Analysis of Perishable Queueing-Inventory System with Positive Service Time and (\(S - 1, S\)) Replenishment Policy

  • Agassi Melikov
  • Mammad ShahmaliyevEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 800)


In this paper, model of inventory system with positive service time and perishable inventory is studied. It is assumed that some demands do not acquire the item after service completion and order replenishment lead time is a positive random variable. \((S-1, S)\) order replenishment policy is applied. The exact and approximate methods are developed for calculation of joint distributions of the inventory level and number of customers in the system. The formulas for the system performance measures calculation are given as well. The high accuracy of formulas are confirmed by numerical experiments. The problem of choosing the optimal server rate to minimize the total cost is solved.


Perishable inventory systems Positive service time (\(S -1, S\)) order replenishment policy Calculation methods 


  1. 1.
    Sigman, K., Simchi-Levi, D.: Light traffic heuristic for an M/G/1 queue with limited inventory. Ann. Oper. Res. 40, 371–380 (1992)CrossRefzbMATHGoogle Scholar
  2. 2.
    Melikov, A.Z., Molchanov, A.A.: Stock optimization in transport/storage systems. Cybernetics 27(3), 484–487 (1992)zbMATHGoogle Scholar
  3. 3.
    Krishnamoorthy, A., Lakshmy, B., Manikandan, R.: A survey on inventory models with positive service time. OPSEARCH 48(2), 153–169 (2011)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Krishnamoorthy, A., Manikandan, R., Lakshmy, B.: Revisit to queueing-inventory system with positive service time. Ann. Oper. Res. 233, 221–236 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Krishnamoorthy, A., Manikandan, R., Shajin, D.: Analysis of a multi-server queueing-inventory system. Adv. Oper. Res. (Hindawi Publ. Corp.) 2015, 16 (2015). Article ID: 747328Google Scholar
  6. 6.
    Baron, O., Berman, O., Perry, D.: Continuous review inventory models for perishable items ordered in batches. Math. Methods Oper. Res. 72, 217–247 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Lawrence, A.S., Sivakumar, B., Arivarignan, G.: A perishable inventory system with service facility and finite source. Appl. Math. Model. 37, 4771–4786 (2013)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Goyal, S., Giri, B.: Recent trends in modeling of deteriorating inventory. Eur. J. Oper. Res. 134, 1–16 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Karaesmen, I., Scheller-Wolf, A., Deniz, B.: Managing perishable and aging inventories: review and future research directions. In: Kempf, K., Keskinocak, P., Uzsoy, R. (eds.) Planning Production and Inventories in the Extended Enterprise. ISOR, vol. 151, pp. 393–436. Springer, Boston (2011). doi: 10.1007/978-1-4419-6485-4_15 CrossRefGoogle Scholar
  10. 10.
    Nahmias, S.: Perishable Inventory Theory. Springer, Heidelberg (2011)CrossRefzbMATHGoogle Scholar
  11. 11.
    Sivakumar, B., Arivarignan, G.: A perishable inventory system with service facilities and negative customers. Adv. Model. Optim. 7, 193–210 (2006)zbMATHGoogle Scholar
  12. 12.
    Manuel, P., Sivakumar, B., Arivarignan, G.: A perishable inventory system with service facilities, MAP arrivals and PH-service times. J. Syst. Sci. Syst. Eng. 16, 62–73 (2007)CrossRefGoogle Scholar
  13. 13.
    Manuel, P., Sivakumar, B., Arivarignan, G.: A perishable inventory system with service facilities and retrial customers. Comput. Ind. Eng. 54, 484–501 (2008)CrossRefGoogle Scholar
  14. 14.
    Amirthakodi, M., Radhamami, V., Sivakumar, B.: A perishable inventory system with service facility and feedback customers. Ann. Oper. Res. 233, 25–55 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Hamadi, H.M., Sangeetha, N., Sivakumar, B.: Optimal control of service parameter for a perishable inventory system maintained at service facility with impatient customers. Ann. Oper. Res. 233, 3–23 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Berman, O., Sapna, K.P.: Optimal service rate of service facility with perishable inventory items. Nav. Res. Logist. 49, 464–482 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Jajaraman, B., Sivakumar, B., Arivarignan, G.: A perishable inventory system with postponed demands and multiple server vacations. Model. Simul. Eng. (Hindawi Publ. Corp.) 2012, 17 (2012). Article ID: 620960Google Scholar
  18. 18.
    Melikov, A.Z., Ponomarenko, L.A., Shahmaliyev, M.: Models of perishable queueing-inventory system with repeated customers. J. Autom. Inf. Sci. 48(2), 22–38 (2016)CrossRefGoogle Scholar
  19. 19.
    Kalpakam, S., Sapna, K.P.: (S-1, S) perishable systems with stochastic lead times. Math. Comput. Model. 21(6), 95–104 (1995)CrossRefzbMATHGoogle Scholar
  20. 20.
    Kranenburg, A.A., van Houtum, G.J.: Cost optimization in the (S-1, S) lost sales inventory model with multiple demand classes. Oper. Res. Lett. 35, 493–502 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Isotupa, K.P.S.: Cost analysis of an (S-1, S) inventory system with two demand classes and rationing. Ann. Oper. Res. 233, 411–421 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Jaccard, P.: Etude de la distribution florale dans une portion des Alpes et du Jura. Bull. de la Soc. Vaud. des Sci. Nat. 37, 547–579 (1901). (in French)Google Scholar

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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Deparment of Computer SciencesNational Aviation Academy of AzerbaijanBakuAzerbaijan

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