Quantity discounts: An overview and practical guide for buyers and sellers

Foundations and Trends in Technology, Information and Operations Management

Volumn 8, Issue 1-2, 2014, Pages 1-130

  Munson, Charles L ^a   Jackson, Jonathan ^a  

^a WASHINGTON STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

SUPPLY CHAINS;

BUSINESS-TO-BUSINESS TRANSACTIONS; BUYERS AND SELLERS; CONTRACT NEGOTIATION; PRACTICAL GUIDE; PRICE DISCOUNT; QUANTITY DISCOUNT; SOLUTION ALGORITHMS;

SALES;

EID: 84930447371     PISSN: 15719545     EISSN: None     Source Type: Journal    
DOI: 10.1561/0200000041     Document Type: Article

References (269)

1. P. L. Abad. Determining optimal selling price and lot size when the supplier offers all-unit quantity discounts. Decision Sciences, 19(3):622-634, 1988a.
2. P. L. Abad. Joint price and lot-size determination when supplier offers incremental quantity discounts. Journal of the Operational Research Society, 39(6):603-607, 1988b.
3. P. L. Abad. Supplier pricing and lot sizing when demand is price sensitive. European Journal of Operational Research, 78(3):334-354, 1994.
4. P. L. Abad. Optimal price and lot size when the supplier offers a temporary price reduction over an interval. Computers and Operations Research, 30(1):63-74, 2003.
5. P. L. Abad and V. Aggarwal. Incorporating transport cost in the lot size and pricing decisions with downward sloping demand. International Journal of Production Economics, 95(3):297-305, 2005.
6. N. Aissaoui, M. Haouari, and E. Hassini. Supplier selection and order lot sizing modeling: A review. Computers & Operations Research, 34(12):3516-3540, 2007.
7. G. M. Allenby, T. S. Shively, S. Yang, and M. J. Garratt. A choice model for packaged goods: Dealing with discrete quantities and quantity discounts. Marketing Science, 23(1):95-108, 2004.
8. N. Altintas, F. Erhun, and S. Tayur. Quantity discounts under demand uncertainty. Management Science, 54(4):777-792, 2008.
9. K. S. Anand and R. Aron. Group buying on the web: A comparison of price-discovery mechanisms. Management Science, 49(11):1546-1562, 2003.
10. R. Anupindi and Y. Bassok. Approximations for multiproduct contracts with stochastic demands and business volume discounts: single supplier case. IIE Transactions, 30(8):723-734, 1998.
11. F. J. Arcelus and J. E. Rowcraft. All-units quantity-freight discounts with disposals. European Journal of Operational Research, 57(1):77-88, 1992.
12. F. J. Arcelus and G. Srinivasan. Delay of payments for extraordinary purchases. Journal of the Operational Research Society, 44:785-795, 1993.
13. F. J. Arcelus and G. Srinivasan. Discount strategies for one-time-only sales. IIE Transactions, 27(5):618-624, 1995.
14. A. Ardalan. Optimal ordering policies in response to a sale. IIE Transactions, 20(3):292-294, 1988.
15. A. Ardalan. Optimal prices and order quantities when temporary price discounts result in increase in demand. European Journal of Operational Research, 72(1):52-61, 1994.
16. D. C. Aucamp. Nonlinear freight costs in the EOQ problem. European Journal of Operational Research, 9(1):61-63, 1982.
17. D. C. Aucamp. A solution to the multiple set-up problem. International Journal of Production Research, 22(4):549-554, 1984.
18. D. C. Aucamp and P. J. Kuzdrall. Lot sizes for one-time-only sales. Journal of the Operational Research Society, 37(1):79-86, 1986.
19. R. L. Aull-Hyde. Evaluation of supplier-restricted purchasing options under temporary price discounts. IIE Transactions, 24(2):184-186, 1992.
20. L. M. Austin. 'Project EOQ': A success story in implementing academic research. Interfaces, 7(4):1-12, 1977.
21. S. Balachander and K. Srinivasan. Quantity discounts, manufacturer and channel profit maximization: Impact of retailer heterogeneity. Marketing Letters, 9(2):169-179, 1998.
22. A. Banerjee. A joint economic-lot-size model for purchaser and vendor. Decision Sciences, 17(3):292-311, 1986a.
23. A. Banerjee. On 'a quantity discount pricing model to increase vendor profits'. Management Science, 32(11):1513-1517, 1986b.
24. Y. Bassok and R. Anupindi. Analysis of supply contracts with total minimum commitment. IIE Transactions, 29(5):373-381, 1997.
25. P. S. Bender, R. W. Brown, M. H. Isaac, and J. F. Shapiro. Improving purchasing productivity at IBM with a normative decision support system. Interfaces, 15(3):106-115, 1985.
26. W. C. Benton. Purchase quantity discount procedures and MRP. Journal of Purchasing and Materials Management, 19(1):30-34, 1983.
27. W. C. Benton. Muliple price breaks and alternative purchase lot-sizing procedures in material requirements planning systems. International Journal of Production Research, 23(5):1025-1047, 1985.
28. W. C. Benton. Quantity discount decisions under conditions of multiple items, multiple suppliers and resource limitations. International Journal of Production Research, 29(10):1953-1961, 1991.
29. W. C. Benton and S. Park. A classification on determining the lot size under quantity discounts. European Journal of Operational Research, 92(2):219-238, 1996.
30. W. C. Benton and D. C. Whybark. Materials requirement planning (MRP) and purchase discounts. Journal of Operations Management, 2(2):137-143, 1982.
31. F. Bernstein and A. Federgruen. Pricing and replenishment strategies in a distribution system with competing retailers. Operations Research, 51(3):409-426, 2003.
32. F. Bernstein, F. Chen, and A. Federgruen. Coordinating supply chains with simple pricing schemes: The role of vendor-managed inventories. Management Science, 52(10):1483-1492, 2006.
33. M. Boyle and C. Wolf. To boost buying power, Wal-Mart woos partners. Bloomberg Businessweek, 4199:23-24, Oct. 11 2010.
34. R. L. Bregman. Experimental comparison of MRP purchase discount methods. Journal of the Operational Research Society, 42(3):235-245, 1991.
35. R. L. Bregman and E. A. Silver. A modification of the Silver-Meal heuristic to handle MRP purchase discount situations. Journal of Operational Research Society, 44(7):717-723, 1993.
36. J. M. Buchanan. The theory of monopolistic quantity discounts. Review of Economic Studies, 20(3):199-208, 1953.
37. F. P. Buffa and J. R. Munn. A recursive algorithm for order cycle-time that minimizes logistics cost. Journal of Operational Research Society, 40(4):367-377, 1989.
38. J. Buquid, D. Gibson, and P. Huppert. Hd Supply Facilities Maintenance uses diluted discounts to optimize purchasing opportunities. Interfaces, 41(2):135-148, 2011.
39. G. J. Burke, J. Carrillo, and A. J. Vakharia. Heuristics for sourcing from multiple suppliers with alternative quantity discounts. European Journal of Operational Research, 186(1):317-329, 2008a.
40. G. J. Burke, J. Geunes, H. Edwin Romeijn, and A. Vakharia. Allocating procurement to capacitated suppliers with concave quantity discounts. Operations Research Letters, 36(1):103-109, 2008b.
41. A. Burnetas, S. M. Gilbert, and C. E. Smith. Quantity discounts in single-period supply contracts with asymmetric demand information. IIE Transactions, 39(5):465-479, 2007.
42. T. H. Burwell, S. D. Dinesh, K. E. Fitzpatrick, and M. R. Roy. A note on determining optimal selling price and lot size under all-units quantity discounts. Decision Sciences, 21(2):471-474, 1990.
43. T. H. Burwell, S. D. Dinesh, K. E. Fitzpatrick, and M. R. Roy. An inventory model with planned shortages and price dependent demand. Decision Sciences, 22(5):1187-1191, 1991.
44. T. H. Burwell, S. D. Dinesh, K. E. Fitzpatrick, and M. R. Roy. Economic lot size models for price-dependent demand under quantity and freight discounts. International Journal of Production Economics, 48(2):141-155, 1997.
45. G. P. Cachon and A. G. Kök. Competing manufacturers in a retail supply chain: On contractual form and coordination. Management Science, 56(3):571-589, 2010.
46. G. P. Cachon and M. A. Lariviere. Supply chain coordination with revenue-sharing contracts: Strengths and limitations. Management Science, 51(1):30-44, 2005.
47. G. Calzolari and V. Denicolò. On the anti-competitive effects of quantity discounts. International Journal of Industrial Organization, 29(3):337-341, 2011.
48. D. G. Cantellow, S. L. Burton, and R. M. Laing. An automatic model for purchase decisions. Operational Research Quarterly, 20(Special Conference Issue):25-42, 1969.
49. A. K. Chakravarty. Joint inventory replenishments with group discounts based on invoice value. Management Science, 30(9):1105-1112, 1984.
50. A. K. Chakravarty. Multiproduct purchase scheduling with limited budget and/or group discounts. Computers and Operations Research, 12(5):493-505, 1985.
51. A. K. Chakravarty. Quantity discounted inventory replenishment with limited storage space. INFOR, 24(1):12-25, 1986.
52. A. K. Chakravarty and G. E. Martin. Optimal joint buyer-seller discount pricing model. Computers and Operations Research, 15(3):271-281, 1988.
53. A. K. Chakravarty and G. E. Martin. Discount pricing policies for inventories subject to declining demand. Naval Research Logistics, 36(1):89-102, 1989.
54. A. K. Chakravarty and G. E. Martin. Operational economies of a process positioning determinant. Computers and Operations Research, 18(6):515-530, 1991.
55. C.-T. Chang and S.-C. Chang. On the inventory model with variable lead time and price-quantity discount. Journal of the Operational Research Society, 52(10):1151-1158, 2001.
56. C.-T. Chang, C.-L. Chin, and M.-F. Lin. On the single item multi-supplier system with variable lead-time, price-quantity discount and resource constraints. Applied Mathematics and Computation, 182(1):89-97, 2006.
57. H.-C. Chang. 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, 2013.
58. S. S. Chaudhry, F. G. Forst, and J. L. Zydiak. Vendor selection with price breaks. European Journal of Operational Research, 70(1):52-66, 1993.
59. B. Chen and C. L. Munson. Resource allocation with lumpy demand: To speed or not to speed? Naval Research Logistics, 51(3):363-385, 2004.
60. F. Chen, A. Federgruen, and Y.-S. Zheng. Coordination mechanisms for a distribution system with one supplier and multiple retailers. Management Science, 47(5):693-708, 2001.
61. J.-M. Chen and T.-H. Chen. The multi-item replenishment problem in a two-echelon supply chain: The effect of centralization versus decentralization. Computers and Operations Research, 32(12):3191-3207, 2005.
62. R. R. Chen and L. W. Robinson. Optimal multiple-breakpoint quantity discount schedules for customers with heterogeneous demands: All-unit or incremental? IIE Transactions, 44(3):199-214, 2012.
63. S.-P. Chen and Y.-H. Ho. Analysis of the newsboy problem with fuzzy demands and incremental discounts. International Journal of Production Economics, 129(1):169-177, 2011.
64. X. Chen. Inventory centralization games with price-dependent demand and quantity discount. Operations Research, 57(6):1394-1406, 2009.
65. W.-C. Chiang, J. Fitzsimmons, Z. Huang, and S. X. Li. A game-theoretic approach to quantity discount problems. Decision Sciences, 25(1):153-168, 1994.
66. C.-C. Chiou. Observation on: 'Channel coordination and volume discounts with price-sensitive demand'. International Journal of Production Economics, 118(2):545-546, 2009.
67. S. Chopra and P. Meindl. Supply Chain Management: Strategy, Planning and Operation. Prentice Hall, Upper Saddle River, NJ, 4th edition, 2010.
68. C. Chung, D. T. Chiang, and C. Lu. An optimal algorithm for the quantity discount problem. Journal of Operations Management, 7(1):165-177, 1987.
69. C.-S. Chung, S.-H. Hum, and O. Kirca. Coordinated replenishment dynamic lot-sizing problem with quantity discounts. European Journal of Operational Research, 94(1):122-133, 1996.
70. C.-S. Chung, S.-H. Hum, and O. Kirca. Optimal procedure for the coordinated replenishment dynamic lot-sizing problem with quantity discounts. Naval Research Logistics, 47(8):686-695, 2000.
71. C. J. Corbett and X. de Groote. Supplier's optimal quantity discount policy under asymmetric information. Management Science, 46(3):444-450, 2000.
72. Y. Crama, R. J. Pascual, and A. Torres. Optimal procurement decisions in the presence of total quantity discounts and alternative product recipes. European Journal of Operational Research, 159(2):364-378, 2004.
73. M. Dada and K. N. Srikanth. Pricing policies for quantity discounts. Management Science, 33(10):1247-1252, 1987.
74. N. E. Dahel. Vendor selection and order quantity allocation in volume discount environment. Supply Chain Management, 8(4):335-342, 2003.
75. M. A. Darwish. Joint determination of order quantity and reorder point of continuous review model under quantity and freight rate discounts. Computers and Operations Research, 35(12):3902-3917, 2008.
76. C. Das. A generalized discount structure and some dominance rules for selecting the price-break EOQ. European Journal of Operational Research, 34(1):27-38, 1988.
77. C. Das. Algorithm for selecting quantity discounts from realistic schedules. Journal of the Operational Research Society, 41(2):165-172, 1990.
78. R. A. Davis and N. Gaither. Optimal ordering policies under conditions of extended payment privileges. Management Science, 31(4):499-509, 1985.
79. M. Diaby and A. Martel. Dynamic lot sizing for multi-echelon distribution systems with purchasing and transportation price discounts. Operations Research, 41(1):48-59, 1993.
80. R. J. Dolan. Quantity discounts: Managerial issues and research opportunities. Marketing Science, 6(1):1-22, 1987.
81. Z. Drezner and G. O. Wesolowsky. Multi-buyer discount pricing. European Journal of Operational Research, 40(1):38-42, 1989.
82. R. Du, A. Banerjee, and S.-L. Kim. Coordination of two-echelon supply chains using wholesale price discount and credit option. International Journal of Production Economics, 143(2):327-334, 2013.
83. F. Erhun and S. Tayur. Enterprise-wide optimization of total landed cost at a grocery retailer. Operations Research, 51(3):343-353, 2003.
84. A. Federgruen and C.-Y. Lee. The dynamic lot size model with quantity discount. Naval Research Logistics, 37(5):707-713, 1990.
85. B. Foubert and E. Gijsbrechts. Please or squeeze? Brand performance implications of constrained and unconstrained multi-item promotions. European Journal of Operational Research, 202(3):880-892, 2010.
86. J. K. Friend. Stock control with random opportunities for replenishment. Operational Research Quarterly, 11(3):130-136, 1960.
87. A. A. Gaballa. Minimum cost allocation of tenders. Operational Research Quarterly, 25(3):389-398, 1974.
88. A. Gabor. A note on block tariffs. Review of Economic Studies, 23(1):32-41, 1955.
89. N. Gaither and M. Park. Analysis on constrained, one-time, multi-item discount offers. IIE Transactions, 23(3):228-235, 1991.
90. E. Gerstner and J. Hess. Why do hot dogs come in packs of 10 and buns in 8s or 12s? A demand side investigation. Journal of Business, 60(4):491-517, 1987.
91. P. Ghandforoush and J. C. Loo. Non-linear procurement model with quantity discounts. Journal of the Operational Research Society, 43(11):1087-1093, 1992.
92. M. B. Goldman, H. E. Leland, and D. S. Sibley. Optimal nonuniform prices. Review of Economic Studies, 51(2):305-319, 1984.
93. D. R. Goossens, A. J. T. Maas, F. C. R. Spieksma, and J. J. van de Klundert. Exact algorithms for procurement problems under a total quantity discount structure. European Journal of Operational Research, 178(2):603-626, 2007.
94. S. K. Goyal. An integrated inventory model for a single supplier-single customer problem. International Journal of Production Research, 15(11):107-111, 1976.
95. S. K. Goyal. Determination of a supplier's economic ordering policy. Journal of the Operational Research Society, 38(9):853-857, 1987a.
96. S. K. Goyal. Comment on: A generalized quantity discount pricing model to increase supplier's profits. Management Science, 33(12):1635-1636, 1987b.
97. S. K. Goyal. A joint economic-lot-size model for purchaser and vendor: A comment. Decision Sciences, 19(1):236-241, 1988.
98. S. K. Goyal and O. K. Gupta. Simple approach to the discount purchase problem. Journal of the Operational Research Society, 41(12):1169-1170, 1990.
99. S. K. Goyal and Y. P. Gupta. Integrated inventory models: The buyer-vendor coordination. European Journal of Operational Research, 41(3):261-269, 1989.
100. S. K. Goyal and G. Srinivasan. The individually responsible and rational decision approach to economic lot sizes for one vendor and many purchasers: A comment. Decision Sciences, 23(3):777-784, 1992.
101. Z. J. Gu and S. Yang. Quantity discount dependent consumer preferences and competitive nonlinear pricing. Journal of Marketing Research, 47(6):1100-1113, 2010.
102. F. Güder, J. Zydiak, and S. Chaudhry. Capacitated multiple item ordering with incremental quantity discounts. Journal of the Operational Research Society, 45(10):1197-1205, 1994.
103. H. Gurnani. 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, 2001.
104. G. Hadley and T. M. Whitin. Analysis of Inventory Systems. Prentice Hall, Englewood Cliffs, NJ, 1963.
105. C. Haksever and J. Moussourakis. Determining order quantities in multi-product inventory systems subject to multiple constraints and incremental discounts. European Journal of Operational Research, 184(3):930-945, 2008.
106. R. W. Hall. Price changes and order quantities: Impacts on discount rate and storage costs. IIE Transactions, 24(2):104-110, 1992.
107. R. Hammami, C. Temponi, and Y. Frein. A scenario-based stochastic model for supplier selection in global context with multiple buyers, currency fluctuation uncertainties and price discounts. European Journal of Operational Research, 233(1):159-170, 2014.
108. J. Heizer and B. Render. Operations Management: Sustainability and Supply Chain Management. Prentice Hall, Upper Saddle River, NJ, 11th edition, 2014.
109. G. Hohner, J. Rich, E. Ng, G. Reid, A. J. Davenport, J. R. Kalagnanam, H. S. Lee, and C. An. Combinatorial and quantity-discount procurement auctions benefit Mars, Incorporated and its suppliers. Interfaces, 33(1):23-35, 2003.
110. C.-C. Hsieh, C.-H. Wu, and Y.-J. Huang. Ordering and pricing decisions in a two-echelon supply chain with asymmetric demand information. European Journal of Operational Research, 190(2):509-525, 2008.
111. J. Hu and C. L. Munson. Dynamic demand lot-sizing rules for incremental quantity discounts. Journal of the Operational Research Society, 53(8):855-863, 2002.
112. J. Hu and C. L. Munson. Incorporating quantity discounts and their inventory impacts into the centralized purchasing decision. European Journal of Operational Research, 201(2):581-592, 2010.
113. J. Hu and C. L. Munson. Improved profit functions for newsvendor models with normally distributed demand. International Journal of Procurement Management, 4(1):20-36, 2011.
114. J. Hu, C. L. Munson, and E. A. Silver. A modified Silver-Meal heuristic for dynamic lot sizing under incremental quantity discounts. Journal of the Operational Research Society, 55(6):671-673, 2004.
115. Q. Hu, L. B. Schwarz, and N. A. Uhan. The impact of group purchasing organizations on healthcare-product supply chains. Manufacturing and Service Operations Management, 14(1):7-23, 2012.
116. G. Hua, S. Wang, and T. C. E. Cheng. Optimal pricing and order quantity for the newsvendor problem with free shipping. International Journal of Production Economics, 135(1):162-169, 2012a.
117. G. Hua, S. Wang, and T. C. E. Cheng. Optimal order lot sizing and pricing with free shipping. European Journal of Operational Research, 218(2):435-441, 2012b.
118. Y.-S. Huang, W.-J. Su, and Z.-L. Lin. A study on lead-time discount coordination for deteriorating products. European Journal of Operational Research, 215(2):358-366, 2011.
119. A. P. Hurter and F. C. Kaminsky. An application of regenerative stochastic processes to a problem in inventory control. Operations Research, 15(3):467-472, 1967.
120. A. P. Hurter and F. C. Kaminsky. Inventory control with a randomly available discount purchase price. Operational Research Quarterly, 19(4):433-444, 1968a.
121. A. P. Hurter and F. C. Kaminsky. Inventory control with random and regular replenishment. The Journal of Industrial Engineering, 19(8):380-385, 1968b.
122. H. Hwang and K. H. Kim. Supplier's discount policy with a single price break point. Engineering Costs and Production Economics, 10(4):279-286, 1986.
123. H. Hwang, D. H. Moon, and S. W. Shinn. An EOQ model with quantity discounts for both purchasing price and freight cost. Computers and Operations Research, 17(1):73-78, 1990.
124. C. A. Ingene and M. E. Parry. Channel coordination when retailers compete. Marketing Science, 14(4):360-377, 1995.
125. K. Iwaniec. An inventory model with full load ordering. Management Science, 25(4):374-384, 1979.
126. R. Iyengar and K. Jedidi. A conjoint model of quantity discounts. Marketing Science, 31(2):334-350, 2012.
127. J. Jackson. Quantity discounts, capacity decisions, and channel structure choices in supply chains. Unpublished dissertation, Washington State University, Pullman, WA, 2015.
128. A. P. Jeuland and S. M. Shugan. Coordination in marketing channels. In D. Gautschi, editor, Productivity and Efficiency in Distribution Systems, Chapter 2. Elsevier Publishing Co., New York, 1983a.
129. A. P. Jeuland and S. M. Shugan. Managing channel profits. Marketing Science, 2(3):239-272, 1983b.
130. A. P. Jeuland and S. M. Shugan. Reply to: Managing channel profits: Comment. Marketing Science, 7(1):103-106, 1988.
131. P. N. Joglekar. Comments on 'A quantity discount pricing model to increase vendor profits'. Management Science, 34(11):1391-1398, 1988.
132. P. N. Joglekar and S. Tharthare. The individually responsible and rational decision approach to economic lot sizes for one vendor and many purchasers. Decision Sciences, 21(3):492-506, 1990.
133. J. V. Jucker and M. J. Rosenblatt. Single-period inventory model with demand uncertainty and quantity discounts. Naval Research Logistics, 32(4):537-550, 1985.
134. B. Kalkanci, K.-Y. Chen, and F. Erhun. Contract complexity and performance under asymmetric demand information: An experimental evaluation. Management Science, 57(4):689-704, 2011.
135. H.-Y. Kang and A. H. I. Lee. A stochastic lot-sizing model with multi-supplier and quantity discounts. International Journal of Production Research, 51(1):245-263, 2013.
136. M. Kaspi and M. J. Rosenblatt. An improvement of Silver's algorithm for the joint replenishment problem. IIE Transactions, 15(3):264-267, 1983.
137. P. Katz, A. Sadrian, and P. Tendick. Telephone companies analyze price quotations with Bellcore's PDSS software. Interfaces, 24(1):50-63, 1994.
138. G. Y. Ke and J. H. Bookbinder. Discount pricing for a family of items: The supplier's optimal decisions. International Journal of Production Economics, 135(1):255-264, 2012.
139. P. Keskinocak and S. Savasaneril. Collaborative procurement among competing buyers. Naval Research Logistics, 55(6):516-540, 2008.
140. M. Khouja. The newsboy problem with multiple discounts offered by suppliers and retailers. Decision Sciences, 27(3):589-599, 1996.
141. K. H. Kim and H. Hwang. Incremental discount pricing schedule with multiple customers and single price break. European Journal of the Operational Research, 35(1):71-79, 1988.
142. K. H. Kim and H. Hwang. Simultaneous improvement of supplier's profit and buyer's cost by utilizing quantity discount. Journal of the Operational Research Society, 40(3):255-265, 1989.
143. T. W. Knowles and P. Pantumsinchai. All-units discounts for standard container sizes. Decision Sciences, 19(4):848-857, 1988.
144. R. Kohli and H. Park. A cooperative game theory model of quantity discounts. Management Science, 35(6):693-707, 1989.
145. R. Kohli and H. Park. Coordinating buyer-seller transactions across multiple products. Management Science, 40(9):1145-1150, 1994.
146. A. Kokangul and Z. Susuz. Integrated analytical hierarch process and mathematical programming to supplier selection problem with quantity discount. Applied Mathematical Modelling, 33(3):1417-1429, 2009.
147. S. Kolay and G. Shaffer. Contract design with a dominant retailer and a competitive fringe. Management Science, 59(9):2111-2116, 2013.
148. L. J. Krajewski, L. P. Ritzman, and M. K. Malhotra. Operations Management: Processes and Supply Chains. Prentice Hall, Upper Saddle River, NJ, 10th edition, 2013.
149. S. Ladany and A. Sternlieb. The interactions of economic ordering quantities and marketing policies. AIIE Transactions, 6(1):35-40, 1974.
150. R. L. LaForge. MRP lot sizing with quantity discounts. Computers and Operations Research, 12(6):579-587, 1985.
151. R. Lal and R. Staelin. An approach for developing an optimal discount pricing policy. Management Science, 30(12):1524-1539, 1984.
152. A. H. L. Lau, H.-S. Lau, and J.-C. Wang. Designing a quantity discount scheme for a newsvendor-type product with numerous heterogeneous retailers. European Journal of Operational Research, 180(2):585-600, 2007a.
153. A. H. L. Lau, H.-S. Lau, and J.-C. Wang. Pricing and volume discounting for a dominant retailer with uncertain manufacturing cost information. European Journal of Operational Research, 183(2):848-870, 2007b.
154. C.-Y. Lee. The economic order quantity for freight discount costs. IIE Transactions, 18(3):318-320, 1986.
155. C.-Y. Lee. A solution to the multiple set-up problem with dynamic demand. IIE Transactions, 21(3):266-270, 1989.
156. H. L. Lee and M. J. Rosenblatt. A generalized quantity discount pricing model to increase supplier's profits. Management Science, 32(9):1177-1185, 1986.
157. J.-Y. Lee. Quantity discounts based on the previous order in a two-period inventory model with demand uncertainty. Journal of the Operational Research Society, 59(7):1004-1011, 2008.
158. H. Leland and R. Meyer. Monopoly pricing structures with imperfect discrimination. Bell Journal of Economics, 7(2):449-462, 1976.
159. M. Levy, W. Cron, and R. Novack. A decision support system for determining a quantity discount pricing policy. Journal of Business Logistics, 6(2):110-141, 1985.
160. C.-L. Li, V. N. Hsu, and W.-Q. Xiao. Dynamic lot sizing with batch ordering and truckload discounts. Operations Research, 52(4):639-654, 2004.
161. C.-L. Li, J. Ou, and V. N. Hsu. Dynamic lot sizing with all-units discount and resales. Naval Research Logistics, 59(3-4):230-243, 2012.
162. J. Li and L. Liu. Supply chain coordination with quantity discount policy. International Journal of Production Economics, 101(1):89-98, 2006.
163. G. L. Lilien, P. Kotler, and K. S. Moorthy. Marketing Models. Prentice Hall, Englewood Cliffs, NJ, 1992.
164. T.-Y. Lin. Coordination policy for a two-stage supply chain considering quantity discounts and overlapped delivery with imperfect quality. Computers and Industrial Engineering, 66(1):53-62, 2013.
165. S. A. Lippman. Optimal inventory policy with multiple set-up costs. Management Science, 16(1):118-138, 1969.
166. S. A. Lippman. Economic order quantities and multiple set-up costs. Management Science, 18(1):39-47, 1971.
167. R. A. Low and J. F. Waddington. The determination of the optimum joint replenishment policy for a group of discount-connected stock lines. Operational Research Quarterly, 18(4):443-462, 1967.
168. L. L. Lu, Y. Qiu, and W. Chiang. A multi-item ordering problem with business volume discounts. Working paper, U. S. West Technologies, Boulder, CO, 1994.
169. D. Manerba and R. Mansini. An exact algorithm for the capacitated total quantity discount problem. European Journal of Operational Research, 222(2):287-300, 2012.
170. D. Manerba and R. Mansini. An effective matheuristic for the capacitated total quantity discount problem. Computers and Operations Research, 41(1):1-11, 2014.
171. R. Mansini, M. W. P. Savelsbergh, and B. Tocchella. The supplier selection problem with quantity discounts and truckload shipping. Omega, 40(4):445-455, 2012.
172. E. P. Markowski. Criteria for evaluating purchase quantity decisions in response to future price increases. European Journal of Operational Reesearch, 47(3):364-370, 1990.
173. M. V. Marn and R. L. Rosiello. Managing price, gaining profit. Harvard Business Review, 70(5):84-94, 1992.
174. M. B. McConnel and D. T. Galligan. The use of integer programming to select bulls across breeding companies with volume discounts. Journal of Dairy Science, 87(10):3542-3549, 2004.
175. T. W. McGuire and R. Staelin. Channel efficiency, incentive compatibility, transfer pricing and market structure: An equilibrium analysis of channel relationships. In Carman and Bucklin, editors, Research in Marketing: Distribution Channels and Institutions, volume 8. JAI Press, 1986.
176. A. Mehrez and D. Ben-Arieh. All-unit discounts, multi-item inventory model with stochastic demand, service level constraints and finite horizon. International Journal of Production Research, 29(8):1615-1628, 1991.
177. A. Mendoza and J. A. Ventura. Incorporating quantity discounts to the EOQ model with transportation costs. International Journal of Production Economics, 113(2):754-765, 2008.
178. S. H. Mirmohammadi, S. Shadrokh, and F. Kianfar. An efficient optimal algorithm for the quantity discount problem in material requirement planning. Computers and Operations Research, 36(6):1780-1788, 2009.
179. S. M. J. Mirzapour Al-e-hashem, A. Baboli, and Z. Sazvar. A stochastic aggregate production planning model in a green supply chain: Considering flexible lead times, nonlinear purchase and shortage cost functions. European Journal of Operational Research, 230(1):26-41, 2013.
180. A. K. Mishra. Selective discount for supplier-buyer coordination using common replenishment epochs. European Journal of Operational Research, 153(3):751-756, 2004.
181. J. P. Monahan. Quantity discount pricing model to increase vendor profits. Management Science, 30(6):720-726, 1984.
182. K. S. Moorthy. Managing channel profits: Comment. Marketing Science, 6(4):375-379, 1987.
183. C. L. Munson. The appeal of partially centralized purchasing policies. International Journal of Procurement Management, 1(1-2):117-143, 2007.
184. C. L. Munson and J. Hu. Incorporating quantity discounts and their inventory impacts into the centralized purchasing decision. European Journal of Operational Research, 201(2):581-592, 2010.
185. C. L. Munson and M. J. Rosenblatt. Theories and realities of quantity discounts: An exploratory study. Production and Operations Management, 7(4):352-369, 1998.
186. C. L. Munson and M. J. Rosenblatt. Coordinating a three-level supply chain with quantity discounts. IIE Transactions, 33(5):371-384, 2001.
187. C. L. Munson, J. Hu, and M. J. Rosenblatt. Teaching the costs of uncoordinated supply chains. Interfaces, 33(3):24-39, 2003.
188. M. M. Murphy. Price discrimination, market separation and the multi-part tariff. Economic Inquiry, 14(4):587-599, 1977.
189. N. Murthy, S. Soni, and S. Ghosh. A framework for facilitating sourcing and allocation decisions for make-to-order items. Decision Sciences, 35(4):609-637, 2004.
190. R. Nanda and H.-K. Nam. Quantity discounts using a joint lot size model under learning effects - single buyer case. Computers and Industrial Engineering, 22(2):211-221, 1992.
191. R. Nanda and H.-K. Nam. Quantity discounts using a joint lot size model under learning effects - multiple buyers case. Computers and Industrial Engineering, 24(3):487-494, 1993.
192. W. Y. Oi. A Disneyland dilemma: Two-part tariffs for a Mickey Mouse monopoly. The Quarterly Journal of Economics, 85(1):77-96, 1971.
193. P. Pantumsinchai and T. W. Knowles. Standard container size discounts and the single period inventory problem. Decision Sciences, 22(3):612-619, 1991.
194. S. Papachristos and K. Skouri. An inventory model with deteriorating items, quantity discount, pricing and time-dependent partial backlogging. International Journal of Production Economics, 83(3):247-256, 2003.
195. M. Parlar and Q. Wang. Discounting decisions in a supplier-buyer relationship with a linear buyer's demand. IIE Transactions, 26(2):34-41, 1994.
196. P. P.-E. Pei, D. Simchi-Levi, and T. I. Tunca. Sourcing flexibility, spot trading and procurement contract structure. Operations Research, 59(3):578-601, 2011.
197. H. Pirkul and O. A. Aras. Capacitated multiple item ordering problem with quantity discounts. IIE Transactions, 17(3):206-211, 1985.
198. D. A. Popken. An algorithm for the multivariate, multicommodity flow problem with freight consolidation and inventory costs. Operations Research, 42(2):274-286, 1994.
199. M. Prince, J. Geunes, and J. C. Smith. Procurement allocation planning with multiple suppliers under competition. International Journal of Production Research, 51(23-24):6900-6922, 2013.
200. H. Qin, M. Luo, X. Gao, and A. Lim. The freight allocation problem with all-units quantity-based discount: A heuristic algorithm. Omega, 40(4):415-423, 2012.
201. Y. Qin, H. Tang, and C. Guo. Channel coordination and volume discounts with price-sensitive demand. International Journal of Production Economics, 105(1):43-53, 2007.
202. J. Raju and Z. J. Zhang. Channel coordination in the presence of a dominant retailer. Marketing Science, 24(2):254-262, 2005.
203. A. Rao. Quantity discounts in today's markets. Journal of Marketing, 44(4):44-51, 1980.
204. B. Q. Rieksts and J. A. Ventura. Optimal inventory policies with two modes of freight transportation. European Journal of Operational Research, 186(2):576-585, 2008.
205. Y. Rong, Z.-J. Shen, and C. A. Yano. Cheaper by the pallet? Multi-item procurement with standard batch sizes. IIE Transactions, 44(6):405-418, 2012.
206. M. J. Rosenblatt and H. L. Lee. Improving profitability with quantity discounts under fixed demand. IIE Transactions, 17(4):388-395, 1985.
207. P. A. Rubin and W. C. Benton. Jointly constrained order quantities with all-units discounts. Naval Research Logistics, 40(2):255-278, 1993.
208. P. A. Rubin and W. C. Benton. Evaluating jointly constrained order quantity complexities for incremental discounts. European Journal of Operational Research, 149(3):557-570, 2003.
209. P. A. Rubin, D. M. Dilts, and B. A. Barron. Economic order quantities with quantity discounts: Grandma does it best. Decision Sciences, 14(2):270-281, 1983.
210. R. M. Russell and L. J. Krajewski. Optimal purchase and transportation cost lot sizing for a single item. Decision Sciences, 22(4):940-952, 1991.
211. K. Ryu and E. Yücesan. A fuzzy newsvendor approach to supply chain coordination. European Journal of Operational Research, 200(2):421-438, 2010.
212. A. A. Sadrian and Y. S. Yoon. Procurement decision support system in business volume discount environments. Operations Research, 42(1):14-23, 1994.
213. L. A. San-José and J. García-Laguna. 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, 2009.
214. T. Sandholm, D. Levine, M. Concordia, P. Martyn, R. Hughes, J. Jacobs, and D. Begg. Changing the game in strategic sourcing at Procter & Gamble: Expressive competition enabled by optimization. Interfaces, 36(1):55-68, 2006.
215. D. P. Sari, A. Rusdiansyah, and L. Huang. Models of joint economic lot-sizing problem with time-based temporary price discounts. International Journal of Production Economics, 139(1):145-154, 2012.
216. S. P. Sarmah, D. Acharya, and S. K. Goyal. Buyer vendor coordination models in supply chain management. European Journal of Operational Research, 175(1):1-15, 2006.
217. F. Schotanus, J. Telgen, and L. de Boer. Unfair allocation of gains under the Equal Price allocation method in purchasing groups. European Journal of Operational Research, 187(1):162-176, 2008.
218. F. Schotanus, J. Telgen, and L. Deboer. Unraveling quantity discounts. Omega, 37(3):510-521, 2009.
219. S. P. Sethi. A quantity discount lot size model with disposals. International Journal of Production Research, 22(1):31-39, 1984.
220. C.-S. Shi and C.-T. Su. Integrated inventory model of returns-quantity discounts contract. Journal of the Operational Research Society, 55(3):240-246, 2004.
221. H. Shin and W. C. Benton. A quantity discount approach to supply chain coordination. European Journal of Operational Research, 180(2):601-616, 2007.
222. S. W. Shinn, H. Hwang, and S. S. Park. Joint price and lot size determination under conditions of delay in payments and quantity discounts for freight cost. European Journal of Operational Research, 91(3):528-542, 1996.
223. S. M. Shugan. Brand loyalty programs: Are they shams? Marketing Science, 24(2):185-193, 2005.
224. E. A. Silver. A simple method of determining order quantities in joint replenishments under deterministic demand. Management Science, 22(12):1351-1361, 1976.
225. S. Sinha and S. P. Sarmah. Single-vendor multi-buyer discount pricing model under stochastic demand environment. Computers & Industrial Engineering, 59(4):945-953, 2010.
226. D. E. Sprott, K. C. Manning, and A. D. Miyazaki. Grocery price setting and quantity surcharges. Journal of Marketing, 67(3):34-46, 2003.
227. R. Srivastava and W. C. Benton. Purchase quantity discounts and open order rescheduling in an assemble-to-order environment: The hidden economic tradeoffs. European Journal of Operational Research, 110(2):261-271, 1998.
228. H. Stadtler. A general quantity discount and supplier selection mixed integer programming model. OR Spectrum, 29(4):723-744, 2007.
229. R. Subramaniam and E. Gal-Or. Quantity discounts in differentiated consumer product markets. Marketing Science, 28(1):180-192, 2009.
230. E. S. Subramanyam and S. Kumaraswamy. EOQ formula under varying marketing policies and conditions. AIIE Transactions, 13(4):312-314, 1981.
231. S. Syam and B. Shetty. Coordinated replenishments from multiple suppliers with price discounts. Naval Research Logistics, 45(6):579-598, 1998.
232. S. G. Taylor and C. Bradley. Optimal ordering strategies for announced price increases. Operations Research, 33(2):312-325, 1985.
233. T. A. Taylor and W. Xiao. Does a manufacturer benefit from selling to a better-forecasting retailer? Management Science, 56(9):1584-1598, 2010.
234. H. Tempelmeier. A simple heuristic for dynamic demand order sizing and supplier selection with time-varying data. Production and Operations Management, 11(4):499-515, 2002.
235. R. J. Tersine. Economic replenishment strategies for announced price increases. European Journal of Operational Research, 92(2):266-280, 1996.
236. R. J. Tersine and S. Barman. Economic inventory transport lot sizing with quantity discounts and freight rate discounts. Decision Sciences, 22(5):1171-1179, 1991.
237. R. J. Tersine and S. Barman. Optimal lot sizes for unit and shipping discount situations. IIE Transactions, 26(2):97-101, 1994.
238. R. J. Tersine and S. Barman. Economic purchasing strategies for temporary price discounts. European Journal of Operational Research, 80(2):328-343, 1995.
239. A. Toptal. Replenishment decisions under an all-units discount schedule and stepwise freight costs. European Journal of Operational Research, 198(2):504-510, 2009.
240. J.-F. Tsai. An optimization approach for supply chain management models with quantity discount policy. European Journal of Operational Research, 177(2):982-994, 2007.
241. I. Turner. An independent system for the evaluation of contract tenders. Journal of the Operational Research Society, 39(6):551-561, 1988.
242. J. van de Klundert, J. Kuipers, F. C. R. Spieksma, and M. Winkels. Selecting telecommunication carriers to obtain volume discounts. Interfaces, 35(2):124-132, 2005.
243. F. A. van der Duyn Schouten, M. J. G. van Eijs, and R. M. J. Heuts. Coordinated replenishment systems with discount opportunities. International Journal of Production Research, 32(12):2879-2895, 1994.
244. S. Viswanathan and R. Piplani. Coordinating supply chain inventories through common replenishment epochs. European Journal of Operational Research, 129(2):277-286, 2001.
245. S. Viswanathan and Q. Wang. Discount pricing decisions in distribution channels with price-sensitive demand. European Journal of Operational Research, 149(3):571-587, 2003.
246. H. M. Wagner and T. M. Whitin. Dynamic version of the economic lot size model. Management Science, 50(12):1770-1774, 1958.
247. Q. Wang. Determination of suppliers' optimal quantity discount schedules with heterogeneous buyers. Naval Research Logistics, 49(1):46-59, 2002.
248. Q. Wang. Coordinating independent buyers with integer-ratio time coordination and quantity discounts. Naval Research Logistics, 51(3):316-331, 2004.
249. Q. Wang and R. Wang. Quantity discount pricing policies for heterogeneous retailers with price sensitive demand. Naval Research Logistics, 52(7):645-658, 2005.
250. Q. Wang and Z. Wu. Improving a supplier's quantity discount gain from many different buyers. IIE Transactions, 32(11):1071-1079, 2000.
251. Q. Wang, Y. Chay, and Z. Wu. Streamlining inventory flows with time discounts to improve the profits of a decentralized supply chain. International Journal of Production Economics, 132(2):230-239, 2011.
252. B. Wansink. Can package size accelerate usage volume? Journal of Marketing, 60(3):1-14, 1996.
253. H.-M. Wee. Deteriorating inventory model with quantity discount, pricing and partial backordering. International Journal of Production Economics, 59(1):511-518, 1999.
254. Z. K. Weng. Modeling quantity discounts under general price-sensitive demand functions: Optimal policies and relationships. European Journal of Operational Research, 86(2):300-314, 1995a.
255. Z. K. Weng. Channel coordination and quantity discounts. Management Science, 41(9):1509-1522, 1995b.
256. Z. K. Weng and R. T. Wong. General models for the supplier's all-unit quantity discount policy. Naval Research Logistics, 40(7):971-991, 1993.
257. K. Wertenbroch. Consumption self-control by rationing purchase quantities of virtue and vice. Marketing Science, 17(4):317-337, 1998.
258. R. B. Wilson. Nonlinear Pricing. Oxford University Press, New York, 1993.
259. W. Xia and Z. Wu. Supplier selection with multiple criteria in volume discount environments. OMEGA, 35(5):494-504, 2007.
260. J. Xu and L. L. Lu. Dynamic lot size model with quantity discount: Counterexamples and correction. Naval Research Logistics, 45(4):419-422, 1998.
261. J. Xu, L. L. Lu, and F. Glover. The deterministic multi-item dynamic lot size problem with joint business volume discount. Annals of Operations Research, 96(1-4):317-337, 2000.
262. P. C. Yang. Pricing strategy for deteriorating items using quantity discount when demand is price sensitive. European Journal of Operational Research, 157(2):389-397, 2004.
263. S. Yang, K.-S. Hong, and C. Lee. Supply chain coordination with stock-dependent demand rate and credit incentives. International Journal of Production Economics, 157(Nov.):105-111, 2014.
264. P.-S. You. A heuristic approach for multiple item and location ordering problem with quantity discount and capacity constraint. Journal of the Operational Research Society, 56(3):307-316, 2005.
265. G. Zhang. The multi-product newsboy problem with supplier quantity discounts and a budget constraint. European Journal of Operational Research, 206(2):350-360, 2010.
266. G. Zhang and L. Ma. Optimal acquisition policy with quantity discounts and uncertain demands. International Journal of Production Research, 47(9):2409-2425, 2009.
267. J.-L. Zhang and J. Chen. Supplier selection and procurement decisions with uncertain demand, fixed selection costs and quantity discounts. Computers and Operations Research, 40(11):2703-2710, 2013.
268. Y.-W. Zhou. 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, 2007.
269. Y.-W. Zhou, J. Min, and S. K. Goyal. Supply-chain coordination under an inventory-level-dependent demand rate. International Journal of Production Economics, 113(2):518-527, 2008.