Volume 12 • Issue 2 • PP: 32-51 • 2025
A Multi-Server Queuing-Inventory System with Attraction-Retention Mechanisms for Impatient Customers and Catastrophes in Warehouse
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This paper presents a multi-server Markovian queuing-inventory system (MQIS) that incorporates attractionretention (AR) mechanisms for impatient customers and models catastrophic inventory losses within a warehouse setting. The system consists of C identical servers, a limited waiting area, and a storage capacity of Q items. Periodic disruptions may destroy all inventory in the system, compelling waiting customers either to remain until stock is replenished or to exit the system. A subset of servers may take joint vacations when no customers are waiting. To analyze this queuing-inventory system (QIS), we derive balance equations using a three-dimensional continuous-time Markov chain framework, solving for steady-state solutions through a recursive method. We then derive performance metrics and identify special-case queuing-inventory models within the broader system. A cost-loss model is formulated to optimize the service rate and server vacation strategies, minimizing overall costs. A genetic algorithm is employed to conduct a cost analysis. We collected primary data from the Ethio Telecom district head office in Arba Minch, Ethiopia to validate our theoretical findings. The empirical analysis serves a dual purpose: to investigate performance measure sensitivity to parameter variations and to discuss an optimization problem aimed at minimizing expected total cost (ETC) while assessing the impacts of AR mechanisms and catastrophic events on ETC.
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