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Optimal control of service parameter for a perishable inventory system maintained at service facility with impatient customers

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  • Hilal Al Hamadi
  • N. Sangeetha
  • B. Sivakumar

Abstract

This paper deals with the problem of optimally controlling the service rates for the perishable inventory system at service facilities with impatient customers. We consider a finite capacity inventory system with Poisson demands and exponentially distributed service times. The maximum inventory level is fixed at $$S$$ S . The ordering policy is $$(s,Q)$$ ( s , Q ) policy, that is, whenever the inventory level drops to $$s$$ s , an order for $$Q(=S-s)$$ Q ( = S - s ) items is placed. The ordered items are received after a random time which is also distributed as exponential. The waiting customer independently reneges the system after an exponentially distributed amount of time. The items in the inventory have shelf life times that are assumed to follow an exponential distribution. Here we determine the service rates to be employed at each instant of time so that the long run total expected cost rate is minimized. The problem is modelled as a semi-Markov decision problem. The stationary optimal policy is computed using linear programming algorithm and the results are illustrated numerically. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Hilal Al Hamadi & N. Sangeetha & B. Sivakumar, 2015. "Optimal control of service parameter for a perishable inventory system maintained at service facility with impatient customers," Annals of Operations Research, Springer, vol. 233(1), pages 3-23, October.
    • Handle: RePEc:spr:annopr:v:233:y:2015:i:1:p:3-23:10.1007/s10479-014-1627-1
    DOI: 10.1007/s10479-014-1627-1
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    References listed on IDEAS

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    1. O. Berman & K.P. Sapna, 2002. "Optimal service rates of a service facility with perishable inventory items," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(5), pages 464-482, August.
    2. Yadavalli, V.S.S. & Sivakumar, B. & Arivarignan, G., 2008. "Inventory system with renewal demands at service facilities," International Journal of Production Economics, Elsevier, vol. 114(1), pages 252-264, July.
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    Cited by:

    1. Klaus Werner Schmidt & Öncü Hazır, 2019. "Formulation and solution of an optimal control problem for industrial project control," Annals of Operations Research, Springer, vol. 280(1), pages 337-350, September.
    2. R. Suganya & Lewis Nkenyereye & N. Anbazhagan & S. Amutha & M. Kameswari & Srijana Acharya & Gyanendra Prasad Joshi, 2021. "Perishable Inventory System with N-Policy, MAP Arrivals, and Impatient Customers," Mathematics, MDPI, vol. 9(13), pages 1-15, June.
    3. V. Radhamani & B. Sivakumar & G. Arivarignan, 2022. "A Comparative Study on Replenishment Policies for Perishable Inventory System with Service Facility and Multiple Server Vacation," OPSEARCH, Springer;Operational Research Society of India, vol. 59(1), pages 229-265, March.
    4. Emre Berk & Ülkü Gürler & Saeed Poormoaied, 2020. "On the $$\varvec{(Q,r)}$$(Q,r) policy for perishables with positive lead times and multiple outstanding orders," Annals of Operations Research, Springer, vol. 284(1), pages 81-98, January.
    5. Kai Li & Yuqian Pan & Bayi Cheng & Bohai Liu, 2018. "The Setting and Optimization of Quick Queue," Journal of Optimization Theory and Applications, Springer, vol. 178(3), pages 1014-1026, September.
    6. Yang Yang & Jianming Yao, 2021. "Resource integration optimization of convenience service platforms adopting dynamic service modes in new retail," Frontiers of Business Research in China, Springer, vol. 15(1), pages 1-19, December.
    7. N. Nithya & N. Anbazhagan & S. Amutha & K. Jeganathan & Gi-Cheon Park & Gyanendra Prasad Joshi & Woong Cho, 2023. "Controlled Arrivals on the Retrial Queueing–Inventory System with an Essential Interruption and Emergency Vacationing Server," Mathematics, MDPI, vol. 11(16), pages 1-24, August.

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