Performance Analysis of Neutrosophic Multi-Server Queuing-Inventory System under Catastrophic Conditions

Berhanu Mekonen Alemu; Natesan Thillaigovindan; Getinet Alemayehu Wole

Authors

Berhanu Mekonen Alemu Department of Mathematics, College of Natural and Computational Sciences, Arba Minch University, Arba Minch, Ethiopia.
Natesan Thillaigovindan Department of Mathematics, College of Natural and Computational Sciences, Arba Minch University, Arba Minch, Ethiopia.
Getinet Alemayehu Wole Department of Mathematics, College of Natural and Computational Sciences, Haramaya University, Harar, Ethiopia.

Keywords:

Neutrosophic Logic; Multi-Server Queuing-Inventory System; Customer At traction and Retention; Impatient Customers; Inventory Optimization; Asynchronous Server Vacations.

Abstract

In this study, we introduce a Neutrosophic-based framework for analyzing a finite
capacity multi-server queuing-inventory system (MQIS) that integrates attraction
retention mechanisms for impatient customers and addresses catastrophic inventory
disruptions. Recognizing the limitations of purely deterministic and probabilis
tic models in uncertain environments, we adopt Single-Valued Trapezoidal Neutro
sophic Numbers (SVTNNs) to represent key system parameters such as arrival rates,
service rates, attraction intensities, retention probabilities, and catastrophe occur
rences. The system operates under Markovian assumptions, with arrivals modeled
by a Poisson process, service and vacation times following exponential distributions,
and inventory replenished via an (s,S) policy. To facilitate steady-state analysis, the
Neutrosophic model is transformed into equivalent deterministic models through the
application of Zadeh’s extension principle combined with the (α,β,γ)-cut method.
Furthermore, a cost optimization problem is formulated to identify optimal ser
vice configurations, solved using a genetic algorithm. A numerical illustration is
provided to demonstrate the model’s ability to capture uncertainty and improve
decision-making in complex service environments