operating costs and increasing competitiveness in the future. Journal: Int. J. of Mathematics in Operational Research Pages: 344-360 Issue: 3 Volume: 33 Year: 2026 Keywords: inventory replenishment model; genetic algorithm; mixed integer linear programming. File-URL: http://www.inderscience.com/link.php?id=152310 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:ids:ijmore:v:33:y:2026:i:3:p:344-360 Template-Type: ReDIF-Article 1.0 Author-Name: Marzieh Saneei Author-X-Name-First: Marzieh Author-X-Name-Last: Saneei Author-Name: Mehdi Seifbarghy Author-X-Name-First: Mehdi Author-X-Name-Last: Seifbarghy Author-Name: Mohsen Hamidi Author-X-Name-First: Mohsen Author-X-Name-Last: Hamidi Title: Sustainable supplier selection and order allocation using hybrid fuzzy weighting methods, scenario-based programming, and flexible robust optimisation Abstract: In this research, a sustainable supplier selection and order allocation problem under uncertainty is modelled and solved. To weigh supplier selection criteria, four fuzzy methods have been applied. To determine suppliers' scores, two approaches of fuzzy Taguchi loss function (F-TLF) and fuzzy technique for order preference by similarity to ideal solution (F-TOPSIS) are used. Suppliers' scores are then incorporated into an objective function of a multi-objective optimisation model to allocate orders to suppliers. Three models of scenario-based programming, flexible robust programming, and a new scenario-based and flexible robust hybrid programming are presented. The optimisation objectives are minimising purchasing cost, maximising supplier desirability, and maximising value of purchasing from best suppliers. To solve the models, a hybrid method of Lai and Hwang and Torabi-Hassini is proposed. The three models have been solved using real data from the electronics industry. Journal: Int. J. of Mathematics in Operational Research Pages: 238-285 Issue: 2 Volume: 33 Year: 2026 Keywords: supplier selection and order allocation; SSOA; fuzzy Taguchi loss function; F-TLF; flexible robust optimisation. File-URL: http://www.inderscience.com/link.php?id=152311 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:ids:ijmore:v:33:y:2026:i:2:p:238-285 Template-Type: ReDIF-Article 1.0 Author-Name: Tiara Alamanda Author-X-Name-First: Tiara Author-X-Name-Last: Alamanda Author-Name: Dharma Lesmono Author-X-Name-First: Dharma Author-X-Name-Last: Lesmono Author-Name: Jonathan Hoseana Author-X-Name-First: Jonathan Author-X-Name-Last: Hoseana Title: EOQ-type inventory models incorporating discount policies and carbon emission with warehouse capacity and capital constraints Abstract: In 2019, Kristiyani and Daryanto proposed an EOQ-type inventory model which takes into account the company's total carbon emission, and assumes that the item's purchase obeys the all-unit-discount policy. In this paper, we construct a modification of the model, by replacing the all-unit-discount policy with the incremental-discount policy. Furthermore, we complement both models with warehouse capacity and capital constraints. Using both models, we compute numerically the optimal order quantity satisfying both constraints, in the scenario of a building materials company in Bandung, Indonesia. At the obtained optimal state, we analyse the sensitivity of both the company's total cost and total carbon emission with respect to some of the models' parameters. The results show that both quantities depend particularly significantly on the fuel consumption of the vehicle used to transport the purchased items from the supplier to the company's warehouse. Journal: Int. J. of Mathematics in Operational Research Pages: 327-343 Issue: 3 Volume: 33 Year: 2026 Keywords: economic order quantity; EOQ; carbon emission; all-unit discount; incremental discount; warehouse capacity; capital. File-URL: http://www.inderscience.com/link.php?id=152313 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:ids:ijmore:v:33:y:2026:i:3:p:327-343 Template-Type: ReDIF-Article 1.0 Author-Name: Lyes Ikhlef Author-X-Name-First: Lyes Author-X-Name-Last: Ikhlef Author-Name: Karim Labadi Author-X-Name-First: Karim Author-X-Name-Last: Labadi Title: Kernel estimation analysis of the finite source M/G /1 queue with retrial and vacation Abstract: In this work, we study the finite source queueing system with retrial and vacation when the service distribution of customers is unknown. We compute the qualitative analysis of this queueing system by the use of the Markov regenerative process and the kernel method. The two main quantities, one step transition probability matrix <i>P</i> of the embedded Markov chain (<i>EMC</i>) defined at regenerative instants and the mean time matrix <i>A</i>, that the queue spends in any state between two successive regeneration instants, for the system considered are obtained. The matrix <i>P</i> (resp. <i>A</i>) depends on the probability density function (<i>pdf</i>) (resp. cumulative distribution function (<i>cdf</i>)) of the service time. These two functions (<i>pdf</i> and <i>cdf</i>) are unknown and are estimated by using the two asymmetric kernels gamma and Birnbaum-Saunders. Finally, we establish an algorithm which gives us the estimators of: the one step transition probability matrix <i>P</i>, the mean time matrix <i>A</i>, the probability distribution of the number of customers in the orbit and the state of the server and the characteristics of our queueing system considered. Journal: Int. J. of Mathematics in Operational Research Pages: 198-214 Issue: 2 Volume: 33 Year: 2026 Keywords: retrial model; Markov regenerative process; gamma kernel; estimation; vacation policy. File-URL: http://www.inderscience.com/link.php?id=152314 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:ids:ijmore:v:33:y:2026:i:2:p:198-214 Template-Type: ReDIF-Article 1.0 Author-Name: Sonia Dua Author-X-Name-First: Sonia Author-X-Name-Last: Dua Author-Name: Sandeep Kumar Mogha Author-X-Name-First: Sandeep Kumar Author-X-Name-Last: Mogha Author-Name: Himani Dem Author-X-Name-First: Himani Author-X-Name-Last: Dem Title: An optimal inventory system under markdown dependent demand environment Abstract: In this article, a deterministic inventory model for deteriorating items is studied with markdown dependent demand under discount for inventory management. The discount policy has been used to moderate the inventory and growth of profit or rate of sale. A model developed gives the maximum annual profit and established the relationship between demand dependent factors and discount policy. Sensitivity analysis studies behaviour of the model against the changes in some key parameters. Journal: Int. J. of Mathematics in Operational Research Pages: 215-237 Issue: 2 Volume: 33 Year: 2026 Keywords: inventory model; markdown dependent demand; discount policy; carbon emission. File-URL: http://www.inderscience.com/link.php?id=152316 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:ids:ijmore:v:33:y:2026:i:2:p:215-237 Template-Type: ReDIF-Article 1.0 Author-Name: Tissawat Asavanant Author-X-Name-First: Tissawat Author-X-Name-Last: Asavanant Author-Name: Hiroshi Morita Author-X-Name-First: Hiroshi Author-X-Name-Last: Morita Title: Short-term origin-destination demand forecasting in rail transit systems: parallel model architecture and gravity approach Abstract: Short-term origin-destination (OD) forecasting in passenger rail transit is notoriously difficult due to the high magnitude of scale, dimension, noise, and skewness of the OD matrices. Additionally, unforeseen OD data remains an issue for the data-driven models. In this paper, we address the issue of unforeseen OD data in real-time forecasting case, by using the adjusted parallel model architecture (APMA), a forecasting improvement strategy, and the reconstruction of the problem into an origin-based vector sum projection gravity (OVG) model. The forecasting problem can be split into concatenation and chained forecasting scenarios. Variations of the APMA model are tested on real-time datasets from Bangkok Subway. The proposed APMA-OVG model performs satisfactorily when compared to recent benchmarks for the unforeseen data on the concatenation case. The performance deteriorates in the chained forecast case due to accumulated error of the step-wise forecasting process when forecasting steps are broken down. Journal: Int. J. of Mathematics in Operational Research Pages: 412-431 Issue: 3 Volume: 33 Year: 2026 Keywords: parallel model architecture; PMA; origin-destination matrices; gravity model; hybrid model; public transportation network; short-term forecasting. File-URL: http://www.inderscience.com/link.php?id=152318 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:ids:ijmore:v:33:y:2026:i:3:p:412-431 Template-Type: ReDIF-Article 1.0 Author-Name: R. Poornima Author-X-Name-First: R. Author-X-Name-Last: Poornima Author-Name: K. Kirupa Author-X-Name-First: K. Author-X-Name-Last: Kirupa Title: Supplementary variable technique approach on retrial queue with feedback and backup server during Bernoulli's lengthy vacation and random repairs Abstract: This paper explores a steady-state retrial queueing system with a single server, coupled with a backup server. Client arrivals occur in batches following a compound Poisson process. If the server is idle, one of the clients from the batch receives service immediately, and the remaining clients enter the orbit. Otherwise, the entire incoming batch joins the orbit. Unsatisfied clients after receiving service may become feedback clients. After the completion of each service, the server may enter a vacation period of random length. The server has the option to extend its vacation with certain probability. Breakdowns of the main server can occur at any point during the busy state. Repairs of the server commence without delay. During vacation and repair time of the main server, clients receive service from a backup server. Performance metrics, such as the mean of the system size, mean of the orbit size, server availability and server failure frequency are computed. Cost analysis has been carried out with the cost parameters. The stochastic decomposition law is verified for the proposed model. Numerical results are also presented to validate the impact of parameters on the system. Journal: Int. J. of Mathematics in Operational Research Pages: 361-390 Issue: 3 Volume: 33 Year: 2026 Keywords: batch arrival; Bernoulli extended vacation; backup server; random breakdown and feedback. File-URL: http://www.inderscience.com/link.php?id=152319 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:ids:ijmore:v:33:y:2026:i:3:p:361-390 Template-Type: ReDIF-Article 1.0 Author-Name: A. Prashanthi Author-X-Name-First: A. Author-X-Name-Last: Prashanthi Author-Name: R. Ravinder Reddy Author-X-Name-First: R. Ravinder Author-X-Name-Last: Reddy Title: Performance comparison of random forest and BILSTM for intrusion detection in cyber security environment Abstract: The widespread adoption of the internet has led to an increase in network attacks, making traditional signature-based detection methods less effective against zero-day attacks. This research examines the efficacy of anomaly-based detection techniques in identifying these threats, using two artificial intelligence models: CNN-BiLSTM and random forest classifier. Data for training and testing these models was sourced from the CICIDS2017 dataset. Results showed a high success rate, with CNN-BiLSTM achieving 95% and random forest classifier achieving 98%. These findings suggest that anomaly-based detection offers a robust strategy for detecting zero-day network attacks. The research also underscores the necessity of assessing detection systems through various performance metrics, including accuracy, precision, recall, and F1 score. Such metrics provide a comprehensive understanding of an algorithm's effectiveness in diverse scenarios, which is crucial for developing more advanced and secure network security systems capable of addressing emerging threats. Journal: Int. J. of Mathematics in Operational Research Pages: 168-183 Issue: 2 Volume: 33 Year: 2026 Keywords: anomaly-based detection; zero-day attacks; machine learning; BiLSTM; random forest classifier; CICIDS2017. File-URL: http://www.inderscience.com/link.php?id=152320 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:ids:ijmore:v:33:y:2026:i:2:p:168-183 Template-Type: ReDIF-Article 1.0 Author-Name: R. Kalyanaraman Author-X-Name-First: R. Author-X-Name-Last: Kalyanaraman Author-Name: K. Vidya Author-X-Name-First: K. Author-X-Name-Last: Vidya Title: M/G/1 queue with regular and optional phases of services and vacations Abstract: This paper deals with a non-Markovian single server queue with phase type service and phase type vacation. The service time and vacation time of each phase is generally distributed. The probability generating function of number of customers in the system at an arbitrary time point and at departure point is obtained in steady state. Some important performance measures are derived. Some numerical illustrations are also provided. Journal: Int. J. of Mathematics in Operational Research Pages: 391-411 Issue: 3 Volume: 33 Year: 2026 Keywords: phase type service; phase type vacation; probability generating function; performance measures. File-URL: http://www.inderscience.com/link.php?id=152321 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:ids:ijmore:v:33:y:2026:i:3:p:391-411 Template-Type: ReDIF-Article 1.0 Author-Name: Sandeep Kumar Author-X-Name-First: Sandeep Author-X-Name-Last: Kumar Author-Name: Robin Singh Author-X-Name-First: Robin Author-X-Name-Last: Singh Author-Name: Mukesh Kumar Author-X-Name-First: Mukesh Author-X-Name-Last: Kumar Author-Name: Birjesh Kumar Author-X-Name-First: Birjesh Author-X-Name-Last: Kumar Author-Name: Deepak Kumar Author-X-Name-First: Deepak Author-X-Name-Last: Kumar Author-Name: Rahul Singh Author-X-Name-First: Rahul Author-X-Name-Last: Singh Title: Study of a production inventory policy with finite products life, few imperfect products and demand reliant on stock-level Abstract: The current work is about an inventory policy that permits a few imperfect products for reproduction, and this permission results in some deterioration. The life of products is considered finite, and demand is taken as stock-level dependent. The model has additionally taken into consideration the consistent manufacturing rate, which ends after a favoured stage of stocks, and that is the top stage of it. Caused by demand for products, imperfect items, and decay in products, the inventory lowers to zero, at which point the manufacturing cycle begins once more. To verify and illustrate the study, some numerical examples are carried out and bound to delineate the use and appropriateness of the inventory policy. Also, a sensitivity analysis is presented. The present study finds the entire optimal inventory cost, the optimal ordering cost, and the ordering cycle that maximise the expected total prot per unit of time. Journal: Int. J. of Mathematics in Operational Research Pages: 184-197 Issue: 2 Volume: 33 Year: 2026 Keywords: production; imperfect products; stock-level; deterioration; optimal. File-URL: http://www.inderscience.com/link.php?id=152322 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:ids:ijmore:v:33:y:2026:i:2:p:184-197 Template-Type: ReDIF-Article 1.0 Author-Name: Irene Orayag Mamites Author-X-Name-First: Irene Orayag Author-X-Name-Last: Mamites Title: Fuzzy best-worst method for analysing the threats of AI in education Abstract: AI integration to support functional operations has been a growing interest in the literature owing to the numerous perceived and actual benefits. While this has been widely considered in several industries, integrating AI in education (AIEd) has been limited primarily due to diverse requirements in the educational platform. As such, it is difficult to pinpoint the threat that hampers such innovation. To provide an analytical framework to analyse the threats of applying AIEd, this paper employs the fuzzy best-worst method (BWM). To illustrate the framework, a case study in a state university in the Philippines is conducted. Interesting results revealed that the stakeholders prioritise threats related to the knowledge-based implementation of AI technologies, followed by threats related to the evaluation of the type of technologies available. Such results provide a guideline to stakeholders to address high-priority threats before integrating AIEd. Journal: Int. J. of Mathematics in Operational Research Pages: 1-18 Issue: 5 Volume: 33 Year: 2026 Keywords: artificial intelligence; education; fuzzy set theory; best-worst method; BWM. File-URL: http://www.inderscience.com/link.php?id=152325 File-Format: text/html File-Restriction: Open Access Handle: RePEc:ids:ijmore:v:33:y:2026:i:5:p:1-18