Analysis of a queueing-inventory system with Client Choice Service under a modified (s, S) reorder policy

K. Lawrence; N. Anbazhagan; S. Amutha; Tran Son Hai; Woong Cho; Gyanendra Prasad Joshi; K. Lawrence; N. Anbazhagan; S. Amutha; Tran Son Hai; Woong Cho; Gyanendra Prasad Joshi

doi:10.3934/jimo.2026096

Journal of Industrial and Management Optimization

2026, Volume 22, Issue 6: 2624-2646. doi: 10.3934/jimo.2026096

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Research article

Analysis of a queueing-inventory system with Client Choice Service under a modified (s, S) reorder policy

1.
Department of Mathematics, Alagappa University, Karaikudi, 630003, Tamilnadu, India
2.
Ramanujan Centre for Higher Mathematics, Alagappa University, Karaikudi, 630003, Tamilnadu, India
3.
Information Technology Department, University of Pedagogy, Ho Chi Minh City, Vietnam
4.
Department of Advanced AI Engineering, Kangwon National University, Samcheok-25913, Republic of Korea

Received: 05 December 2025 Revised: 23 April 2026 Accepted: 27 April 2026 Published: 12 May 2026
60K25, 90B05, 91B70

This study investigates a novel queueing-inventory system governed by a newly proposed Client Choice Policy, which extends the modified (s, S) ordering policy. The system considers a maximum capacity of S units of raw material. Upon the arrival of a client, the raw material is processed into finished goods after some random time. Client arrivals follow a Markovian arrival process (MAP) and a finite waiting platform is available. A reorder point is fixed as s. At the time of replenishment, the inventory gets filled up to the level of S units. In addition to that, the clients in the waiting platform may choose to purchase the raw materials. Clients who accept this offer leave the system immediately with the raw material, while the others remain in the queue to receive the finished goods. The numerical cost analysis estimates the expected total cost using steady-state probabilities derived from the finite generator matrix. The total cost is computed as the weighted sum of holding, replenishment, processing, and waiting costs. By evaluating these costs over different parameter combinations, the optimal policy that minimizes the expected total cost is identified numerically.
- clients choice policy,
- dual choice service,
- modified (s, S) policy,
- Markovian arrival process
Citation: K. Lawrence, N. Anbazhagan, S. Amutha, Tran Son Hai, Woong Cho, Gyanendra Prasad Joshi. Analysis of a queueing-inventory system with Client Choice Service under a modified (s, S) reorder policy[J]. Journal of Industrial and Management Optimization, 2026, 22(6): 2624-2646. doi: 10.3934/jimo.2026096

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Abstract

This study investigates a novel queueing-inventory system governed by a newly proposed Client Choice Policy, which extends the modified (s, S) ordering policy. The system considers a maximum capacity of S units of raw material. Upon the arrival of a client, the raw material is processed into finished goods after some random time. Client arrivals follow a Markovian arrival process (MAP) and a finite waiting platform is available. A reorder point is fixed as s. At the time of replenishment, the inventory gets filled up to the level of S units. In addition to that, the clients in the waiting platform may choose to purchase the raw materials. Clients who accept this offer leave the system immediately with the raw material, while the others remain in the queue to receive the finished goods. The numerical cost analysis estimates the expected total cost using steady-state probabilities derived from the finite generator matrix. The total cost is computed as the weighted sum of holding, replenishment, processing, and waiting costs. By evaluating these costs over different parameter combinations, the optimal policy that minimizes the expected total cost is identified numerically.

References

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