The bullwhip effect: Progress, trends and directions

European Journal of Operational Research

Volumn 250, Issue 3, 2016, Pages 691-701

  Wang, Xun ^a   Disney, Stephen M ^a  

^a CARDIFF UNIVERSITY   (United Kingdom)

Author keywords

Bullwhip effect; Literature review; Supply chain management

Indexed keywords

OPERATIONS RESEARCH;

ANALYTICAL METHODOLOGY; BULLWHIP EFFECTS; COORDINATION STRATEGY; EXPERIMENTAL RESEARCH; FUTURE RESEARCH DIRECTIONS; LITERATURE REVIEWS; REPLENISHMENT POLICY; SUPPLY CHAIN STRUCTURES;

SUPPLY CHAIN MANAGEMENT;

EID: 84938153931     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ejor.2015.07.022     Document Type: Review

References (168)

1. Adenso-Díaz B., Moreno P., Gutiérrez E., Lozano S. An analysis of the main factors affecting bullwhip in reverse supply chains International Journal of Production Economics 135 2 2012 917 928
2. Agrawal S., Sengupta R.N., Shanker K. Impact of information sharing and lead time on bullwhip effect and on hand inventory European Journal of Operational Research 192 2 2009 576 593
3. Akkermans H., Vos B. Amplification in service supply chains: an exploratory case study from the telecom industry Production and Operations Management 12 2003 204 223
4. Akkermans H., Voss C. The service bullwhip effect International Journal of Operations & Production Management 33 6 2013 765 788
5. Allen D.S. Seasonal production smoothing Federal Reserve Bank of St. Louis Review 81 5 1999 21 40
6. Alwan L.C., Liu J.J., Yao D.-Q. Stochastic characterization of upstream demand processes in a supply chain IIE Transactions 35 2003 207 219
7. Ali M.M., Boylan J.E. On the effect of non-optimal forecasting methods on supply chain downstream demand IMA Journal of Management Mathematics 23 2012 81 98
8. Ancarani A., Di Mauro C., D'Urso D. A human experiment on inventory decisions under supply uncertainty International Journal of Production Economics 142 1 2013 61 73
9. Anderson E.G. Jr., Morrice D.J. A simulation game for teaching services-oriented supply chain Production and Operations Management 9 1 2000 40 55
10. Anderson E.G., Morrice D.J., Lundeen G. The "physics" of capacity and backlog management in service and custom manufacturing supply chains System Dynamics Review 21 2005 217 247
11. Åström K.J. Introduction to stochastic control theory 1970 Academic Press New York
12. Aviv Y. A time-series framework for supply-chain inventory management Operational Research 51 2 2003 210 227
13. Babai M.Z., Boylan J.E., Syntetos A.A., Ali M.M. Reduction of the value of information sharing as demand becomes strongly auto-correlated International Journal of Production Economics 2015 10.1016/j.ijpe.2015.05.005 in press
14. Baganha M.P., Cohen M.A. The stabilising effect of inventory in supply chains Operations Research 46 3 1998 572 583
15. Balakrishnan A., Geunes J., Pangburn M.S. Coordinating supply chains by controlling upstream variability propagation Manufacturing & Service Operations Management 6 2 2004 163 183
16. Beamon B.M. Supply chain design and analysis: models and methods International Journal of Production Economics 55 1998 281 294
17. Bishop W.S. Volatility of derived demand in industrial markets and its management implications Journal of Marketing 48 4 1984 95 103
18. Blanchard O.J. The production and inventory behavior of the American automobile industry Journal of Political Economy 91 3 1983 365 400
19. Blinder A.S. Can the production smoothing model of inventory behavior be saved? The Quarterly Journal of Economics 101 3 1986 431 454
20. Blinder A.S., Maccini L.J. Taking stock: a critical assessment of recent research on inventories Journal of Economic Perspectives 5 1 1991 73 96
21. Boute R.N., Disney S.M., Lambrecht M.R., Van Houdt B. An integrated production and inventory model to dampen upstream demand variability in the supply chain European Journal of Operational Research 178 1 2007 121 142
22. Boute, R.N., & Van Miegham, J.A. (2015). Global dual sourcing and order smoothing: The impact of capacity and leadtimes. Management Science, 61(9), 2080-2099. http://dx.doi.org/10.1287/mnsc.2014.1992.
23. Box G.E.P., Jenkins G.M. Time series analysis, forecasting and control 1970 Holden-Day San Francisco
24. Bray R.L., Mendelson H. Information transmission and the bullwhip effect: an empirical investigation Management Science 58 5 2012 860 875
25. Bray R.L., Mendelson H. Production smoothing and the bullwhip effect Manufacturing and Service Operations Management 17 2 2015 208 220
26. Burbidge J.L. The new approach to production Production Engineer 40 12 1961 769 784
27. Cachon G.P. Managing supply chain demand variability with scheduled ordering policies Management Science 45 6 1999 843 856
28. Cachon G.P., Lariviere M.A. An equilibrium analysis of linear, proportional and uniform allocation of scarce capacity IIE Transactions 31 1999 835 849
29. Cachon G.P., Lariviere M.A. Capacity choice and allocation: strategic behavior and supply chain performance Management Science 45 8 1999 1091 1108
30. Cachon G.P., Lariviere M.A. Capacity allocation using past sales: when to turn-and-earn Management Science 45 5 1999 685 703
31. Cachon G.P., Randall T., Schmidt G.M. In search of the bullwhip effect Manufacturing & Service Operations Management 9 4 2007 457 479
32. Cannella S., Ciancimino E. On the bullwhip avoidance phase: supply chain collaboration and order smoothing International Journal of Production Research 48 22 2010 6739 6776
33. Cantor D.E., Katok E. Production smoothing in a serial supply chain: a laboratory investigation Transportation Research Part E 48 4 2012 781 794
34. Caplin A.S. The variability of aggregate demand with (S,s) inventory policies Econometrica 53 6 1985 1395 1409
35. Chatfield D.C., Kim J.G., Harrison T.P. The bullwhip effect - impact of stochastic lead time, information quality, and information sharing: a simulation study Production and Operations Management 13 4 2004 340 353
36. Chatfield D.C. Underestimating the bullwhip effect: a simulation study of the decomposability assumption International Journal of Production Research 51 1 2013 230 244
37. Chen L., Lee H.L. Information sharing and order variability control under a generalized demand model Management Science 55 5 2009 781 797
38. Chen L., Lee H.L. Bullwhip effect measurement and its implications Operations Research 60 2012 771 784
39. Chen T.-K., Liao H.-H., Kuo H.-J. Internal liquidity risk, financial bullwhip effects, and corporate bond yield spreads: supply chain perspectives Journal of Banking & Finance 37 7 2013 2434 2456
40. Chen F., Dresner Z., Ryan J.K., Simchi-Levi D. Quantifying the bullwhip effect in a simple supply chain: the impact of forecasting, lead times, and information Management Science 46 3 2000 436 443
41. Chen F., Ryan J.K., Simchi-Levi D. The impact of exponential smoothing forecasts on the bullwhip effect Naval Research Logistics 47 2000 269 286
42. Chen F., Samroengraja R. Order volatility and supply chain costs Operations Research 52 5 2004 707 722
43. Chen F., Li J., Zhang H. Managing downstream competition via capacity allocation Production and Operations Management 22 2 2013 426 446
44. Chen Y.F., Disney S.M. The myopic order-up-to policy with a feedback controller International Journal of Production Research 45 2 2007 351 368
45. Cho S.-H., Tang C.S. Technical note - capacity allocation under retail competition: uniform and competitive allocations Operations Research 62 1 2014 72 80
46. Clark J.M. Business acceleration and the law of demand: a technical factor in economic cycles Journal of Political Economy 25 3 1917 217 235
47. Clark A.J., Scarf H.E. Optimal policies for a multi-echelon inventory problem Management Science 6 4 1960 475 490
48. Croson R., Donohue K. Upstream versus downstream information and its impact on the bullwhip effect System Dynamics Review 21 2005 249 260
49. Croson R., Donohue K. Behavioral causes of the bullwhip effect and the observed value of inventory information Management Science 52 3 2006 323 336
50. Croson R., Donohue K., Katok E., Sterman J. Order stability in supply chains: coordination risk and the role of coordination stock Production and Operations Management 23 2 2014 176 196
51. Dejonckheere J., Disney S.M., Lambrecht M.R., Towill D.R. Measuring and avoiding the bullwhip effect: a control theoretic approach European Journal of Operational Research 147 3 2003 567 590
52. Dejonckheere J., Disney S.M., Lambrecht M.R., Towill D.R. The impact of information enrichment on the bullwhip effect in supply chains: a control engineering perspective European Journal of Operational Research 153 3 2004 727 750
53. Delhoum S., Scholz-Reiter B. The influence of decision patterns of inventory control on the bullwhip effect based on a simulation game of a production network Production Planning & Control 20 8 2009 666 677
54. Deziel D.P., Eilon S. A linear production-inventory control rule Production Engineer 43 1967 93 104
55. Disney S.M., Towill D.R. The effect of vendor managed inventory (VMI) dynamics on the bullwhip effect in supply chains International Journal of Production Economics 85 2003 199 215
56. Disney S.M., Towill D.R., van de Velde W. Variance amplification and the golden ratio in production and inventory control International Journal of Production Economics 90 2004 295 309
57. Disney S.M., Lambrecht M., Towill D.R., Van de Velde W. The value of coordination in a two echelon supply chain: sharing information, policies and parameters IIE Transactions 40 3 2008 341 355
58. Dong Y., Dresner M., Yao Y. Beyond information sharing: an empirical analysis of vendor-managed inventory Production and Operations Management 23 2014 817 828
59. Dominiguez R., Framinan J.M., Cannella S. Serial vs. Divergent supply chain networks: a comparative analysis of the bullwhip effect International Journal of Production Research 52 7 2014 2194 2210
60. Dooley K.J., Yan T., Mohan S., Gopalakrishnan M. Inventory management and the bullwhip effect during the 2007-2009 recession: evidence from the manufacturing sector Journal of Supply Chain Management 46 1 2010 12 18
61. Duc T.T.H., Luong H.T., Kim Y.D. A measure of bullwhip effect in supply chains with a mixed autoregressive-moving average demand process European Journal of Operational Research 187 2008 243 256
62. Duc T.T.H., Luong H.T., Kim Y.D. A measure of the bullwhip effect in supply chains with stochastic lead time International Journal of Advanced Manufacturing Technology 38 2008 1201 1212
63. Fair N.C. The production-smoothing model is alive and well Journal of Monetary Economics 24 3 1989 363 370
64. Flores B., Olson D., Pearce S. Use of cost and accuracy measures in forecasting method selection: a physical distribution example International Journal of Production Research 31 1993 139 160
65. Forrester J. Industrial dynamics 1961 MIT Press Cambridge, MA
66. Gaalman G. Optimal aggregation of multi-item production smoothing models Management Science 24 16 1978 1733 1739
67. Gaalman G. Bullwhip reduction for ARMA demand: The proportional order-up-to policy versus the full-state-feedback policy Automatica 42 2006 1283 1290
68. Gaalman G., Disney S.M. State space investigation of bullwhip with ARMA(1,1) demand processes International Journal of Production Economics 104 2 2006 327 339
69. Gaalman G., Disney S.M. On bullwhip in a family of order-up-to policies with ARMA(2,2) demand and arbitrary lead-times International Journal of Production Economics 121 2 2009 454 463
70. Gaalman G., Disney S.M. Bullwhip behavior in the order-up-to policy with ARIMA demand 4th World Conference on Production & Operations Management 2012 Amsterdam
71. Gaur V., Giloni A., Seshadri S. Information sharing in a supply chain under ARMA demand Management Science 51 6 2005 961 969
72. Gavirneni S. Price fluctuations, information sharing, and supply chain performance European Journal of Operational Research 174 2006 1651 1663
73. Ghali M.A. Inventories, production smoothing, and the accelerator: some empirical evidence The Quarterly Journal of Economics 88 1 1974 149 157
74. Ghali M.A. Seasonality, aggregation and the testing of the production smoothing hypothesis American Economic Review 77 3 1987 464 469
75. Ghali M.A. Production-planning horizon, production smoothing, and convexity of the cost functions International Journal of Production Economics 81-82 2003 67 74
76. Geary S., Disney S.M., Towill D.R. On bullwhip in the supply chain - historical review, present practice and expected likely impact International Journal of Production Economics 101 1 2006 2 18
77. Giard V., Sali M. The bullwhip effect in supply chains: a study of contingent and incomplete literature International Journal of Production Research 51 13 2013 3880 3893
78. Gilbert K. An ARIMA supply chain model Management Science 51 2 2005 305 310
79. Govindan K., Soleimani H., Kannan D. Reverse logistics and closed-loop supply chain: a comprehensive review to explore the future European Journal of Operational Research 240 3 2014 603 626
80. Graves S.C., Kletter D.B., Hetzel W.B. A dynamic model for requirement planning with application to supply chain optimization Operations Research 46 1998 S35 S49
81. Graves S.C. A single-item inventory model for a nonstationary demand process Manufacturing & Service Operations Management 1 1 1999 50 61
82. Hamister J.W., Suresh N.C. The impact of pricing policy on sales variability in a supermarket retail context International Journal of Production Economics 111 2 2008 441 455
83. Hammond J.H. Case Barilla Spa N9-694-046 1994 Harvard Business School Publishing Boston
84. Haughton M.A. Distortional bullwhip effects on carriers Transportation Research Part E 45 2009 172 185
85. Hicks J.R. A contribution to the theory of the trade cycle 1950 Clarendon Press Oxford
86. Holland W., Sodhi M.S. Quantifying the effect of batch size and order errors on the bullwhip effect using simulation International Journal of Logistics Research and Applications 7 3 2004 251 261
87. Holt C.C., Modigliani F., Muth J., Simon H. Planning production, inventories and the work force 1960 Prentice-Hall NJ
88. Hosoda T., Disney S.M. On variance amplification in a three-echelon supply chain with minimum mean square error forecasting Omega 34 4 2006 344 358
89. Hosoda T., Disney S.M. The governing dynamics of supply chains: the impact of altruistic behavior Automatica 42 4 2006 1301 1309
90. Hosoda T., Disney S.M. Impact of market demand mis-specification on a two-level supply chain International Journal of Production Economics 121 2 2009 739 751
91. Hosoda T., Disney S.M. On the replenishment policy when the market demand information is lagged International Journal of Production Economics 135 1 2012 458 467
92. Hosoda T., Disney S.M., Gavirneni N. The impact of information sharing, random yield, correlation and lead times in closed loop supply chains European Journal of Operational Research 246 2015 827 836
93. Hwarng H.B., Xie N. Understanding supply chain dynamics: a chaos perspective European Journal of Operational Research 184 2008 1163 1178
94. Hussain M., Drake P.R. Analysis of the bullwhip effect with order batching in multi-echelon supply chains International Journal of Physical Distribution & Logistics Management 41 10 2011 972 990
95. Hussain M., Shome A., Lee D.M. Impact of forecasting methods on variance ratio in order-up-to level policy International Journal of Advanced Manufacturing Technology 59 1 - 4 2012 413 420
96. Jakšič M., Rusjan B. The effect of replenishment policies on the bullwhip effect: a transfer function approach European Journal of Operational Research 184 3 2008 946 961
97. John S., Naim M.M., Towill D.R. Dynamic analysis of a WIP compensated decision support system International Journal of Manufacturing Systems Design 1 4 1994 283 297
98. Kahn J.A. Why is production more volatile than sales? Theory and evidence on the stockout-avoidance motive for inventory-holding The Quarterly Journal of Economics 107 2 1992 481 510
99. Kelle P., Milne A. The effect of (s,S) ordering policy on the supply chain International Journal of Production Economics 59 1-3 1999 113 122
100. Kim J.G., Chatfield D., Harrison T.P., Hayya J.C. Quantifying the bullwhip effect in a supply chain with stochastic lead time European Journal of Operational Research 173 2006 617 636
101. Krane S.D., Braun S.N. Production smoothing evidence from physical-product data Journal of Political Economy 99 3 1991 558 581
102. Lai, R.K. (2005). Bullwhip in a Spanish shop. Harvard NOM Working Paper No. 06-06.
103. Lee H.L., Padmanabhan V., Whang S. Information distortion in a supply chain: the bullwhip effect Management Science 43 4 1997 546 558
104. Lee H.L., So K.C., Tang C.S. The value of information sharing in a two-level supply chain Management Science 46 5 2000 626 643
105. Lee H.L., Whang S. Information sharing in a supply chain International Journal of Technology Management 20 3/4 2000 373 387
106. Lee S.-Y., Klassen R.D., Furlan A., Vinelli A. The green bullwhip effect: transferring environmental requirements along a supply chain International Journal of Production Economics 156 2014 39 51
107. Li Q., Disney S.M., Gaalman G. Avoiding the bullwhip effect using Damped Trend forecasting and the Order-Up-To replenishment policy International Journal of Production Economics 149 2014 3 16
108. Sridharan Li.X.V. Characterizing order processes of using (r, nQ) inventory policies in supply chains Omega 36 6 2008 1096 1104
109. Lin P.-H., Wong D.S.-H., Jang S.-S., Shieh S.-S., Chu J.-Z. Controller design and reduction of bullwhip for a model supply chain system using z-transform analysis Journal of Process Control 14 5 2004 487 499
110. Liu Z. Equilibrium analysis of capacity allocation with demand competition Naval Research Logistics 59 2012 254 265
111. Luong H.T. Measure of bullwhip effect in supply chains with autoregressive demand process European Journal of Operational Research 180 2007 1086 1097
112. Luong H.T., Pien N.H. Measure of bullwhip effect in supply chains: the case of high order autoregressive demand process European Journal of Operational Research 183 2007 197 209
113. Ma Y., Wang N., Che A., Huang Y., Xu J. The bullwhip effect under different information-sharing settings: a perspective on price-sensitive demand that incorporates price dynamics International Journal of Production Research 51 10 2013 3085 3116
114. Magee J.F. Guides to inventory policy Harvard Business Review 34 2 1956 103 116
115. Milne A. The production smoothing model of inventory revisited The Economic Journal 104 423 1994 399 407
116. Min H., Zhou G. Supply chain modelling: Past, present and future Computers & Industrial Engineering 43 2002 231 249
117. Miron J., Zeldes S. Seasonality, cost shocks, and the production smoothing model of inventories Econometrica 56 4 1988 877 908
118. Mitchell W.C. Business Cycles 1913 University of California Press Berkeley
119. Miragliotta G. Layers and mechanisms: a new taxonomy for the bullwhip effect International Journal of Production Economics 104 2006 365 381
120. Miyaoka J., Hausman W. How a base stock policy using "stale" forecasts provides supply chain benefits Manufacturing & Service Operations Management 6 2 2004 149 162
121. Mollick A.V. Production smoothing in the Japanese vehicle industry International Journal of Production Economics 91 2004 63 74
122. Mosekilde E., Larsen E.R. Deterministic chaos in the beer production distribution model System Dynamics Review 4 1988 131 147
123. Nienhaus J., Ziegenbein A., Schoensleben P. How human behaviour amplifies the bullwhip effect - a study based on the beer distribution game online Production Planning & Control 17 6 2006 547 557
124. Noblesse A.M., Boute R.N., Lambrecht M.R., van Houdt B. Characterizing order processes of continuous review (s,S) and (r,nQ) policies European Journal of Operational Research 236 2014 534 547
125. Ohno T. Toyota production system: beyond large-scale production 1988 Productivity Press Portland, Oregon
126. Ouyang Y., Daganzo C. Counteracting the bullwhip effect with decentralized negotiations and advance demand information Physica A 363 1 2006 14 23
127. Ouyang Y. The effect of information sharing on supply chain stability and the bullwhip effect European Journal of Operational Research 182 3 2007 1107 1121
128. Ouyang Y., Li X. The bullwhip effect in supply networks European Journal of Operational Research 201 3 2010 799 810
129. Özelkan E.C., Çakanyildirim M. Reverse bullwhip effect in pricing European Journal of Operational Research 192 1 2009 302 312
130. Papanagnou C.I., Halikias G.D. Supply-chain modelling and control under proportional inventory-replenishment policies International Journal of Systems Science 39 7 2008 699 711
131. Potter A., Disney S.M. Bullwhip and batching: an exploration International Journal on Production Economics 104 2 2006 408 418
132. Raghunathan S. Information sharing in a supply chain: a note on its value when demand is nonstationary Management Science 47 4 2001 605 610
133. Ramey V.A. Nonconvex costs and the behavior of inventories Journal of Political Economy 99 2 1991 306 334
134. Sahin R., Robinson E.P. Flow coordination and information sharing in supply chains: review, implications, and directions for future research Decision Sciences 33 4 2002 505 536
135. Samuelson P.A. A synthesis of the principle of acceleration and the multiplier Journal of Political Economy 47 6 1939 786 797
136. Sarimveis H., Patrinos P., Tarantilis C.D., Kiranoudis C.T. Dynamic modelling and control of supply chain systems: a review Computers & Operations Research 35 11 2008 3530 3561
137. Schisgall O. Eyes on tomorrow: the evolution of Procter & Gamble 1981 J.G. Ferguson New York
138. Schneeweiss C.A. Optimal production smoothing and safety inventory Management Science 20 7 1974 1122 1130
139. Sethi S.P., Thompson G.L. Optimal control theory: applications to management science and economics Second Edition 2000 Norwell, Massachusetts, USA
140. Shan J., Yang S., Yang S., Zhang J. An empirical study of the bullwhip effect in China Production and Operations Management 23 2014 537 551
141. So K.C., Zheng X. Impact of supplier's lead time and forecast demand updating on retailer's order quantity variability in a two-level supply chain International Journal of Production Economics 86 2003 169 179
142. Sodhi M.S., Tang C.S. The incremental bullwhip effect of operational deviations in an arborescent supply chain with requirements planning European Journal of Operational Research 215 2011 374 382
143. Sodhi M.S., Sodhi N.S., Tang C.S. An EOQ model for MRO customers under stochastic price to quantify bullwhip effect for the manufacturer International Journal of Production Economics 155 2014 132 142
144. Steckel J.H., Gupta S., Banerji A. Supply chain decision making: will shorter cycle times and shared point-of-sale information necessarily help? Management Science 50 4 2004 458 464
145. Sterman J.D. Modeling managerial behavior: misperceptions of feedback in a dynamic decision making experiment Management Science 34 3 1989 321 339
146. Su Y., Geunes J. Price promotions, operations cost, and profit in a two-stage supply chain Omega 40 2012 891 905
147. Sucky E. The bullwhip effect in supply chains - An overestimated problem? International Journal of Production Economics 118 2009 311 322
148. Tang O., Naim M.M. The impact of information transparency on the dynamic behaviour of a hybrid manufacturing/remanufacturing system International Journal of Production Research 42 19 2004 4135 4152
149. Tangsucheeva R., Prabhu V. Modeling and analysis of cash-flow bullwhip in supply chain International Journal of Production Economics 145 2013 431 447
150. Taylor D.H. Measurement and analysis of demand amplification across the supply chain International Journal of Logistics Management 10 1999 55 70
151. Towill D.R. Dynamic analysis of an inventory and order based production control system International Journal of Production Research 20 6 1982 671 687
152. Towill D.R., Zhou L., Disney S.M. Reducing the bullwhip effect: looking through the appropriate lens International Journal of Production Economics 108 2007 444 453
153. Vaile R.D., Grether E.T., Cox R. Marketing in the American economy 1952 Ronald New York
154. Wang H.-J. Nominal data and the production smoothing hypothesis Economics Letters 76 2002 245 250
155. Wang X., Disney S.M., Wang J. Stability analysis of constrained inventory systems with transportation delay European Journal of Operational Research 223 1 2012 86 95
156. Wang X., Disney S.M., Wang J. Exploring the oscillatory dynamics of a forbidden returns inventory system International Journal of Production Economics 147 2014 3 12
157. Wangphanich P., Kara S., Kayis B. Analysis of the bullwhip effect in multi-product, multi-stage supply chain systems - a simulation approach International Journal of Production Research 48 15 2010 4501 4517
158. West K.D. A variance bounds test of the linear quadratic inventory model Journal of Political Economy 94 2 1986 374 401
159. Wright D., Yuan X. Mitigating the bullwhip effect by ordering policies and forecasting methods International Journal of Production Economics 113 2 2008 587 597
160. Wu Y.D., Katok E. Learning, communication, and the bullwhip effect Journal of Operations Management 24 6 2006 839 850
161. Xu K., Dong Y., Evers P.T. Towards better coordination of the supply chain Transportation Research Part E 37 1 2001 35 54
162. Yao Y., Zhu K.X. Do electronic linkages reduce the bullwhip effect? An empirical analysis of the U.S. Manufacturing supply chains Information Systems Research 23 3 2012 1042 1055
163. Zangwill W.I. Production smoothing of economic lot sizes with non-decreasing requirements Management Science 13 3 1966 191 209
164. Zhang X. The impact of forecasting methods on the bullwhip effect International Journal of Production Economics 88 2004 15 27
165. Zhang X. Evolution of ARMA demand in supply chains Manufacturing & Service Operations Management 6 2 2004 195 198
166. Zhang X. Delayed demand information and dampened bullwhip effect Operations Research Letters 33 2005 289 294
167. Zhang X., Burke G.J. Analysis of compound bullwhip effect causes European Journal of Operational Research 210 2011 514 526
168. Zhou L., Disney S.M. Bullwhip and inventory variance in a closed loop supply chain OR Spectrum 28 1 2006 127 149