Advertisement

Sādhanā

, 44:95 | Cite as

An inventory system for varying deteriorating pharmaceutical items with price-sensitive demand and variable holding cost under partial backlogging in healthcare industries

  • Mohit RastogiEmail author
  • S R Singh
Article
  • 14 Downloads

Abstract

This paper presents an inventory system for deteriorating pharmaceutical items with price-sensitive demand. Mostly existing studies of pharmaceutical inventory models consider the rate of deterioration as constant, which is not logical in the context of healthcare industries because pharmaceutical products (medicine or drugs) deteriorate significantly. Hence, the rate of deterioration is considered as time-dependent and follows a three-parameter Weibull distribution. In most of the developed models it is believed that the different costs related with inventory remain the same all the time whereas in realistic situations, manufacturing cost of medicine, the cost of maintaining the pharmaceutical products in the cold store or even the cost of keeping the patient’s record increases with time. Thus, the cost of the holding of items is taken as time-dependent. Shortages are allowed in this study and are partially backlogged. The main objective of this study is to optimize the total average cost of the system by computing the optimal ordering quantity and the optimal time interval. Finally, a numerical illustration with sensitivity analysis is given to exemplify the proposed study.

Keywords

Weibull distribution price-sensitive demand pharmaceutical items deterioration shortages partial backlogging 

References

  1. 1.
    Mandal B and Pal A K 1998 Order level inventory system with ramp type demand rate for deteriorating items. J. Interdiscip. Math. 1: 49–66MathSciNetCrossRefGoogle Scholar
  2. 2.
    Chen J M and Lin S C 2003 Optimal replenishment scheduling for inventory items with Weibull distributed deterioration and time-varying demand. J. Inform. Optim. Sci. 24: 1–21MathSciNetzbMATHGoogle Scholar
  3. 3.
    Ghosh S K and Chaudhuri K S 2004 An order-level inventory model for a deteriorating item with Weibull distribution deterioration, time-quadratic demand and shortages. Adv. Model. Optim. 6: 21–35MathSciNetzbMATHGoogle Scholar
  4. 4.
    Jain S and Kumar M 2010 An EOQ inventory model for items with ramp type demand, three-parameter Weibull distribution deterioration and starting with shortage. Yugosl. J. Oper. Res. 20: 249–259MathSciNetCrossRefGoogle Scholar
  5. 5.
    Tripathy C K and Pradhan L M 2012 An EOQ model for three parameter Weibull deterioration with permissible delay in payments and associated salvage value. Int. J. Ind. Eng. Comput. 3: 115–122Google Scholar
  6. 6.
    Kumar S and Singh A K 2016 Optimal time policy for deteriorating items of two-warehouse inventory system with time and stock dependent demand and partial backlogging. Sadhana 41: 541–548MathSciNetzbMATHGoogle Scholar
  7. 7.
    Uthayakumar R and Karuppasamy S K 2016 A pharmaceutical inventory model for healthcare industries with quadratic demand, linear holding cost and shortages. Int. J. Pure Appl. Math. 106: 73–83Google Scholar
  8. 8.
    Panda S, Saha S, Modak N M and Sana S S 2017 A volume flexible deteriorating inventory model with price sensitive demand. TÉKHNE- Rev. Appl. Manag. Stud. 15: 117–123Google Scholar
  9. 9.
    Roy A 2008 An inventory model for deteriorating items with price dependent demand and time varying holding cost. Adv. Model. Optim. 10: 25–37MathSciNetzbMATHGoogle Scholar
  10. 10.
    Chowdhury R R, Ghosh S K and Chaudhuri K S 2014 An order-level inventory model for a deteriorating item with time-quadratic demand and time-dependent partial backlogging with shortages in all cycles. Amer. J. Math. Management Sci. 33: 75–97Google Scholar
  11. 11.
    Tayal S, Singh S R, Sharma R and Singh A P 2015 An EPQ model for non-instantaneous deteriorating item with time dependent holding cost and exponential demand rate. Int. J. Oper. Res. 23: 145–162MathSciNetCrossRefGoogle Scholar
  12. 12.
    Mogale D G, Kumar S K and Tiwari M K 2016 Two stage indian food grain supply chain network transportation-allocation Model. IFAC-PapersOnLine 49: 1767–1772.  https://doi.org/10.1016/j.ifacol.2016.07.838 CrossRefGoogle Scholar
  13. 13.
    Mogale D G, Kumar S K and Tiwari M K 2018 An MINLP model to support the movement and storage decisions of the Indian food grain supply chain. Contr. Eng. Pract. 70: 98–113CrossRefGoogle Scholar
  14. 14.
    Kumar S, Singh A K and Patel M K 2016 Optimization of Weibull deteriorating items inventory model under the effect of price and time dependent demand with partial backlogging. Sadhana 41: 977–984MathSciNetzbMATHGoogle Scholar
  15. 15.
    Rastogi M, Singh S R, Kushwah P and Tayal S 2017 An EOQ model with variable holding cost and partial backlogging under credit limit policy and cash discount. Uncert. Supply Chain Manag. 5: 27–42CrossRefGoogle Scholar
  16. 16.
    San-José L A, Sicilia J and Alcaide-López-de-Pablo D 2018 An inventory system with demand dependent on both time and price assuming backlogged shortages. Eur. J. Oper. Res. 270: 889–897MathSciNetCrossRefGoogle Scholar
  17. 17.
    Sundararajan R and Uthayakumar R 2018 Optimal pricing and replenishment policies for instantaneous deteriorating items with backlogging and permissible delay in payment under inflation. Amer. J. Math. Management Sci. 37: 1–17Google Scholar
  18. 18.
    Mondal B, Bhunia A K and Maiti M 2003 An inventory system of ameliorating items for price dependent demand rate. Comput. Ind. Eng. 45: 443–456CrossRefGoogle Scholar
  19. 19.
    Mukhopadhyay S, Mukherjee R N and Chaudhuri K S 2005 An EOQ model with two parameter Weibull distribution deterioration and price-dependent demand. Internat. J. Math. Ed. Sci. Tech. 36: 25–33MathSciNetCrossRefGoogle Scholar
  20. 20.
    Chang C T, Chen Y J, Tsai T R and Wu S J 2010 Inventory models with stock-and price dependent demand for deteriorating items based on limited shelf space. Yugosl. J. Oper. Res. 20: 55–69MathSciNetCrossRefGoogle Scholar
  21. 21.
    Singh S R and Vishnoi M 2013 Supply chain inventory model with price-dependent consumption rate with ameliorating and deteriorating items and two levels of storage. Int. J. Procur. Manag. 6: 129–151Google Scholar
  22. 22.
    Ahmadi-Javid A and Hoseinpour P 2015 A location-inventory-pricing model in a supply chain distribution network with price-sensitive demands and inventory-capacity constraints. Transport. Res. Part E: Logist. Transport. Rev. 82: 238–255CrossRefGoogle Scholar
  23. 23.
    Sharma S, Singh S R and Ram M 2015 An EPQ model for deteriorating items with price sensitive demand and shortages. Int. J. Oper. Res. 23: 245–255MathSciNetCrossRefGoogle Scholar
  24. 24.
    Rastogi M, Singh S R, Kushwah P and Tayal S 2017 Two warehouse inventory policy with price dependent demand and deterioration under partial backlogging. Deci. Sci. Lett. 6: 11–22CrossRefGoogle Scholar
  25. 25.
    Maiyar L M and Thakkar J J 2017 A combined tactical and operational deterministic food grain transportation model: Particle swarm based optimization approach. Comput. Ind. Eng. 110: 30–42CrossRefGoogle Scholar
  26. 26.
    Maiyar L M and Thakkar J J 2018 Modelling and analysis of inter-modal food grain transportation under hub disruption towards sustainability. Int. J. Prod. Econ.  https://doi.org/10.1016/j.ijpe.2018.07.021 CrossRefGoogle Scholar
  27. 27.
    Mogale D G, Lahoti G, Jha S B, Shukla M, Kamath, N and Tiwari M K 2018 Dual market facility network design under bounded rationality. Algorithms 11: 54;  https://doi.org/10.3390/a11040054 MathSciNetCrossRefGoogle Scholar
  28. 28.
    Rastogi M and Singh S R 2018 A production inventory model for deteriorating products with selling price dependent consumption rate and shortages under inflationary environment. Int. J. Procur. Manag. 11: 36–52Google Scholar
  29. 29.
    Ouyang L Y, Wu K S and Cheng M C 2005 An inventory model for deteriorating items with exponential declining demand and partial backlogging. Yugosl. J. Oper. Res. 15: 277–288MathSciNetCrossRefGoogle Scholar
  30. 30.
    Dye C Y, Ouyang L Y and Hsieh T P 2007 Inventory and pricing strategies for deteriorating items with shortages: A discounted cash flow approach. Comput. Ind. Eng. 52: 29- 40CrossRefGoogle Scholar
  31. 31.
    Singh S R, Singhal S and Gupta P K 2010 A volume flexible inventory model for defective items with multi variate demand and partial backlogging. Int. J. Oper. Res. Optim. 1: 55–69zbMATHGoogle Scholar
  32. 32.
    Sanni S S and Chukwu W I E 2013 An economic order quantity model for items with three parameter Weibull distribution deterioration, ramp-type demand and shortages. Appl. Math. Model. 37: 9698–9706MathSciNetCrossRefGoogle Scholar
  33. 33.
    Mishra U and Tripathy C K 2015 An inventory model for Weibull deteriorating items with salvage value. Int. J. Logis. Sys. Manag. 22: 67–76Google Scholar
  34. 34.
    Singh S R, Rastogi M and Tayal S 2016 An inventory model for deteriorating items having seasonal and stock-dependent demand with allowable shortages. In: Pant M, Deep K, Bansal J, Nagar A and Das K (eds) Proceeding of Fifth International conference on Soft Computing for Problem Solving, Advances in Intelligent Systems and Computing, vol. 437, pp. 501–513. Springer, SingaporeGoogle Scholar
  35. 35.
    Uthayakumar R and Karuppasamy S K 2017 An inventory model for variable deteriorating pharmaceutical items with time dependent demand and time dependent holding cost under trade credit in healthcare industries. Commun. Appl. Anal. 21: 533–549Google Scholar
  36. 36.
    Singh S R and Sharma S 2017 A production reliable model for deteriorating products with random demand and inflation. Int. J. Sys. Sci.: Oper. Logist. 4: 330–338Google Scholar
  37. 37.
    Shekarabi S A H, Gharaei A and Karimi M 2018 Modelling and optimal lot-sizing of integrated multi-level multi-wholesaler supply chains under then shortage and limited warehouse space: generalised outer approximation. Int. J. Sys. Sci.: Oper. Logist.  https://doi.org/10.1080/23302674.2018.1435835
  38. 38.
    Rastogi M, Singh S R and Kushwah P 2018 An inventory model for non-instantaneous deteriorating products having price sensitive demand and partial backlogging of occurring shortages. Int. J. Oper. Quant. Manag. 24: 59–73Google Scholar
  39. 39.
    Mogale D G, Kumar M, Kumar S K and Tiwari M K 2018 Grain silo location-allocation problem with dwell time for optimization of food grain supply chain network. Transport. Res. Part E: Logist. Transport. Rev. 111: 40–69CrossRefGoogle Scholar
  40. 40.
    Gharaei A and Pasandideh S H R 2017 Modeling and optimization of four-level integrated supply chain with the aim of determining the optimum stockpile and period length: Sequential Quadratic Programming. J. Ind. Prod. Eng. 34: 529–541Google Scholar
  41. 41.
    Gharaei A, Pasandideh S H R and Akhavan-Niaki S T 2018 An optimal integrated lot sizing policy of inventory in a bi-objective multi-level supply chain with stochastic constraints and imperfect products. J. Ind. Prod. Eng. 35: 6–20Google Scholar

Copyright information

© Indian Academy of Sciences 2019

Authors and Affiliations

  1. 1.Department of Applied Sciences and HumanitiesIMS Engineering CollegeGhaziabadIndia
  2. 2.Department of MathematicsCCS UniversityMeerutIndia

Personalised recommendations