Analysis of Finite Population Stochastic modeling with State-Dependent Arrival and Service Facilities

K Lakshmanan, Selvaraj Padmasekaran, M Bhuvaneshwari, R Asokan

Abstract


This paper investigates a stock-dependent arrival process(SDAP) and queue-dependent service process(QDSP) in the stochastic queueing-inventory system(SQIS). The arriving units in the system are generated from the finite source population. The arrival process holds the properties of a quasi-random process and its intensity rate is defined based on the two-component demand rate(TCDR). The customer's departure time is exponentially distributed. The concepts of non-SDAP and SDAP, non-QDSP, and QDSP are to be generalized. The inventory system may have the perishable quality of the products. It adopts the $(s, Q)$ reordering policy whenever replenishment is required. Further, the joint probability distribution of a Markov process is derived and necessary system performance measures are computed. The comparative discussion is presented to improve the quality of this model.

Keywords


Stock-dependent arrival process; Non-stock dependent arrival process; Two component demand rate; Finite population; queue-dependent service process

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References


B. Sivakumar A. Shophia Lawrence and G. Arivarignan. A perishable inventory system with service facility and finite source. Applied Mathematical Modelling, 37:4771–4786, 2013.

H. K. Alfares. Inventory model with stock level dependent demand rate and variable holding cost. Int. J. Prod. Econ, 108:259–265, 2007.

R. Jesus Artalejo and Maria Jesus Lopez-Herrero. The single server retrial queue with finite population: A bsde approach. Operational Research, 12:109–31, 2012.

Seo Daewon Avhishek Chatterjee and varshney lav. Capacity of systems with queuelength dependent service quality. IEEE Transactions on Information Theory, 1:1–1,2017.

O. Berman and K. P. Sapna. Optimal service rates of a service facility with perishable inventory items. Naval Research Logistics (NRL), 49:464–482, 2002.

T. K. Datta and A. K. Pal. A note on an inventory model with inventory-level-dependent demand rate. Journal of the Operation Research Society, 41:971–975, 1990.

G. I. Falin and J. R. Artalejo. A finite source retrial queue. European Journal of Operational Research, 108:409–424, 1998.

K. Jeganathan. Finite source markovian inventory system with bonus service for certain customers. Int. J. of Adv. in Aply. Math. and Mech, 2:134–143, 2015.

N. Anbazhagan K. Jeganathan and B. Vigneshwaran. A finite source retrial queue. International Journal of Operations Research and Information Systems (IJORIS), 6:32–52, 2015.

N. Anbazhagan K. Jeganathan, S. Selvakumar and S. Amutha. Stochastic modeling on m/m/1/n inventory system with queue-dependent service rate and retrial facility. AIMS Mathematics, 6:7386–7420, 2021.

K. Srinivasa Rao K. Venkata Subbaiah and B. Satyanarayana. Inventory models for perishable items having demand rate dependent on stock level. OPSEARCH, 41:223–236, 2004.

S. Kalpakam and G. Arivarignan. A continuous review perishable inventory model. Statistics, 19:389–398, 1988.

B. N. Mandal and Phaujdar S. A note on an inventory model with stock-dependent consumption rate. Opsearch, 26:43–46, 1989.

B. Sivakumar N. Sangeetha and G. Arivarignan. Optimal control of production time of perishable inventory system with finite source of customers. Opsearch, 52:412–430,2015.

C. Periyasamy. A finite population perishable inventory system with customers search from the orbit. International Journal of Computational and Applied Mathematics,12, 2017.

K. D. Rathod and P. H. Bhathawala. Inventory model with inventory-level dependent demand rate, variable holding cost and shortages. International Journal of Scientific and Engineering Research, 4:368–372, 2013.

P. S. Reshmi and K. P. Jose. A queueing-inventory system with perishable items and retrial of customers. Malay. J. Mat., 7:165–170, 2019.

Menich Ronald. Optimally of shortest queue routing for dependent service stations. IEEE 26th IEEE Conference on Decision and Control - Los Angeles, California, USA, pages 1069–1072, 1987.

Sana and Shib Sankar. An eoq model for perishable item with stock dependent demand and price discount rate. American Journal of Mathematical and Management Sciences, 30:299–316, 2010.

J. George Shanthikumar and David D. Yao. A finite source retrial queue. Throughput bounds for closed queueing networks with queue-dependent service rates, 9:96–78,1988.

B. Sivakumar. A perishable inventory system with retrial demands and a finite population. Journal of Computational and Applied Mathematics, 224:29–38, 2009.

Abdul Kalam Sudhir Kumar Sahu and Chandan Kumar Sahoo. An inventory model with the demand rate dependent on stock and constant deterioration. journal of Indian Academic Mathematics, 30:221–228, 2008.

A. Tsoularis. Deterministic and stochastic optimal inventory control with logistic stockdependent demand rate. International Journal of Mathematics in Operational Research,6, 2014.

Diana Tom Varghese and Dhanya Shajin. State dependent admission of demands in a finite storage system. International Journal of Pure and Applied Mathematics, 118:917–922, 2018.




DOI: http://dx.doi.org/10.23755/rm.v43i0.715

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