Advertisement

Arabian Journal for Science and Engineering

, Volume 44, Issue 3, pp 1737–1755 | Cite as

EOQ and EPQ Production-Inventory Models with Variable Holding Cost: State-of-the-Art Review

  • Hesham K. AlfaresEmail author
  • Ahmed M. Ghaithan
Review - Systems Engineering
  • 44 Downloads

Abstract

In production-inventory control, economic order quantity (EOQ) and economic production quantity (EPQ) models are used to determine the optimal order quantities for purchasing and manufacturing. Most EOQ and EPQ models are constructed assuming constant costs. Recently, however, EOQ/EPQ models assuming varying costs (i.e., holding, ordering, and purchasing costs) have been receiving considerable attention. The objective of this paper is to review and classify EOQ and EPQ inventory models formulated under the assumption of variable holding costs. The relevant papers are reviewed and classified into three main types: time-dependent holding cost, stock-dependent holding cost, and multiple dependence or other holding cost variability. Additional classification is proposed for the reviewed models according to their objectives, solution methods, and applications. The paper identifies research trends and includes several suggestions for future research directions.

Keywords

Inventory control Optimization Lot sizing Modeling Production economics Variable holding cost 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Harris, F.W.: How many parts to make at once. Fact. Mag. Manag. 10, 135–136 (1913)Google Scholar
  2. 2.
    Taft, E.W.: The most economical production lot. Iron Age. 101, 1410–1412 (1918)Google Scholar
  3. 3.
    Clendenen, G.W.; Rinks, D.B.: The effect of labour costs, holding costs, and uncertainty in demand on pull inventory control policies. Int. J. Prod. Res. 34, 1725–1738 (1996)CrossRefzbMATHGoogle Scholar
  4. 4.
    Van Den Heuvel, W.; Wagelmans, A.P.: A holding cost bound for the economic lot-sizing problem with time-invariant cost parameters. Oper. Res. Lett. 37, 102–106 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Andriolo, A.; Battini, D.; Grubbström, R.W.; Persona, A.; Sgarbossa, F.: A century of evolution from Harris s basic lot size model: Survey and research agenda. Int. J. Prod. Econ. 155, 16–38 (2014)CrossRefGoogle Scholar
  6. 6.
    Bushuev, M.A.; Guiffrida, A.; Jaber, M.Y.; Khan, M.: A review of inventory lot sizing review papers. Manag. Res. Rev. 38, 283–298 (2015)CrossRefGoogle Scholar
  7. 7.
    Lee, Y.-P.; Dye, C.-Y.: An inventory model for deteriorating items under stock-dependent demand and controllable deterioration rate. Comput. Ind. Eng. 63, 474–482 (2012)CrossRefGoogle Scholar
  8. 8.
    Giri, B.C.; Goswami, A.; Chaudhuri, K.S.: An EOQ model for deteriorating items with time varying demand and costs. J. Oper. Res. Soc. 47, 1398–1405 (1996)CrossRefzbMATHGoogle Scholar
  9. 9.
    Shao, Y.E.; Fowler, J.W.; Runger, G.C.: Determining the optimal target for a process with multiple markets and variable holding costs. Int. J. Prod. Econ. 65, 229–242 (2000)CrossRefGoogle Scholar
  10. 10.
    Shao, Y.E.; Fowler, J.W.; Runger, G.C.: A note on determining an optimal target by considering the dependence of holding costs and the quality characteristics. J. Appl. Stat. 32, 813–822 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Balkhi, Z.T.; Tadj, L.: A generalized economic order quantity model with deteriorating items and time varying demand, deterioration, and costs. Int. Trans. Oper. Res. 15, 509–517 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Roy, A.: An inventory model for deteriorating items with price dependent demand and time varying holding cost. Adv. Model. Optim. 10, 25–37 (2008)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Tripathy, C.K.; Mishra, U.: An inventory model for Weibull deteriorating items with price dependent demand and time-varying holding cost. Appl. Math. Sci. 4, 2171–2179 (2010)zbMATHGoogle Scholar
  14. 14.
    Mishra, V.K.; Sahab Singh, L.: Deteriorating inventory model for time dependent demand and holding cost with partial backlogging. Int. J. Manag. Sci. Eng. Manag. 6, 267–271 (2011)Google Scholar
  15. 15.
    Mishra, V.K.; Singh, L.S.; Kumar, R.: An inventory model for deteriorating items with time-dependent demand and time-varying holding cost under partial backlogging. J. Ind. Eng. Int. 9, 1–5 (2013)CrossRefGoogle Scholar
  16. 16.
    Guchhait, P.; Maiti, M.K.; Maiti, M.: Production-inventory models for a damageable item with variable demands and inventory costs in an imperfect production process. Int. J. Prod. Econ. 144, 180–188 (2013)CrossRefGoogle Scholar
  17. 17.
    Mishra, V.K.: An inventory model of instantaneous deteriorating items with controllable deterioration rate for time dependent demand and holding cost. J. Ind. Eng. Manag. 6, 495–506 (2013)Google Scholar
  18. 18.
    Mishra, V.K.: Controllable deterioration rate for time-dependent demand and time-varying holding cost. Yugosl. J. Oper. Res. 24, 87–98 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Karmakar, B.: Inventory models with ramp-type demand for deteriorating items with partial backlogging and time-varing holding cost. Yugosl. J. Oper. Res. 24, 249–266 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Palanivel, M.; Uthayakumar, R.: An EPQ model for deteriorating items with variable production cost, time dependent holding cost and partial backlogging under inflation. OPSEARCH 52, 1–17 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Choudhury, K.D.; Karmakar, B.; Das, M.; Datta, T.K.: An inventory model for deteriorating items with stock-dependent demand, time-varying holding cost and shortages. OPSEARCH 52, 55–74 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Rangarajan, K.; Karthikeyan, K.: Analysis of an EOQ Inventory Model for Deteriorating Items with Different Demand Rates. Appl. Math. Sci. 9, 2255–2264 (2015)Google Scholar
  23. 23.
    Dutta, D.; Kumar, P.: A partial backlogging inventory model for deteriorating items with time-varying demand and holding cost. Int. J. Math. Oper. Res. 7, 281–296 (2015a)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Tayal, S.; Singh, S.R.; Sharma, R.; Singh, A.P.: An EPQ model for non-instantaneous deteriorating item with time dependent holding cost and exponential demand rate. Int. J. Oper. Res. 23, 145–162 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Alfares, H.K.; Ghaithan, A.M.: Inventory and pricing model with price-dependent demand, time-varying holding cost, and quantity discounts. Comput. Ind. Eng. 94, 170–177 (2016)CrossRefGoogle Scholar
  26. 26.
    Giri, B.C.; Bardhan, S.: Coordinating a two-echelon supply chain with price and inventory level dependent demand, time dependent holding cost, and partial backlogging. Int. J. Math. Oper. Res. 8, 406–423 (2016)MathSciNetGoogle Scholar
  27. 27.
    Sivashankari, C.K.: Production inventory model with deteriorating items with constant, linear and quadratic holding cost-a comparative study. Int. J. Oper. Res. 27, 589–609 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Pervin, M.; Roy, S.K.; Weber, G.-W.: Analysis of inventory control model with shortage under time-dependent demand and time-varying holding cost including stochastic deterioration. Ann. Oper. Res. 260, 437–460 (2018a)MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Pervin, M.; Roy, S.K.; Weber, G.W.: A Two-echelon inventory model with stock-dependent demand and variable holding cost for deteriorating items. Numer. Algebra Control Optim. 7, 21–50 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Patel, R.; Sheikh, S.R.: Inventory model with different deterioration rates under linear demand and time varying holding cost. Int. J Math. Stat. Invent. 3, 36–42 (2015)Google Scholar
  31. 31.
    Rajeswari, N.; Vanjikkodi, T.; Sathyapriya, K.: Optimization in fuzzy inventory model for linearly deteriorating items, with power demand, partial backlogging and linear holding cost. Optimization 169, 0975–8887 (2017)Google Scholar
  32. 32.
    Chandra, S.: An inventory model with ramp type demand, time varying holding cost and price discount on backorders. Uncertain Supply Chain Manag. 5, 51–58 (2017)CrossRefGoogle Scholar
  33. 33.
    Rastogi, M.; Singh, S.; Kushwah, P.; Tayal, S.: An EOQ model with variable holding cost and partial backlogging under credit limit policy and cash discount. Uncertain Supply Chain Manag. 5, 27–42 (2017)CrossRefGoogle Scholar
  34. 34.
    Pervin, M.; Roy, S.K.; Weber, G.W.: An integrated inventory model with variable holding cost under two levels of trade-credit policy. Numer. Algebra Control Optim. 8, 169–191 (2018b)MathSciNetCrossRefGoogle Scholar
  35. 35.
    Karuppasamy, S.K.; Uthayakumar, R.: A deterministic pharmaceutical inventory model for variable deteriorating items with time-dependent demand and time-dependent holding cost in healthcare industries. In: Panda, B., Sharma, S., Batra, U. (eds.) Innovations in Computational Intelligence. pp. 199–210. Springer, Berlin (2018)Google Scholar
  36. 36.
    Sen, N.; Saha, S.: An inventory model for deteriorating items with time dependent holding cost and shortages under permissible delay in payment. Int. J. Procure. Manag. 11, 518–531 (2018)CrossRefGoogle Scholar
  37. 37.
    Sharma, S.; Singh, S.; Singh, S.R.: An inventory model for deteriorating items with expiry date and time varying holding cost. Int. J. Procure. Manag. 11, 650–666 (2018)CrossRefGoogle Scholar
  38. 38.
    Tripathi, R.: Inventory model with different demand rate and different holding cost. Int. J. Ind. Eng. Comput. 4, 437–446 (2013)Google Scholar
  39. 39.
    Dutta, D.; Kumar, P.: A partial backlogging inventory model for deteriorating items with time-varying demand and holding cost: an interval number approach. Croat. Oper. Res. Rev. 6, 321–334 (2015b)MathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    Tripathi, R.P.; Mishra, S.M.: EOQ model with linear time dependent demand and different holding cost functions. Int. J. Math. Oper. Res. 9, 452–466 (2016)MathSciNetCrossRefGoogle Scholar
  41. 41.
    Shah, N.H.; Soni, H.N.; Patel, K.A.: Optimizing inventory and marketing policy for non-instantaneous deteriorating items with generalized type deterioration and holding cost rates. Omega 41, 421–430 (2013)CrossRefGoogle Scholar
  42. 42.
    Rabbani, M.; Zia, N.P.; Rafiei, H.: Coordinated replenishment and marketing policies for non-instantaneous stock deterioration problem. Comput. Ind. Eng. 88, 49–62 (2015)CrossRefGoogle Scholar
  43. 43.
    Weiss, H.J.: Economic order quantity models with nonlinear holding costs. Eur. J. Oper. Res. 9, 56–60 (1982)CrossRefzbMATHGoogle Scholar
  44. 44.
    Goh, M.: EOQ models with general demand and holding cost functions. Eur. J. Oper. Res. 73, 50–54 (1994)CrossRefzbMATHGoogle Scholar
  45. 45.
    Giri, B.C.; Chaudhuri, K.S.: Deterministic models of perishable inventory with stock-dependent demand rate and nonlinear holding cost. Eur. J. Oper. Res. 105, 467–474 (1998)CrossRefzbMATHGoogle Scholar
  46. 46.
    Chang, C.-T.: Inventory models with stock-dependent demand and nonlinear holding costs for deteriorating items. Asia-Pac. J. Oper. Res. 21, 435–446 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  47. 47.
    Ferguson, M.; Jayaraman, V.; Souza, G.C.: Note: an application of the EOQ model with nonlinear holding cost to inventory management of perishables. Eur. J. Oper. Res. 180, 485–490 (2007)CrossRefzbMATHGoogle Scholar
  48. 48.
    Mahata, G.C.; Goswami, A.: Fuzzy EOQ models for deteriorating items with stock dependent demand and non-linear holding costs. Int. J. Appl. Math. Comput. Sci. 5, 94–98 (2009)Google Scholar
  49. 49.
    Pando, V.; Garcı, J.; San-José, L.A.; Sicilia, J.: Maximizing profits in an inventory model with both demand rate and holding cost per unit time dependent on the stock level. Comput. Ind. Eng. 62, 599–608 (2012a)CrossRefGoogle Scholar
  50. 50.
    San-José, L.A.; Sicilia, J.; González-de-la-Rosa, M.; Febles-Acosta, J.: An economic order quantity model with nonlinear holding cost, partial backlogging and ramp-type demand. Eng. Optim. 50, 1164–1177 (2018)MathSciNetCrossRefGoogle Scholar
  51. 51.
    Tripathi, R.P.: Deterministic inventory models with nonlinear time-dependent and stock-dependent holding cost under non-increasing time-sensitive demand. Int. J. Econ. Bus. Res. 16, 326–336 (2018)CrossRefGoogle Scholar
  52. 52.
    San-José, L.A.; Sicilia, J.; García-Laguna, J.: Analysis of an EOQ inventory model with partial backordering and non-linear unit holding cost. Omega 54, 147–157 (2015)CrossRefGoogle Scholar
  53. 53.
    Khalilpourazari, S.; Pasandideh, S.H.R.: Multi-item EOQ model with nonlinear unit holding cost and partial backordering: moth-flame optimization algorithm. J. Ind. Prod. Eng. 34, 42–51 (2017)Google Scholar
  54. 54.
    Tripathi, R.P.; Singh, D.: Inventory model with stock dependent demand and different holding cost functions. Int. J. Ind. Syst. Eng. 21, 68–82 (2015)Google Scholar
  55. 55.
    Sundara Rajan, R.; Uthayakumar, R.: Analysis and optimization of an EOQ inventory model with promotional efforts and back ordering under delay in payments. J. Manag. Anal. 4, 159–181 (2017)Google Scholar
  56. 56.
    Yadav, A.S.; Swami, A.: A partial backlogging production-inventory lot-size model with time-varying holding cost and Weibull deterioration. Int. J. Procure. Manag. 11, 639–649 (2018)CrossRefGoogle Scholar
  57. 57.
    Valliathal, M.; Uthayakumar, R.: Designing a new computational approach of partial backlogging on the economic production quantity model for deteriorating items with non-linear holding cost under inflationary conditions. Optim. Lett. 5, 515–530 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  58. 58.
    Alfares, H.K.: Inventory model with stock-level dependent demand rate and variable holding cost. Int. J. Prod. Econ. 108, 259–265 (2007)CrossRefGoogle Scholar
  59. 59.
    Urban, T.L.: An extension of inventory models with discretely variable holding costs. Int. J. Prod. Econ. 114, 399–403 (2008)CrossRefGoogle Scholar
  60. 60.
    Alfares, H.K.: An EPQ model with variable holding cost. Int. J. Ind. Eng. Theory Appl. Pract. 19, 232–240 (2012)Google Scholar
  61. 61.
    Sazvar, Z.; Baboli, A.; Jokar, M.R.A.: A replenishment policy for perishable products with non-linear holding cost under stochastic supply lead time. Int. J. Adv. Manuf. Technol. 64, 1087–1098 (2013)CrossRefGoogle Scholar
  62. 62.
    Gupta, V.; Singh, S.R.: An integrated inventory model with fuzzy variables, three-parameter Weibull deterioration and variable holding cost under inflation. Int. J. Oper. Res. 18, 434–451 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  63. 63.
    Alfares, H.K.: Production-inventory system with finite production rate, stock-dependent demand, and variable holding cost. RAIRO-Oper. Res. 48, 135–150 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  64. 64.
    Alfares, H.K.: Maximum-profit inventory model with stock-dependent demand, time-dependent holding cost, and all-units quantity discounts. Math. Model. Anal. 20, 715–736 (2015a)MathSciNetCrossRefGoogle Scholar
  65. 65.
    Alfares, H.K.: Production and inventory planning with variable holding cost and all-units quantity discounts. INFOR Inf. Syst. Oper. Res. 53, 170–177 (2015b)MathSciNetGoogle Scholar
  66. 66.
    Tyagi, A.: An optimization of an inventory model of decaying-lot depleted by declining market demand and extended with discretely variable holding costs. Int. J. Ind. Eng. Comput. 5, 71–86 (2014)Google Scholar
  67. 67.
    Adida, E.; Perakis, G.: A nonlinear continuous time optimal control model of dynamic pricing and inventory control with no backorders. Nav. Res. Logist. NRL. 54, 767–795 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  68. 68.
    Federgruen, A.; Wang, M.: A continuous review model with general shelf age and delay-dependent inventory costs. Probab. Eng. Inf. Sci. 29, 507–525 (2015a)MathSciNetCrossRefzbMATHGoogle Scholar
  69. 69.
    Federgruen, A.; Wang, M.: Inventory models with shelf-age and delay-dependent inventory costs. Oper. Res. 63, 701–715 (2015b)MathSciNetCrossRefzbMATHGoogle Scholar
  70. 70.
    O’Neill, B.; Sanni, S.: Profit optimisation for deterministic inventory systems with linear cost. Comput. Ind. Eng. 122, 303–317 (2018)CrossRefGoogle Scholar
  71. 71.
    Muhlemann, A.P.; Valtis-Spanopoulos, N.P.: A variable holding cost rate EOQ model. Eur. J. Oper. Res. 4, 132–135 (1980)CrossRefzbMATHGoogle Scholar
  72. 72.
    Abou-El-Ata, M.O.; Kotb, K.A.M.: Multi-item EOQ inventory model with varying holding cost under two restrictions: a geometric programming approach. Prod. Plan. Control 8, 608–611 (1997)CrossRefGoogle Scholar
  73. 73.
    Berman, O.; Perry, D.: An EOQ model with state-dependent demand rate. Eur. J. Oper. Res. 171, 255–272 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  74. 74.
    Scarpello, G.M.; Ritelli, D.: EOQ when holding costs grow with the stock level: well-posedness and solutions. Adv. Model. Optim. 10, 233–240 (2008)MathSciNetzbMATHGoogle Scholar
  75. 75.
    Gayen, M.; Pal, A.K.: A two ware house inventory model for deteriorating items with stock dependent demand rate and holding cost. Oper. Res. 9, 153–165 (2009)zbMATHGoogle Scholar
  76. 76.
    Pando, V.; García-Laguna, J.; Sn-José, L.A.: Optimal policy for profit maximising in an EOQ model under non-linear holding cost and stock-dependent demand rate. Int. J. Syst. Sci. 43, 2160–2171 (2012b)MathSciNetCrossRefzbMATHGoogle Scholar
  77. 77.
    Yang, C.-T.: An inventory model with both stock-dependent demand rate and stock-dependent holding cost rate. Int. J. Prod. Econ. 155, 214–221 (2014)CrossRefGoogle Scholar
  78. 78.
    Das, K.; Roy, T.K.; Maiti, M.: Multi-item inventory model with quantity-dependent inventory costs and demand-dependent unit cost under imprecise objective and restrictions: a geometric programming approach. Prod. Plan. Control 11, 781–788 (2000)CrossRefGoogle Scholar
  79. 79.
    Frenk, J.B.G.; Kaya, M.; Pourghannad, B.: Generalizing the ordering cost and holding-backlog cost rate functions in EOQ-type inventory models. In: Choi, T.M. (ed.) Handbook of EOQ Inventory Problems. pp. 79–119. Springer, Berlin (2014)Google Scholar
  80. 80.
    Gupta, R.K.; Bhunia, A.K.; Goyal, S.K.: An application of genetic algorithm in solving an inventory model with advance payment and interval valued inventory costs. Math. Comput. Model. 49, 893–905 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  81. 81.
    Bhunia, A.K.; Shaikh, A.A.; Cárdenas-Barrón, L.E.: A partially integrated production-inventory model with interval valued inventory costs, variable demand and flexible reliability. Appl. Soft Comput. 55, 491–502 (2017)CrossRefGoogle Scholar
  82. 82.
    Wahab, M.I.M.; Jaber, M.Y.: Economic order quantity model for items with imperfect quality, different holding costs, and learning effects: a note. Comput. Ind. Eng. 58, 186–190 (2010)CrossRefGoogle Scholar
  83. 83.
    Pando, V.; San-José, L.A.; García-Laguna, J.; Sicilia, J.: An economic lot-size model with non-linear holding cost hinging on time and quantity. Int. J. Prod. Econ. 145, 294–303 (2013)CrossRefGoogle Scholar
  84. 84.
    Hsu, V.N.: Dynamic economic lot size model with perishable inventory. Manag. Sci. 46, 1159–1169 (2000)CrossRefzbMATHGoogle Scholar
  85. 85.
    Hsu, V.N.; Lowe, T.J.: Dynamic economic lot size models with period-pair-dependent backorder and inventory costs. Oper. Res. 49, 316–321 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  86. 86.
    Hsu, V.N.: An economic lot size model for perishable products with age-dependent inventory and backorder costs. IIE Trans. 35, 775–780 (2003)CrossRefGoogle Scholar
  87. 87.
    Pal, B.; Sana, S.S.; Chaudhuri, K.: A distribution-free newsvendor problem with nonlinear holding cost. Int. J. Syst. Sci. 46, 1269–1277 (2015)CrossRefzbMATHGoogle Scholar
  88. 88.
    Tyagi, A.: Optimal lot size for an item when holding cost is moved by depletion rate of inventory above a certain stock level. Uncertain Supply Chain Manag. 3, 381–396 (2015)CrossRefGoogle Scholar
  89. 89.
    Tyagi, A.P.; Pandey, R.K.; Singh, S.: An optimal replenishment policy for non-instantaneous deteriorating items with stock-dependent demand and variable holding cost. Int. J. Oper. Res. 21, 466–488 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  90. 90.
    Shaw, D.X.; Wagelmans, A.P.: An algorithm for single-item capacitated economic lot sizing with piecewise linear production costs and general holding costs. Manag. Sci. 44, 831–838 (1998)CrossRefzbMATHGoogle Scholar
  91. 91.
    Chu, L.Y.; Hsu, V.N.; Shen, Z.-J.M.: An economic lot-sizing problem with perishable inventory and economies of scale costs: Approximation solutions and worst case analysis. Nav. Res. Logist. NRL. 52, 536–548 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  92. 92.
    Smith, R.L.; Zhang, R.Q.: Infinite horizon production planning in time-varying systems with convex production and inventory costs. Manag. Sci. 44, 1313–1320 (1998)CrossRefzbMATHGoogle Scholar
  93. 93.
    Ghate, A.; Smith, R.L.: Optimal backlogging over an infinite horizon under time-varying convex production and inventory costs. Manuf. Serv. Oper. Manag. 11, 362–368 (2009)CrossRefGoogle Scholar
  94. 94.
    Maity, A.K.; Maity, K.; Maiti, M.: A production-recycling-inventory system with imprecise holding costs. Appl. Math. Model. 32, 2241–2253 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  95. 95.
    Teunter, R.H.: A reverse logistics valuation method for inventory control. Int. J. Prod. Res. 39, 2023–2035 (2001)CrossRefzbMATHGoogle Scholar
  96. 96.
    Akçali, E.; Bayindir, Z.P.: Analyzing the effects of inventory cost setting rules in a disassembly and recovery environment. Int. J. Prod. Res. 46, 267–288 (2008)CrossRefzbMATHGoogle Scholar
  97. 97.
    Bouras, A.: Optimal Control for Advertised Production Planning in a Three-Level Stock System with Deteriorating Items: Case of a Continuous-Review Policy. Arab. J. Sci. Eng. 40, 2829–2840 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  98. 98.
    Alamri, A.A.: Theory and methodology on the global optimal solution to a general reverse logistics inventory model for deteriorating items and time-varying rates. Comput. Ind. Eng. 60, 236–247 (2011)CrossRefGoogle Scholar
  99. 99.
    Moarefdoost, M.M.; Zokaee, S.; Haji, R.: Economic lot size formula under vmi program with poisson demand. Arab. J. Sci. Eng. 39, 7459–7465 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  100. 100.
    Firoozi, Z.; Tang, S.H.; Ariafar, S.; Ariffin, M.: An optimization approach for a joint location inventory model considering quantity discount policy. Arab. J. Sci. Eng. 38, 983–991 (2013)MathSciNetCrossRefGoogle Scholar

Copyright information

© King Fahd University of Petroleum & Minerals 2018

Authors and Affiliations

  1. 1.King Fahd University of Petroleum & MineralsDhahranSaudi Arabia

Personalised recommendations