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Neural Computing and Applications

, Volume 31, Issue 6, pp 1931–1948 | Cite as

A two-warehouse inventory model for non-instantaneous deteriorating items with interval-valued inventory costs and stock-dependent demand under inflationary conditions

  • Ali Akbar Shaikh
  • Leopoldo Eduardo Cárdenas-BarrónEmail author
  • Sunil Tiwari
Original Article

Abstract

This research work develops a two-warehouse inventory model for non-instantaneous deteriorating items with interval-valued inventory costs and stock-dependent demand under inflationary conditions. The proposed inventory model permits shortages, and the backlogging rate is variable and dependent on the waiting time for the next order, and inventory parameters are interval-valued. The main aim of this research is to obtain the retailer’s optimal replenishment policy that minimizes the present worth of total cost per unit time. The optimization problems of the inventory model have been formulated and solved using two variants of particle swarm optimization (PSO) and interval order relations. The efficiency and effectiveness of the inventory model are validated with numerical examples and a sensitivity analysis. The proposed inventory model can assist a decision maker in making important replenishment decisions.

Keywords

Inventory Non-instantaneous deterioration Two warehouses Partial backlogging Stock-dependent demand Inflation Interval-valued cost Particle swarm optimization 

Mathematics Subject Classification

90B05 

Notes

Acknowledgements

The authors are thankful to the anonymous reviewers for their comments and suggestions which have helped to improve the quality of the paper. The work was done when the third author was doing his Ph.D. from University of Delhi. The second author was supported by the Tecnológico de Monterrey Research Group in Industrial Engineering and Numerical Methods 0822B01006. The third author is grateful to his parents, wife, children Aditi Tiwari and Aditya Tiwari for their valuable support during the development of this paper.

Compliance with ethical standards

Conflict of interest

The authors declare that there are no conflicts of interest regarding the publication of this paper.

References

  1. 1.
    Ghare PM, Schrader GF (1963) A model for exponentially decaying inventory. J Ind Eng 14(5):238–243Google Scholar
  2. 2.
    Covert RP, Philip GC (1973) An EOQ model for items with Weibull distribution deterioration. AIIE Trans 5(4):323–326CrossRefGoogle Scholar
  3. 3.
    Nahmias S (1982) Perishable inventory theory: a review. Oper Res 30(4):680–708MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Raafat F (1991) Survey of literature on continuously deteriorating inventory models. J Oper Res Soc 42(1):27–37zbMATHCrossRefGoogle Scholar
  5. 5.
    Goyal SK, Giri BC (2001) Recent trends in modeling of deteriorating inventory. Eur J Oper Res 134(1):1–16MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Bakker M, Riezebos J, Teunter RH (2012) Review of inventory systems with deterioration since 2001. Eur J Oper Res 221(2):275–284MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Janssen L, Claus T, Sauer J (2016) Literature review of deteriorating inventory models by key topics from 2012 to 2015. Int J Prod Econ 182:86–112CrossRefGoogle Scholar
  8. 8.
    Wu KS, Ouyang LY, Yang CT (2006) An optimal replenishment policy for non-instantaneous deteriorating items with stock-dependent demand and partial backlogging. Int J Prod Econ 101(2):369–384CrossRefGoogle Scholar
  9. 9.
    Ouyang LY, Wu KS, Yang CT (2006) A study on an inventory model for non-instantaneous deteriorating items with permissible delay in payments. Comput Ind Eng 51(4):637–651CrossRefGoogle Scholar
  10. 10.
    Ouyang LY, Wu KS, Yang CT (2008) Retailer’s ordering policy for non-instantaneous deteriorating items with quantity discount, stock dependent demand and stochastic backorder rate. J Chin Inst Ind Eng 25(1):62–72Google Scholar
  11. 11.
    Wu KS, Ouyang LY, Yang CT (2009) Coordinating replenishment and pricing policies for non-instantaneous deteriorating items with price-sensitive demand. Int J Syst Sci 40(12):1273–1281MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Jaggi CK, Verma P (2010) An optimal replenishment policy for non-instantaneous deteriorating items with two storage facilities. Int J Serv Oper Inf 5(3):209–230Google Scholar
  13. 13.
    Chang CT, Teng JT, Goyal SK (2010) Optimal replenishment policies for non-instantaneous deteriorating items with stock-dependent demand. Int J Prod Econ 123(1):62–68CrossRefGoogle Scholar
  14. 14.
    Geetha KV, Uthayakumar R (2010) Economic design of an inventory policy for non-instantaneous deteriorating items under permissible delay in payments. J Comput Appl Math 233(10):2492–2505MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Soni HN, Patel KA (2012) Optimal pricing and inventory policies for non-instantaneous deteriorating items with permissible delay in payment: fuzzy expected value model. Int J Ind Eng Comput 3(3):281–300Google Scholar
  16. 16.
    Maihami R, Kamalabadi IN (2012) Joint pricing and inventory control for non-instantaneous deteriorating items with partial backlogging and time and price dependent demands. Int J Prod Econ 136(1):116–122CrossRefGoogle Scholar
  17. 17.
    Maihami R, Kamalabadi IN (2012) Joint control of inventory and its pricing for non-instantaneously deteriorating items under permissible delay in payments and partial backlogging. Math Comput Model 55(5–6):1722–1733MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    Shah NH, Soni HN, Patel KA (2013) Optimizing inventory and marketing policy for non-instantaneous deteriorating items with generalized type deterioration and holding cost rates. Omega 41(2):421–430CrossRefGoogle Scholar
  19. 19.
    Dye CY (2013) The effect of preservation technology investment on a non-instantaneous deteriorating inventory model. Omega 41(5):872–880CrossRefGoogle Scholar
  20. 20.
    Jaggi CK, Tiwari S (2014) Two warehouse inventory model for non-instantaneous deteriorating items with price dependent demand and time varying holding cost. In: Parakash O (ed) Mathematical modelling and applications. LAMBERT Academic Publisher, Saarbrücken, pp 225–238Google Scholar
  21. 21.
    Jaggi CK, Sharma A, Tiwari S (2015) Credit financing in economic ordering policies for non-instantaneous deteriorating items with price dependent demand under permissible delay in payments: a new approach. Int J Ind Eng Comput 6(4):481–502Google Scholar
  22. 22.
    Jaggi CK, Cárdenas-Barrón LE, Tiwari S, Shafi A (2017) Two-warehouse inventory model with imperfect quality items under deteriorating conditions and permissible delay in payments. Sci Iran Trans E Ind Eng 24(1):390–412Google Scholar
  23. 23.
    Jaggi CK, Tiwari S, Goel SK (2017) Credit financing in economic ordering policies for non-instantaneous deteriorating items with price dependent demand and two storage facilities. Ann Oper Res 248(1–2):253–280MathSciNetzbMATHCrossRefGoogle Scholar
  24. 24.
    Hartley VR (1976) Operations research—a managerial emphasis. Good Year, Santa Monica, pp 315–317Google Scholar
  25. 25.
    Sarma KVS (1987) A deterministic order level inventory model for deteriorating items with two storage facilities. Eur J Oper Res 29(1):70–73MathSciNetzbMATHCrossRefGoogle Scholar
  26. 26.
    Yang HL (2004) Two-warehouse inventory models for deteriorating items with shortages under inflation. Eur J Oper Res 157(2):344–356MathSciNetzbMATHCrossRefGoogle Scholar
  27. 27.
    Yang HL (2006) Two-warehouse partial backlogging inventory models for deteriorating items under inflation. Int J Prod Econ 103(1):362–370CrossRefGoogle Scholar
  28. 28.
    Wee HM, Yu JC, Law ST (2005) Two-warehouse inventory model with partial backordering and Weibull distribution deterioration under inflation. J Chin Inst Ind Eng 22(6):451–462Google Scholar
  29. 29.
    Pal P, Das CB, Panda A, Bhunia AK (2005) An application of real-coded genetic algorithm (for mixed integer non-linear programming in an optimal two-warehouse inventory policy for deteriorating items with a linear trend in demand and a fixed planning horizon). Int J Comput Math 82(2):163–175MathSciNetzbMATHCrossRefGoogle Scholar
  30. 30.
    Lee CC (2006) Two-warehouse inventory model with deterioration under FIFO dispatching policy. Eur J Oper Res 174(2):861–873MathSciNetzbMATHCrossRefGoogle Scholar
  31. 31.
    Chung KJ, Huang TS (2007) The optimal retailer’s ordering policies for deteriorating items with limited storage capacity under trade credit financing. Int J Prod Econ 106(1):127–145CrossRefGoogle Scholar
  32. 32.
    Hsieh TP, Dye CY, Ouyang LY (2008) Determining optimal lot size for a two-warehouse system with deterioration and shortages using net present value. Eur J Oper Res 191(1):182–192MathSciNetzbMATHCrossRefGoogle Scholar
  33. 33.
    Liao JJ, Huang KN (2010) Deterministic inventory model for deteriorating items with trade credit financing and capacity constraints. Comput Ind Eng 59(4):611–618CrossRefGoogle Scholar
  34. 34.
    Das B, Maity K, Maiti M (2007) A two warehouse supply-chain model under possibility/necessity/credibility measures. Math Comput Model 46(3–4):398–409zbMATHCrossRefGoogle Scholar
  35. 35.
    Niu B, Xie J (2008) A note on “Two-warehouse inventory model with deterioration under FIFO dispatch policy”. Eur J Oper Res 190(2):571–577zbMATHCrossRefGoogle Scholar
  36. 36.
    Rong M, Mahapatra NK, Maiti M (2008) A two warehouse inventory model for a deteriorating item with partially/fully backlogged shortage and fuzzy lead time. Eur J Oper Res 189(1):59–75MathSciNetzbMATHCrossRefGoogle Scholar
  37. 37.
    Dey JK, Mondal SK, Maiti M (2008) Two storage inventory problem with dynamic demand and interval valued lead-time over finite time horizon under inflation and time-value of money. Eur J Oper Res 185(1):170–194MathSciNetzbMATHCrossRefGoogle Scholar
  38. 38.
    Maiti MK (2008) Fuzzy inventory model with two warehouses under possibility measure on fuzzy goal. Eur J Oper Res 188(3):746–774MathSciNetzbMATHCrossRefGoogle Scholar
  39. 39.
    Lee CC, Hsu SL (2009) A two-warehouse production model for deteriorating inventory items with time-dependent demands. Eur J Oper Res 194(3):700–710MathSciNetzbMATHCrossRefGoogle Scholar
  40. 40.
    Bhunia AK, Shaikh AA (2011) A two warehouse inventory model for deteriorating items with time dependent partial backlogging and variable demand dependent on marketing strategy and time. Int J Inventory Control Manag 1(2):95–110Google Scholar
  41. 41.
    Liang Y, Zhou F (2011) A two-warehouse inventory model for deteriorating items under conditionally permissible delay in payment. Appl Math Model 35(5):2221–2231MathSciNetzbMATHCrossRefGoogle Scholar
  42. 42.
    Bhunia AK, Shaikh AA, Maiti AK, Maiti M (2013) A two warehouse deterministic inventory model for deteriorating items with a linear trend in time dependent demand over finite time horizon by elitist real-coded genetic algorithm. Int J Ind Eng Comput 4(2):241–258Google Scholar
  43. 43.
    Yang HL, Chang CT (2013) A two-warehouse partial backlogging inventory model for deteriorating items with permissible delay in payment under inflation. Appl Math Model 37(5):2717–2726MathSciNetzbMATHCrossRefGoogle Scholar
  44. 44.
    Jaggi CK, Pareek S, Khanna A, Sharma R (2014) Credit financing in a two-warehouse environment for deteriorating items with price-sensitive demand and fully backlogged shortages. Appl Math Model 38(21–22):5315–5333MathSciNetzbMATHCrossRefGoogle Scholar
  45. 45.
    Bhunia AK, Shaikh AA, Sharma G, Pareek S (2015) A two storage inventory model for deteriorating items with variable demand and partial backlogging. J Ind Prod Eng 32(4):263–272Google Scholar
  46. 46.
    Bhunia AK, Shaikh AA, Sahoo S (2016) A two-warehouse inventory model for deteriorating item under permissible delay in payment via particle swarm optimization. Int J Logist Syst Manag 24(1):45–69CrossRefGoogle Scholar
  47. 47.
    Jaggi CK, Tiwari S, Shafi A (2015) Effect of deterioration on two-warehouse inventory model with imperfect quality. Comput Ind Eng 88:378–385CrossRefGoogle Scholar
  48. 48.
    Tiwari S, Cárdenas-Barrón LE, Khanna A, Jaggi CK (2016) Impact of trade credit and inflation on retailer’s ordering policies for non-instantaneous deteriorating items in a two-warehouse environment. Int J Prod Econ 176:154–169CrossRefGoogle Scholar
  49. 49.
    Taleizadeh AA, Niaki STA, Aryanezhad MB (2009) A hybrid method of Pareto, TOPSIS and genetic algorithm to optimize multi-product multi-constraint inventory control systems with random fuzzy replenishments. Math Comput Model 49(5–6):1044–1057MathSciNetzbMATHCrossRefGoogle Scholar
  50. 50.
    Taleizadeh AA, Niaki STA, Meibodi RG (2013) Replenish-up-to multi-chance-constraint inventory control system under fuzzy random lost-sale and backordered quantities. Knowl Based Syst 53:147–156CrossRefGoogle Scholar
  51. 51.
    Taleizadeh AA, Barzinpour F, Wee HM (2011) Meta-heuristic algorithms for solving a fuzzy single-period problem. Math Comput Model 54(5–6):1273–1285MathSciNetzbMATHCrossRefGoogle Scholar
  52. 52.
    Tat R, Taleizadeh AA, Esmaeili M (2015) Developing economic order quantity model for non-instantaneous deteriorating items in vendor-managed inventory (VMI) system. Int J Syst Sci 46(7):1257–1268zbMATHCrossRefGoogle Scholar
  53. 53.
    Hansen E, Walster GW (2003) Global optimization using interval analysis. Marcel Dekker, New YorkzbMATHGoogle Scholar
  54. 54.
    Sahoo L, Bhunia AK, Kapur PK (2012) Genetic algorithm based multi-objective reliability optimization in interval environment. Comput Ind Eng 62(1):152–160CrossRefGoogle Scholar
  55. 55.
    Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. In: Proceedings of the sixth international symposium on micro machine and human science, pp 39–43Google Scholar
  56. 56.
    Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceeding of the IEEE international conference on neural networks, vol IV, pp 1942–1948Google Scholar
  57. 57.
    Clerc M (1999) The swarm and queen: towards a deterministic and adaptive particle swarm optimization. In: Proceedings of IEEE congress on evolutionary computation, pp 1951–1957Google Scholar
  58. 58.
    Clerc M, Kennedy J (2002) The particle swarm: explosion, stability, and convergence in a multi-dimensional complex space. IEEE Trans Evol Comput 6(1):58–73CrossRefGoogle Scholar
  59. 59.
    Xi M, Sun J, Xu W (2008) An improved quantum-behaved particle swarm optimization algorithm with weighted mean best position. Appl Math Comput 205(2):751–759zbMATHGoogle Scholar

Copyright information

© The Natural Computing Applications Forum 2017

Authors and Affiliations

  1. 1.School of Engineering and SciencesTecnológico de MonterreyMonterreyMexico
  2. 2.Department of Operational Research, Faculty of Mathematical Sciences, New Academic BlockUniversity of DelhiDelhiIndia
  3. 3.The Logistics Institute - Asia PacificNational University of SingaporeSingaporeSingapore

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