Advanced Payment

  • Ata Allah Taleizadeh
Chapter

Abstract

The optimal order quantity can influentially be affected by payment timing and the reaction of customers when the vendor runs out of stock. When an order is placed, the time of the payment can take three possible points (1) Prepayment: At the time the order is placed or prior to delivery, (2) Instant payment: At the time of delivery and (3) Delayed payment: At some time after delivery. In the competitive environment of business, it is normally observed that a wholesaler requires some payment when an order from a retailer is placed. Further, there are situations in which if a retailer gives an extra advance payment (AP), then he may get some price discount at the time of final payment (e.g. brick and tile factories announce such an offer at the beginning of the season). Generally speaking, it could be claimed that the main purpose of AP is either financing the procurement cost of material or controlling the risk of cancelling the orders. However, by paying a certain percentage of the total purchase cost per cycle as an advance payment to the wholesaler, the retailer sacrifices the interest on the amount of money paid as AP. In this chapter different schemes of advcaned payments are presented.

References

  1. Abad, P. L. (1996). Optimal pricing and lot-sizing under conditions of perishability and partial backordering. Management Science, 42(8), 1093–1104.CrossRefGoogle Scholar
  2. Abad, P. L. (2007). Buyers response to a temporary price reduction incorporating freight costs. European Journal of Operational Research, 182(3), 1073–1083.CrossRefGoogle Scholar
  3. Aggarwal, S. P., & Jaggi, C. K. (1995). Ordering policies of deteriorating items under permissible delay in payments. Journal of the Operational Research Society, 46, 658–662.CrossRefGoogle Scholar
  4. Al Kindi, M., & Sarker, B. R. (2011). Optimal inventory system with two backlog costs in response to a discount offer. Production Planning and Control, 22(3), 325–333.CrossRefGoogle Scholar
  5. Alfares, H. K., & Ghaithan, M. (2016). Inventory and pricing model with price-dependent demand, time-varying, holding cost, and quantity discounts. Computers & Industrial Engineering, 94, 170–177.CrossRefGoogle Scholar
  6. Arcelus, F. J., & Srinivasan, G. (1990). Delay of payments VS. price discounts for extraordinary purchases: The buyers perspective. Engineering Costs and Production Economics, 19(1–3), 273–279.CrossRefGoogle Scholar
  7. Ardalan, A. (1988). Optimal ordering policies in response to a sale. IIE Transactions, 20, 292–294.Google Scholar
  8. Bai, Q. G., & Xu, J. T. (2011). Optimal solutions for the economic lot-sizing problem with multiple suppliers and cost structures. Journal of Applied Mathematics and Computing, 37(1–2), 331–345.CrossRefGoogle Scholar
  9. Baker, R. C. (1976). Inventory policy for items on sale during regular replenishments. Production and Inventory Management, 17, 55–64.Google Scholar
  10. Benton, W. C., & Park, S. (1996). A classification of literature on determining the lot size under quantity discount. European Journal of Operational Research, 92(2), 219–238.CrossRefGoogle Scholar
  11. Bregman, R. L. (1992). The effect of the timing of disbursements on order quantities. Journal of the Operational Research Society, 43(10), 971–977.CrossRefGoogle Scholar
  12. Burke, G. J., Carrillo, J., & Vakharia, A. J. (2008). Heuristics for sourcing from multiple suppliers with alternative quantity discounts. European Journal of Operational Research, 186(1), 317–329.CrossRefGoogle Scholar
  13. Burwell, T. H., Dave, D. S., Fitzpatrick, K. E., & Roy, M. R. (1997). Economic lot size model for price dependent demand under quantity and freight discounts. International Journal of Production Economics, 48(2), 141–155.CrossRefGoogle Scholar
  14. Cardenas-Barron, L. E. (2009). Optimal ordering policies in response to a discount offer: Corrections. International Journal of Production Economics, 122(2), 783–789.CrossRefGoogle Scholar
  15. Cardenas-Barron, L. E. (2012). A comprehensive note on: An economic order quantity with imperfect quality and quantity discount. Applied Mathematical Modelling, 36(12), 6338–6340.CrossRefGoogle Scholar
  16. Cardenas-Barron, L. E., Smith, N. R., & Goyal, S. K. (2010). Optimal order size to take advantage of a one-time discount offer with allowed backorders. Applied Mathematical Modelling, 34(6), 1642–1652.CrossRefGoogle Scholar
  17. Chang, C. T. (2004). An EOQ model with deteriorating items under inflation when supplier credits linked to order quantity. International Journal of Production Economics, 88(3), 307–316.CrossRefGoogle Scholar
  18. Chang, C. H. (2013). A note on an economic lot size model for price-dependent demand under quantity and freight discounts. International Journal of Production Economics, 144(1), 175–179.CrossRefGoogle Scholar
  19. Chang, H. J., & Dye, C. Y. (2001). An inventory model for deteriorating items with partial backlogging and permissible delay in payments. International Journal of Systems Science, 32(3), 345–352.CrossRefGoogle Scholar
  20. Chang, H. J., & Dye, C. Y. (2010). An EOQ model with deteriorating items in response to a temporary sale price. Production Planning & Control: The Management of Operations, 11(5), 464–473.CrossRefGoogle Scholar
  21. Chang, C. T., Ouyang, L. Y., & Teng, J. T. (2003). An EOQ model for deteriorating items under supplier credits linked to ordering quantity. Applied Mathematical Modelling, 27(12), 983–996.CrossRefGoogle Scholar
  22. Chang, H. J., Lin, W. F., & Ho, J. F. (2011). Closed-form solutions for Wees and martins EOQ models with a temporary price discount. International Journal of Production Economics, 131(2), 528–534.CrossRefGoogle Scholar
  23. Chen, J. M. (1998). An inventory model for deteriorating items with time-proportional demand and shortages under inflation and time discounting. International Journal of Production Economics, 55(1), 21–30.CrossRefGoogle Scholar
  24. Chen, C. K., & Jo Min, K. (1995). Optimal inventory and disposal policies in response to a sale. International Journal of Production Economics, 42(1), 17–27.CrossRefGoogle Scholar
  25. Chen, L. H., & Kang, F. S. (2007). Integrated vendor–buyer cooperative inventory models with variant permissible delay in payments. European Journal of Operational Research, 183(2), 658–673.CrossRefGoogle Scholar
  26. Chen, L. H., & Kang, F. S. (2010). Integrated inventory models considering the two-level trade credit policy and a price-negotiation scheme. European Journal of Operational Research, 205(1), 47–58.CrossRefGoogle Scholar
  27. Chen, L. H., & Ouyang, L. Y. (2006). Fuzzy inventory model for deteriorating items with permissible delay in payment. Applied Mathematics and Computation, 182(1), 711–726.CrossRefGoogle Scholar
  28. Chen, S. C., Cárdenas-Barrón, L. E., & Teng, J. T. (2014). Retailer’s economic order quantity when the supplier offers conditionally permissible delay in payments link to order quantity. International Journal of Production Economics, 155, 284–291.CrossRefGoogle Scholar
  29. Chu, P., Chung, K. J., & Lan, S. P. (1998). Economic order quantity of deteriorating items under permissible delay in payments. Computers & Operations Research, 25(10), 817–824.CrossRefGoogle Scholar
  30. Chung, K. J. (2013). A note on the article economic order quantity with trade credit financing for non-decreasing demand. Omega, 41(2), 441.CrossRefGoogle Scholar
  31. Chung, K. J., & Huang, Y. F. (2003). The optimal cycle time for EPQ inventory model under permissible delay in payments. International Journal of Production Economics, 84(3), 307–318.CrossRefGoogle Scholar
  32. Chung, K. J., & Huang, C. K. (2009). An ordering policy with allowable shortage and permissible delay in payments. Applied Mathematical Modelling, 33(5), 2518–2525.CrossRefGoogle Scholar
  33. Chung, K. J., & Liao, J. J. (2004). Lot-sizing decisions under trade credit depending on the ordering quantity. Computers & Operations Research, 31(6), 909–928.CrossRefGoogle Scholar
  34. Chung, K. J., & Liao, J. J. (2009). The optimal ordering policy of the EOQ model under trade credit depending on the ordering quantity from the DCF approach. European Journal of Operational Research, 196(2), 563–568.CrossRefGoogle Scholar
  35. Chung, C. J., Wee, H. M., & Chen, L. Y. (2013). Retailers replenishment policy for deteriorating item in response to future cost increase and incentive-dependent sale. Mathematical and Computer Modelling, 57(3), 536–550.CrossRefGoogle Scholar
  36. Covert, R. P., & Philip, G. C. (1973). An EOQ model for items with Weibull distribution deterioration. AIIE transactions, 5(4), 323–326.CrossRefGoogle Scholar
  37. Das, K., & Maiti, M. (2003). Inventory of a differential item sold from two shops under single management with shortages and variable demand. Applied Mathematical Modelling, 27(7), 535–549.CrossRefGoogle Scholar
  38. Dave, U., & Pandya, B. (1985). Inventory returns and special sales in a lot-size system with constant rate of deterioration. European Journal of Operational Research, 19(3), 305–312.CrossRefGoogle Scholar
  39. Diabat, A., Taleizadeh, A. A., & Lashgari, M. (2017). A lot sizing model with partial down-stream delayed payment, partial up-stream advance payment, and partial backordering for deteriorating items. Journal of Manufacturing Systems, 45, 322–342.Google Scholar
  40. Dye, C. Y., & Chang, H. J. (2007). Purchase inventory decision models for deteriorating items with a temporary sale price. Information and Management Science, 18(1), 17–35.Google Scholar
  41. Ebrahim, R. M., Razmi, J., & Haleh, H. (2009). Scatter search algorithm for supplier selection and order lot sizing under multiple price discount environment. Advances in Engineering Software, 40(9), 766–776.CrossRefGoogle Scholar
  42. Feess, E., & Wohlschlegel, A. (2010). All-unit discounts and the problem of surplus division. Review of Industrial Organization, 37(3), 161–178.CrossRefGoogle Scholar
  43. Geetha, K. V., & Uthayakumar, R. (2014). Evaluation of supply chain with quality improvement under trade credit and freight rate discount. Operational Research Society of India, 51(3), 463–478.Google Scholar
  44. Ghare, P. M., & Schrader, G. F. (1963). A model for exponentially decaying inventory. Journal of Industrial Engineering, 14(5), 238–243.Google Scholar
  45. Goh, M., & Sharafali, M. (2002). Price-dependent inventory models with discount offers at random times. Production and Operations Management, 11(2), 139.CrossRefGoogle Scholar
  46. Goossens, D. R., Maas, A. J. T., Spieksma, F. C. R., & van de Klundert, J. J. (2007). Exact algorithms for procurement problems under a total quantity discount structure. European Journal of Operational Research, 178(2), 603–626.CrossRefGoogle Scholar
  47. Goyal, S. K. (1985). Economic order quantity under conditions of permissible delay in payments. Journal of the Operational Research Society, 36, 335–338.CrossRefGoogle Scholar
  48. Goyal, S. K. (1990). Economic ordering policy during special discount periods for dynamic inventory problems under certainty. Engineering Costs and Production Economics, 20(1), 101–104.CrossRefGoogle Scholar
  49. Goyal, S. K., Srinivasan, G., & Arcelus, F. J. (1991). One time only incentives and inventory policies. European Journal of Operational Research, 54(1), 1–6.CrossRefGoogle Scholar
  50. Guder, F., Zydiak, J., & Chaudhry, S. (1997). Capacitated multiple item ordering with incremental quantity discounts. Journal of the Operational Research Society, 45, 1197–1205.CrossRefGoogle Scholar
  51. Gupta, R., Bhunia, A., & Goyal, S. (2009). An application of genetic algorithm in solving an inventory model with advance payment and interval valued inventory costs. Mathematical and Computer Modelling, 49(5), 893–905.CrossRefGoogle Scholar
  52. Gurnani, H. (2001). A study of quantity discount pricing models with different ordering structures: Order coordination, order consolidation, and multi-tier ordering hierarchy. International Journal of Production Economics, 72(3), 203–225.CrossRefGoogle Scholar
  53. Haksever, C., & Moussourakis, J. (2008). Determining order quantities in multi-product inventory systems subject to multiple constraints and incremental discounts. European Journal of Operational Research, 184(3), 930–945.CrossRefGoogle Scholar
  54. Heng, K. J., Labban, J., & Linn, R. J. (1990). An order-level lot-size inventory model for deteriorating items with finite replenishment rate. Computers & Industrial Engineering, 20(2), 187–197.CrossRefGoogle Scholar
  55. Ho, C. H., Ouyang, L. Y., & Su, C. H. (2008). Optimal pricing, shipment and payment policy for an integrated supplier–buyer inventory model with two-part trade credit. European Journal of Operational Research, 187(2), 496–510.CrossRefGoogle Scholar
  56. Hsieh, T. P., & Dye, C. Y. (2012). A note on the EPQ with partial backordering and phase-dependent backordering rate. Omega, 40(1), 131–133.CrossRefGoogle Scholar
  57. Hsu, W. K., & Yu, H. (2009). EOQ model for imperfective items under a one-time-only discount. Omega, 37(5), 1018–1026.CrossRefGoogle Scholar
  58. Hsu, W. K., & Yu, H. F. (2011). An EOQ model with imperfective quality items under an announced price increase. Journal of the Chinese Institute of Industrial Engineers, 28(1), 34–44.CrossRefGoogle Scholar
  59. Hu, F., & Liu, D. (2010). Optimal replenishment policy for the EPQ model with permissible delay in payments and allowable shortages. Applied Mathematical Modelling, 34(10), 3108–3117.CrossRefGoogle Scholar
  60. Huang, Y. F. (2007). Economic order quantity under conditionally permissible delay in payments. European Journal of Operational Research, 176(2), 911–924.CrossRefGoogle Scholar
  61. Hwang, H., & Shinn, S. W. (1997). Retailers pricing and lot sizing policy for exponentially deteriorating products under the condition of permissible delay in payment. Computers & Operations Research, 24(6), 539–547.CrossRefGoogle Scholar
  62. Hwang, H., Moon, D. H., & Shinn, S. W. (1990). An EOQ model with quantity discounts for both purchasing price and freight cost. Computers & Operations Research, 17(1), 73–78.CrossRefGoogle Scholar
  63. Jackson, E., & Munson, L. (2016). Shared resource capacity expansion decisions for multiple products with quantity discounts. European Journal of Operational Research, 253(3), 602–613.CrossRefGoogle Scholar
  64. Jaggi, C. K., & Aggarwal, S. P. (1994). Credit financing in economic ordering policies of deteriorating items. International Journal of Production Economics, 34(2), 151–155.CrossRefGoogle Scholar
  65. Jaggi, C. K., Goyal, S. K., & Goel, S. K. (2008). Retailer’s optimal replenishment decisions with credit-linked demand under permissible delay in payments. European Journal of Operational Research, 190(1), 130–135.CrossRefGoogle Scholar
  66. Jamal, A. M. M., Sarker, B. R., & Wang, S. (1997). An ordering policy for deteriorating items with allowable shortage and permissible delay in payment. Journal of the Operational Research Society, 48(8), 826–833.CrossRefGoogle Scholar
  67. Karimi-Nasab, M., & Konstantaras, I. (2013). An inventory control model with stochastic review interval and special sale offer. European Journal of Operational Research, 227, 81–87.CrossRefGoogle Scholar
  68. Khouja, M., & Mehrez, A. (1996). Optimal inventory policy under different supplier credit policies. Journal of Manufacturing Systems, 15(5), 334–339.Google Scholar
  69. Kreng, V. B., & Tan, S. J. (2010). The optimal replenishment decisions under two levels of trade credit policy depending on the order quantity. Expert Systems with Applications, 37(7), 5514–5522.Google Scholar
  70. Kumar, Y. U. (2015). Order level inventory model for power pattern-demand with inventory returns and special sales. International Journal of Mathematical Archive, 6(7), 6–10.Google Scholar
  71. Kunreuther, H., & Richard, J. F. (1977). Optimal pricing and inventory decisions for non-seasonal items, Econometrica, 39, 173–175.Google Scholar
  72. Lashgari, M., Taleizadeh, A. A., & Ahmadi, A. (2015). A lot-sizing model with partial up-stream advanced payment and partial down-stream delayed payment in a three-level supply chain. Ann. Oper. Res., 238(1–2), 329–354.Google Scholar
  73. Lashgari, M., Taleizadeh, A. A., & Sana, S. S. (2016). An inventory control problem for deteriorating items with back-ordering and financial considerations under two levels of trade credit linked to order quantity. Journal of Industrial and Management Optimization, 12(3), 1091–1119.CrossRefGoogle Scholar
  74. Lashgary, M., Taleizadeh, A. A., & Sadjadi, S. J. (2017). Ordering policies for non-instantaneous deteriorating items under hybrid partial prepayment, partial delay payment and partial backordering. Journal of the Operational Research Society. In Press.Google Scholar
  75. Lau, H.-S., & Lau, A. H.-L. (1993). Viewpoint: The effect of cost disbursement timings in inventory control. Journal of the Operational Research Society, 44(7), 739–740.CrossRefGoogle Scholar
  76. Lee, H. L., & Rosenblatt, M. J. (1986). The effects of varying marketing policies and conditions on the economic ordering quantity. International Journal of Production Research, 24(3), 593–598.CrossRefGoogle Scholar
  77. Lee, A. H., Kang, H. Y., & Lai, C. M. (2013). Solving lot-sizing problem with quantity discount and transportation cost. International Journal of Systems Science, 44(4), 760–774.CrossRefGoogle Scholar
  78. Liao, J. J. (2007). On an EPQ model for deteriorating items under permissible delay in payments. Applied Mathematical Modelling, 31(3), 393–403.CrossRefGoogle Scholar
  79. Liao, H. C., Tsai, C. H., & Su, C. T. (2000). An inventory model with deteriorating items under inflation when a delay in payment is permissible. International Journal of Production Economics, 63(2), 207–214.CrossRefGoogle Scholar
  80. Lin, T. Y. (2010). An economic order quantity with imperfect quality and quantity discounts. Applied Mathematical Modelling, 34(10), 3158–3165.CrossRefGoogle Scholar
  81. Lin, T. Y. (2011). Inventory model for items with imperfect quality under announced price increases. African Journal of Business Management, 5(12), 4715.Google Scholar
  82. Lin, W. F., & Chang, H. J. (2016). Retailers optimal ordering policies for EOQ model with imperfective items under a temporary discount. Yugoslav Journal of Operations Research, 26(2), 221–242.CrossRefGoogle Scholar
  83. Lin, Y. J., & Ho, C. H. (2011). Integrated inventory model with quantity discount and price-sensitive demand. TOP, 19(1), 177–188.CrossRefGoogle Scholar
  84. Lin, C. S., & Kroll, D. E. (1997). The single item newsboy problem with dual performance measures and quantity discounts. European Journal of Operational Research, 100(3), 562–565.CrossRefGoogle Scholar
  85. Maddah, B. S., Jaber, M. Y., & Abboud, N. E. (2004). Periodic review (s, S) inventory model with permissible delay in payments. Journal of the Operational Research Society, 55(2), 147–159.CrossRefGoogle Scholar
  86. Mahata, P., & Mahata, G. C. (2014). Economic production quantity model with trade credit financing and price-discount offer for non-decreasing time varying demand pattern. International Journal of Procurement Management, 7(5), 563–581.CrossRefGoogle Scholar
  87. Maiti, M. K., & Maiti, M. (2006). Fuzzy inventory model with two warehouses under possibility constraints. Fuzzy Sets and Systems, 157(1), 52–73.CrossRefGoogle Scholar
  88. Maiti, A. K., Maiti, M. K., & Maiti, M. (2009). Inventory model with stochastic lead-time and price dependent demand incorporating advance payment. Applied Mathematical Modelling, 33(5), 2433–2443.CrossRefGoogle Scholar
  89. Manerba, D., & Mansini, R. (2014). An effective matheuristic for the capacitated total quantity discount problem. Computers & Operations Research, 41, 1–11.CrossRefGoogle Scholar
  90. Markowski, E. P. (1990). Criteria for evaluating purchase quantity decisions in response to future price increases. European Journal of Operational Research, 47(3), 364–370.CrossRefGoogle Scholar
  91. Martin, G. E. (1994). Note on an EOQ model with a temporary sale price. International Journal of Production Economics, 37(2), 241–243.CrossRefGoogle Scholar
  92. Mazdeh, M. M., Emadikhiav, M., & Parsa, I. (2015). A heuristic to solve the dynamic lot sizing problem with supplier selection and quantity discount. Computers & Industrial Engineering, 85, 33–43.CrossRefGoogle Scholar
  93. Meena, P. L., & Sarmah, S. P. (2013). Multiple sourcing under supplier failure risk and quantity discount: A genetic algorithm approach. Transportation Research Part E-Logistics & Transportation Review, 50, 84–97.CrossRefGoogle Scholar
  94. Mendoza, A., & Ventura, J. A. (2008). Incorporating quantity discounts to the EOQ model with transportation costs. International Journal of Production Economics, 113(2), 754–765.CrossRefGoogle Scholar
  95. Meng, Y. H., & Song, Y. T. (2016). Optimal policy for competing retailers when the supplier offers a temporary price discount with uncertain demand. In Proceedings of the 6th international Asia conference on industrial engineering and management innovation (pp. 703–712). Paris: Atlantis Press.CrossRefGoogle Scholar
  96. Mirmohammadi, S. H., Shadrokh, S., & Kianfar, F. (2009). An efficient optimal algorithm for the quantity discount problem in material requirement planning. Journal of Computers & Operations Research, 36(6), 1780–1788.CrossRefGoogle Scholar
  97. MISRA, R. B. (1975). Optimum production lot size model for a system with deteriorating inventory. The International Journal of Production Research, 13(5), 495–505.CrossRefGoogle Scholar
  98. Mohanty, D. J., Kumar, R. S., & Goswami, A. (2016). An improved inventory model with random review period and temporary price discount for deteriorating items. International Journal of Systems Assurance Engineering and Management, 7(1), 62–72.CrossRefGoogle Scholar
  99. Mousavi, S. M., Hajipoor, V., Akhavan Niaki, S. T., & Aalikar, N. (2014). A multi-product multi-period inventory control problem under inflation and discount: A parameter-tuned particle swarm optimization algorithm. The International Journal of Advanced Manufacturing Technology, 70(9–12), 1739–1756.CrossRefGoogle Scholar
  100. Montgomery D. C., Bazaraa M. S., & Keswani A. K. (1973). Inventory models with a mixture of backorders and lost sales, Naval Research Logistics Quarterly, 20, 255–263.Google Scholar
  101. Mukherjee, S. P. (1987). Optimum ordering interval for time varying decay rate of inventory. Opsearch, 24(1), 19–24.Google Scholar
  102. Munson, C. L., & Hu, J. (2010). Incorporating quantity discounts and their inventory impacts into the centralized purchasing decision. European Journal of Operational Research, 201(2), 581–592.CrossRefGoogle Scholar
  103. Nguyen, H. N., Rainwater, C. E., Mason, S. J., & Pohl, E. A. (2014). Quantity discount with freight consolidation. Transportation Research Part E, 66, 66–82.CrossRefGoogle Scholar
  104. Ouyang, L. Y., Teng, J. T., & Chen, L. H. (2006). Optimal ordering policy for deteriorating items with partial backlogging under permissible delay in payments. Journal of Global Optimization, 34(2), 245–271.CrossRefGoogle Scholar
  105. Ouyang, L. Y., Wu, K. S., & Yang, C. T. (2008). Retailers ordering policy for non-instantaneous deteriorating items with quantity discount, stock dependent demand and stochastic backorder rate. Journal of the Chinese Institute of Industrial Engineers, 25(1), 62–72.CrossRefGoogle Scholar
  106. Ouyang, L. Y., Teng, J. T., Goyal, S. K., & Yang, C. T. (2009a). An economic order quantity model for deteriorating items with partially permissible delay in payments linked to order quantity. European Journal of Operational Research, 194(2), 418–431.CrossRefGoogle Scholar
  107. Ouyang, L. Y., Yang, C. T., & Yeng, H. F. (2009b). Optimal order policy for deteriorating items in response to temporary price discount linked to order quantity. Tamkang Journal of Mathematics, 40(4), 383–400.Google Scholar
  108. Ouyang, L. Y., Wu, K. S., Yang, C. T., & Yen, H. F. (2016). Optimal order policy in response to announced price increase for deteriorating items with limited special order quantity. International Journal of Systems Science, 47(3), 718–729.CrossRefGoogle Scholar
  109. Panda, S., Saha, S., & Basu, M. (2009). An EOQ model for perishable products with discounted selling price and stock dependent demand. Central European Journal of Operations Research, 17(1), 31–53.CrossRefGoogle Scholar
  110. Papachristos, S., & Skouri, K. (2003). An inventory model with deteriorating items, quantity discount, pricing and time-dependent partial backlogging. International Journal of Production Economics, 83(3), 247–256.CrossRefGoogle Scholar
  111. Park, K. S. (1983). Another inventory model with a mixture of backorders and lost sales. Naval Research Logistics (NRL), 30(3), 397–400.CrossRefGoogle Scholar
  112. Pasandideh, S. H. R., Akhavan Niaki, S. T., & Mousavi, S. M. (2013). Two metaheuristics to solve a multi-item multiperiod inventory control problem under storage constraint and discounts. The International Journal of Advanced Manufacturing Technology, 69(5–8), 1671–1684.CrossRefGoogle Scholar
  113. Pentico, D. W., & Drake, M. J. (2009). The deterministic EOQ with partial backordering: A new approach. European Journal of Operational Research, 194(1), 102–113.CrossRefGoogle Scholar
  114. Pentico, D. W., & Drake, M. J. (2011). A survey of deterministic models for the EOQ and EPQ with partial backordering. European Journal of Operational Research, 214(2), 179–198.CrossRefGoogle Scholar
  115. Pentico, D. W., Drake, M. J., & Toews, C. (2011). The EPQ with partial backordering and phase-dependent backordering rate. Omega, 39(5), 574–577.CrossRefGoogle Scholar
  116. Pourmohammad Zia, N., & Taleizadeh, A. A. (2015). A lot-sizing model with backordering under hybrid linked-to-order multiple advance payments and delayed payment. Transportation Research: Part E, 82, 19–37.CrossRefGoogle Scholar
  117. Ramasesh, R. V., & Rachamadugu, R. (2001). Lot-sizing decisions under limited-time price reduction. Decisions Science, 32(1), 125–144.CrossRefGoogle Scholar
  118. Roy, T., & Chaudhuri, K. S. (2007). An inventory model for a deteriorating item with price-dependent demand and special sale. International Journal of Operational Research, 2(2), 173–187.CrossRefGoogle Scholar
  119. Rubin, P. A., & Benton, W. C. (2003). Evaluating jointly constrained order quantity complexities for incremental discounts. European Journal of Operational Research, 149(3), 557–570.CrossRefGoogle Scholar
  120. Sana, S. S., & Chaudhuri, K. S. (2008). A deterministic EOQ model with delays in payments and price-discount offers. European Journal of Operational Research, 184(2), 509–533.CrossRefGoogle Scholar
  121. San-José, L. A., & Garcia-Laguna, J. (2003). An EOQ model with backorders and all unit discounts. TOP, 11(2), 253–274.CrossRefGoogle Scholar
  122. San-José, L. A., & Garcia-Laguna, J. (2009). Optimal policy for an inventory system with backlogging and all-units discounts: Application to the composite lot size model. European Journal of Operational Research, 192(3), 808–823.CrossRefGoogle Scholar
  123. Sari, D. P., Rusdiansyah, A., & Huang, L. (2012). Models of joints economic lot-sizing problem with time-based temporary price discount. International Journal of Production Economics, 139(1), 145–154.CrossRefGoogle Scholar
  124. Sarker, B. R., & Al Kindi, M. (2006). Optimal ordering policies in response to a discount offer. International Journal of Production Economics, 100(2), 195–211.CrossRefGoogle Scholar
  125. Sarker, B. R., Jamal, A. M. M., & Wang, S. (2000). Supply chain models for perishable products under inflation and permissible delay in payment. Computers & Operations Research, 27(1), 59–75.CrossRefGoogle Scholar
  126. Schotanus, F., Telgen, J., & de Boer, L. (2009). Unraveling quantity discount. Omega, 37(3), 510–521.CrossRefGoogle Scholar
  127. Shah, B. J., Shah, N. H., & Shah, Y. K. (2005). EOQ model for time-dependent deterioration rate with a temporary price discount. Asia-Pacific Journal of Operational Research, 22(4), 479–485.CrossRefGoogle Scholar
  128. Shah, N. H., Jani, M. Y., & Chaudhari, U. (2016). Impact of future price increase on ordering policies for deteriorating items under quadratic demand. International Journal of Industrial Engineering Computations, 7(3), 423–436.CrossRefGoogle Scholar
  129. Shaposhnik, Y., Herer, Y. T., & Naseraldin, H. (2015). Optimal ordering for a probabilistic one-time discount. European Journal of Operational Research, 244(3), 803–814.CrossRefGoogle Scholar
  130. Sharma, S. (2009). On price increase and temporary price reduction with partial backordering. European Journal of Industrial Engineering, 3, 70–89.Google Scholar
  131. Sharma, B. K. (2016). An EOQ model for retailers partial permissible delay in payment linked to order quantity with shortages. Mathematics and Computers in Simulation, 125, 99–112.CrossRefGoogle Scholar
  132. Sheen, G. J., & Tsao, Y. C. (2007). Channel coordination, trade credit and quantity discounts for freight cost. Transportation Research Part E: Logistics and transportation review, 43(2), 112–128.CrossRefGoogle Scholar
  133. Shinn, S. W., & Hwang, H. (2003). Optimal pricing and ordering policies for retailers under order-size-dependent delay in payments. Computers & Operations Research, 30(1), 35–50.CrossRefGoogle Scholar
  134. Shinn, S. W., Hwang, H., & Sung, S. P. (1996). Joint price and lot size determination under conditions of permissible delay in payments and quantity discounts for freight cost. European Journal of Operational Research, 91(3), 528–542.CrossRefGoogle Scholar
  135. Taleizadeh, A. A. (2014a). An economic order quantity model for deteriorating item in a purchasing system with multiple prepayments. Applied Mathematical Modelling, 38(23), 5357–5366.CrossRefGoogle Scholar
  136. Taleizadeh, A. A. (2014b). An EOQ model with partial backordering and advance payments for an evaporating item. International Journal of Production Economics, 155, 185–193.CrossRefGoogle Scholar
  137. Taleizadeh, A. A. (2017a). Lot sizing model with advance payment and disruption in supply under planned partial backordering. International Transactions in Operational Research, 24(4), 783–800.Google Scholar
  138. Taleizadeh A. A., (2017b). Multi Objective Supply Chain Problem using a Novel Hybrid Method of Meta Goal Programming and Firefly Algorithm. Asia-Pacific Journal of Operational Research, 34(4): 1750021.Google Scholar
  139. Taleizadeh, A. A., & Nematollahi, M. (2014). An inventory control problem for deteriorating items with back-ordering and financial considerations. Applied Mathematical Modelling, 38(1), 93–109.CrossRefGoogle Scholar
  140. Taleizadeh, A. A., & Pentico, D. W. (2013). An economic order quantity model with partial backordering and known price increase. European Journal of Operational Research, 28(3), 516–525.CrossRefGoogle Scholar
  141. Taleizadeh, A. A., & Pentico, D. W. (2014). An economic order quantity model with partial backordering and all-units discount. International Journal of Production Economics, 155, 172–184.CrossRefGoogle Scholar
  142. Taleizadeh, A. A., & Tavakkoli, S. (2017). A lot sizing model for decaying item with full advance payment from the buyer and conditional discount from the supplier. Annals of Operations Research.Google Scholar
  143. Taleizadeh, A. A., Aryanezhad, M. B., & Niaki, S. T. A. (2008a). Optimizing multi-products multi-constraints inventory control systems with stochastic replenishments. Journal of Applied Science, 6(1), 1–12.Google Scholar
  144. Taleizadeh, A. A., Niaki, S. T., & Aryanezhad, M. B. (2008b). Multi-product multi-constraint inventory control systems with stochastic replenishment and discount under fuzzy purchasing price and holding costs. American Journal of Applied Sciences, 8(7), 1228–1234.CrossRefGoogle Scholar
  145. Taleizadeh, A. A., Moghadasi, H., Niaki, S. T. A., & Eftekhari, A. K. (2009a). An EOQ-joint replenishment policy to supply expensive imported raw materials with payment in advance. Journal of Applied Science, 8(23), 4263–4273.Google Scholar
  146. Taleizadeh, A. A., Niaki, S. T. A., & Aryanezhad, M. B. (2009b). A hybrid method of Pareto, TOPSIS and genetic algorithm to optimize multi-product multi-constraint inventory control systems with random fuzzy replenishments. Mathematical and Computer Modeling, 49(5), 1044–1057.CrossRefGoogle Scholar
  147. Taleizadeh, A. A., Niaki, S. T. A., & Hosseini, V. (2009c). Optimizing multi product multi constraints bi-objective newsboy problem with discount by hybrid method of goal programming and genetic algorithm. Engineering Optimization, 41(5), 437–457.CrossRefGoogle Scholar
  148. Taleizadeh, A. A., Niaki, S. T. A., & Aryanezhad, M. B. (2010a). Replenish-up-to multi chance-constraint inventory control system with stochastic period lengths and Total discount under fuzzy purchasing price and holding costs. International Journal of System Sciences, 41(10), 1187–1200.CrossRefGoogle Scholar
  149. Taleizadeh, A. A., Niaki, S. T. A., Aryannezhad, M. B., & Tafti, A. F. (2010b). A genetic algorithm to optimize multiproduct multiconstraint inventory control systems with stochastic replenishment intervals and discount. The International Journal of Advanced Manufacturing Technology, 51(1), 311–321.CrossRefGoogle Scholar
  150. Taleizadeh, A. A., Niaki, S. T. A., Shafii, N., Ghavamizadeh-Meibodi, R., & Jabbarzadeh, A. (2010c). A particle swarm optimization approach for constraint joint single buyer single vendor inventory problem with changeable lead-time and (r,Q) policy in supply chain. International Journal of Advanced Manufacturing Technology, 51(9), 1209–1223.CrossRefGoogle Scholar
  151. Taleizadeh, A. A., Barzinpour, F., & Wee, H. M. (2011a). Meta-heuristic algorithms to solve the fuzzy single period problem. Mathematical and Computer Modeling, 54(5), 1273–1285.CrossRefGoogle Scholar
  152. Taleizadeh, A. A., Niaki, S. T. A., & Barzinpour, F. (2011b). Multi-buyer multi-vendor multi-product multi-constraint supply chain problem with stochastic demand and variable lead time. Applied Mathematics and Computation, 217(22), 9234–9253.CrossRefGoogle Scholar
  153. Taleizadeh, A. A., Niaki, S. T. A., & Nikousokhan, R. (2011c). Constraint multiproduct joint-replenishment inventory control problem using uncertain programming. Applied Soft Computing, 11(8), 5143–5154.CrossRefGoogle Scholar
  154. Taleizadeh, A. A., Niaki, S. T. A., & Makui, A. (2012a). Multi-product multi-chance constraint multi-buyer single-vendor supply chain problem with stochastic demand and variable lead time. Expert Systems with Applications, 39, 5338–5348.CrossRefGoogle Scholar
  155. Taleizadeh, A. A., Niaki, S. T. A., & Seyed-Javadi, S. M. (2012b). Multiproduct multichance-constraint stochastic inventory problem with dynamic demand and partial back-ordering: A harmony search algorithm. Journal of Manufacturing Systems, 31(2), 204–213.CrossRefGoogle Scholar
  156. Taleizadeh, A. A., Pentico, D. W., Aryanezhad, M., & Ghoreyshi, S. M. (2012c). An economic order quantity model with partial backordering and a special sale price. European Journal of Operational Research, 221(3), 571–583.CrossRefGoogle Scholar
  157. Taleizadeh, A. A., Mohammadi, B., Cardenas-Barron, L. E., & Samimi, H. (2013a). An EOQ model for perishable product with special sale and shortage. International Journal of Production Economics, 145(1), 318–338.CrossRefGoogle Scholar
  158. Taleizadeh, A. A., Niaki, S. T. A., Aryanezhad, M. B., & Shafii, N. (2013b). A hybrid method of fuzzy simulation and genetic algorithm to optimize multi-product single-constraint inventory control systems with stochastic replenishments and fuzzy-demand. Information Sciences, 220(20), 425–441.CrossRefGoogle Scholar
  159. Taleizadeh, A. A., Niaki, S. T. A., & Ghavamizadeh-Meibodi, R. (2013c). Replenish-up-to multi chance-constraint inventory control system under fuzzy random lost sale and back ordered quantities. Knowledge-Based Systems, 53, 147–156.CrossRefGoogle Scholar
  160. Taleizadeh, A. A., Niaki, S. T. A., & Jalali Naini, G. (2013d). Optimizing multiproduct multiconstraint inventory control systems with stochastic period length and emergency order. Journal of Uncertain Systems, 7(1), 58–71.Google Scholar
  161. Taleizadeh, A. A., Niaki, S. T. A., & Wee, H. M. (2013e). Joint single vendor–single buyer supply chain problem with stochastic demand and fuzzy lead-time. Knowledge-Based Systems, 48, 1–9.CrossRefGoogle Scholar
  162. Taleizadeh, A. A., Pentico, D. W., Aryanezhad, M., & Jabalameli, M. S. (2013f). An economic order quantity model with multiple partial prepayments and partial backordering. Mathematical and Computer Modelling, 57(3), 311–323.CrossRefGoogle Scholar
  163. Taleizadeh, A. A., Pentico, D. W., Jabalameli, M. S., & Aryanezhad, M. (2013g). An EOQ model with partial delayed payment and partial backordering. Omega, 41(2), 354–368.CrossRefGoogle Scholar
  164. Taleizadeh, A. A., Wee, H. M., & Jolai, F. (2013i). Revisiting a fuzzy rough economic order quantity model for deteriorating items considering quantity discount and prepayment. Mathematical and Computer Modelling, 57(5), 1466–1479.CrossRefGoogle Scholar
  165. Taleizadeh, A. A., Stojkovska, I., & Pentico, D. W. (2015). An economic order quantity model with partial backordering and incremental discount. Computers & Industrial Engineering, 82, 21–32.CrossRefGoogle Scholar
  166. Taleizadeh, A. A., Samimi, H., & Mohammadi, B. (2015b). Joint replenishment policy with backordering and special sale. International Journal of Systems Science, 46(7), 1172–1198.CrossRefGoogle Scholar
  167. Taleizadeh, A. A., Akram, R., Lashgari, M., & Heydari, J. (2016a). A three-level supply chain with up-stream and down-stream trade credit periods linked to ordered quantity. Applied Mathematical Modelling, 40, 8777–8793.CrossRefGoogle Scholar
  168. Taleizadeh, A. A., Zarei, H. R., & Sarker, B. R. (2016b). An optimal control of inventory under probabilistic replenishment intervals and known price increase. European Journal of Operational Research, 257(3), 777–791.CrossRefGoogle Scholar
  169. Tavakoli, S., & Taleizadeh, A. A. (2017). An EOQ model for decaying item with full advanced payment and conditional discount. Annals of Operations Research, 259(1–2), 415–436.Google Scholar
  170. Tavakkoli, Sh., Taleizadeh, A. A., San Jose, L. A., (2018). A lot sizing model with advanced payment and planned backordered, Annals of Operations Research, (In Press).Google Scholar
  171. Teng, J. T., & Chang, C. T. (2009). Optimal manufacturer’s replenishment policies in the EPQ model under two levels of trade credit policy. European Journal of Operational Research, 195(2), 358–363.CrossRefGoogle Scholar
  172. Teng, J. T., Min, J., & Pan, Q. (2012). Economic order quantity model with trade credit financing for non-decreasing demand. Omega, 40(3), 328–335.CrossRefGoogle Scholar
  173. Teng, J. T., Cardenas-Barron, L. E., Chang, H. J., Wu, J., & Hu, Y. (2016). Inventory lot-size policies for deteriorating items with expiration dates and advance payments. Applied Mathematical Modelling, 40(19), 8605–8616.CrossRefGoogle Scholar
  174. Tersine, R. J. (1994). Principles of inventory and materials management (4th ed. pp. 113–115). New Jersey: Prentice-Hall.Google Scholar
  175. Tersine, R. J. (1994). Principles of lnventory and Materials Management, New York, North-Holland, 117–120.Google Scholar
  176. Tersine, R. J. (1996). Economic replenishment strategies for announced price increases. European Journal of Operational Research, 92(2), 266–280.Google Scholar
  177. Tersine, R. J., & Barman, S. (1995). Economic purchasing strategies for temporary price discounts. European Journal of Operational Research, 80, 328–343.CrossRefGoogle Scholar
  178. Tersine, R. J., & Schwarzkopf, A. B. (1989). Optimal stock replenishment strategies in response to temporary price reductions. Journal of Business Logistics, 10(2), 123.Google Scholar
  179. Tersine, R. J., Barman, S., & Toelle, R. A. (1995). Composite lot sizing with quantity and freight discount. Computers & Industrial Engineering, 28(1), 107–122.CrossRefGoogle Scholar
  180. Thangam, A. (2012). Optimal price discounting and lot-sizing policies for perishable items in a supply chain under advance payment scheme and two-echelon trade credits. International Journal of Production Economics, 139(2), 459–472.CrossRefGoogle Scholar
  181. Tripathi, R. P., & Tomar, S. S. (2015). Optimal order policy for deteriorating items with time-dependent demand in response to temporary price discount linked to order quantity. International Journal of Mathematical Analysis, 9(23), 1095–1109.CrossRefGoogle Scholar
  182. Tsao, Y. C., & Sheen, G. J. (2008). Dynamic pricing, promotion and replenishment policies for a deteriorating item under permissible delay in payments. Computers & Operations Research, 35(11), 3562–3580.CrossRefGoogle Scholar
  183. Vandana, B. K. S. (2016). An EOQ model for retailers partial permissible delay in payment linked to order quantity with shortages. Mathematics and Computers in Simulation, 125, 99–112.CrossRefGoogle Scholar
  184. Veinott Jr, A. F., & Wagner, H. M. (1965). Computing optimal (s, S) inventory policies. Management Science, 11(5), 525–552.CrossRefGoogle Scholar
  185. Wang, Q., & Wang, R. (2005). Quantity discount pricing policies for heterogeneous retailers with price sensitive demand. Naval Research Logistics (NRL), 52(7), 645–658.CrossRefGoogle Scholar
  186. Wee, H. M. (1999). Deteriorating inventory model with quantity discount, pricing and partial backordering. International Journal of Production Economics, 59(1), 511–518.CrossRefGoogle Scholar
  187. Wee, H. M., & Wang, W. T. (2012). A supplement to the EPQ with partial backordering and phase-dependent backordering rate. Omega, 40(3), 264–266.CrossRefGoogle Scholar
  188. Wee, H. M., & Yu, J. (1997). A deteriorating inventory model with a temporary price discount. International Journal of Production Economics, 53(1), 81–90.Google Scholar
  189. Weng, Z. K. (1995). Modeling quantity discounts under general price sensitive demand functions: Optimal policies and relationships. European Journal of Operational Research, 86(2), 300–314.CrossRefGoogle Scholar
  190. Whitin, T. M. (1955). Inventory control and price theory. Management Science, 2(1), 61–68.CrossRefGoogle Scholar
  191. Yang, C. T., Ouyang, L. Y., Yen, H. F., & Lee, K. L. (2013). Joint pricing and ordering policies for deteriorating item with retail price-dependent demand in response to announced supply price increase. Journal of Industrial and Management Optimization, 9(2), 437–454.CrossRefGoogle Scholar
  192. Yu, H. F., & Hsu, W. K. (2012). An EOQ model with immediate return for imperfect items under an announced price increase. Journal of the Chinese Institute of Industrial Engineers, 29(1), 30–42.CrossRefGoogle Scholar
  193. Zhang, Q., Tsao, Y. C., & Chen, T. H. (2014). Economic order quantity under advance payment. Applied Mathematical Modelling, 38(24), 5910–5921.CrossRefGoogle Scholar
  194. Zhou, Y. W. (2007). A comparison of different quantity discount pricing policies in a two-echelon channel with stochastic and asymmetric demand information. European Journal of Operational Research, 181(2), 686–703.CrossRefGoogle Scholar
  195. Zhou, Y. W., Chen, C., Wu, Y., & Zhou, W. (2014). EPQ models for items with imperfect quality and one-time-only discount. Applied Mathematical Modelling, 39(3–4), 1000–1018.Google Scholar
  196. Zissis, D., Ioannou, G., & Burnetas, A. (2015). Supply chain coordination under discrete information asymmetries and quantity discounts. Omega, 53, 21–29.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Ata Allah Taleizadeh
    • 1
  1. 1.School of Industrial Engineering, College of EngineeringUniversity of TehranTehranIran

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