# American Institute of Mathematical Sciences

January  2009, 5(1): 81-94. doi: 10.3934/jimo.2009.5.81

## Analysis of bullwhip effect in supply chains with heterogeneous decision models

 1 Department of Applied Mathematics, The Hong Kong Polytechnic University, Hunghom, Hong Kong, China 2 Department of Mathematics, Sun Yat-sen University, Guangzhou, China 3 Department of Industrial and Manufacturing Systems Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, China

Received  March 2008 Revised  October 2008 Published  December 2008

In modeling a supply chain, it is often assumed that agents of different echelons adopt similar inventory policies. As a result, bullwhip effect exists across different echelons up the supply chain when the product demand at the retailer level increases and decreases. However, a retailer and a manufacturer are two very different entities in a supply chain, which should employ different decision processes in managing their operations. In view of this, we study the application of heterogeneous decision models for retailers and manufacturers to analyze the bullwhip effect in a supply chain. In particular, we formulate a simple supply chain consisting of many retailers, a manufacturer and a warehouse. The inventory policy of the retailers is simply to use the inventory position to absorb variations in the demand. For the manufacturer, the demand can be met by keeping a higher inventory level or by varying the production rate more frequently. A multi-criteria objective function is formulated and analytic solutions are derived. We illustrate how the bullwhip effect varies for different selections of scaling parameters. By using optimal control theory, we show that the bullwhip effect can be suppressed if a smooth production requirement is enforced.
Citation: K. F. C. Yiu, L. L. Xie, K. L. Mak. Analysis of bullwhip effect in supply chains with heterogeneous decision models. Journal of Industrial & Management Optimization, 2009, 5 (1) : 81-94. doi: 10.3934/jimo.2009.5.81
 [1] Yunan Wu, T. C. Edwin Cheng. Classical duality and existence results for a multi-criteria supply-demand network equilibrium model. Journal of Industrial & Management Optimization, 2009, 5 (3) : 615-628. doi: 10.3934/jimo.2009.5.615 [2] Ciro D'Apice, Rosanna Manzo. A fluid dynamic model for supply chains. Networks & Heterogeneous Media, 2006, 1 (3) : 379-398. doi: 10.3934/nhm.2006.1.379 [3] Gabriella Bretti, Ciro D’Apice, Rosanna Manzo, Benedetto Piccoli. A continuum-discrete model for supply chains dynamics. Networks & Heterogeneous Media, 2007, 2 (4) : 661-694. doi: 10.3934/nhm.2007.2.661 [4] Honglei Xu, Peng Sui, Guanglu Zhou, Louis Caccetta. Dampening bullwhip effect of order-up-to inventory strategies via an optimal control method. Numerical Algebra, Control & Optimization, 2013, 3 (4) : 655-664. doi: 10.3934/naco.2013.3.655 [5] Jing Shi, Tiaojun Xiao. Store assistance and coordination of supply chains facing consumer's return. Journal of Industrial & Management Optimization, 2016, 12 (3) : 991-1007. doi: 10.3934/jimo.2016.12.991 [6] Tsan-Ming Choi. Quick response in fashion supply chains with dual information updating. Journal of Industrial & Management Optimization, 2006, 2 (3) : 255-268. doi: 10.3934/jimo.2006.2.255 [7] Juliang Zhang, Jian Chen. Externality of contracts on supply chains with two suppliers and a common retailer. Journal of Industrial & Management Optimization, 2010, 6 (4) : 795-810. doi: 10.3934/jimo.2010.6.795 [8] Masha Shunko, Srinagesh Gavirneni. Role of transfer prices in global supply chains with random demands. Journal of Industrial & Management Optimization, 2007, 3 (1) : 99-117. doi: 10.3934/jimo.2007.3.99 [9] Min Li, Jiahua Zhang, Yifan Xu, Wei Wang. Effect of disruption risk on a supply chain with price-dependent demand. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-21. doi: 10.3934/jimo.2019095 [10] Ciro D'Apice, Peter I. Kogut, Rosanna Manzo. On relaxation of state constrained optimal control problem for a PDE-ODE model of supply chains. Networks & Heterogeneous Media, 2014, 9 (3) : 501-518. doi: 10.3934/nhm.2014.9.501 [11] K. F. Cedric Yiu, S. Y. Wang, K. L. Mak. Optimal portfolios under a value-at-risk constraint with applications to inventory control in supply chains. Journal of Industrial & Management Optimization, 2008, 4 (1) : 81-94. doi: 10.3934/jimo.2008.4.81 [12] Jason Chao-Hsien Pan, Ku-Kuang Chang, Yu-Cheng Hsiao. Optimal inventory policies for serial-type and assembly-type supply chains with equal sized batch. Journal of Industrial & Management Optimization, 2015, 11 (3) : 1021-1040. doi: 10.3934/jimo.2015.11.1021 [13] Benyong Hu, Xu Chen, Felix T. S. Chan, Chao Meng. Portfolio procurement policies for budget-constrained supply chains with option contracts and external financing. Journal of Industrial & Management Optimization, 2018, 14 (3) : 1105-1122. doi: 10.3934/jimo.2018001 [14] Xueyong Wang, Yiju Wang, Gang Wang. An accelerated augmented Lagrangian method for multi-criteria optimization problem. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-9. doi: 10.3934/jimo.2018136 [15] Katherinne Salas Navarro, Jaime Acevedo Chedid, Whady F. Florez, Holman Ospina Mateus, Leopoldo Eduardo Cárdenas-Barrón, Shib Sankar Sana. A collaborative EPQ inventory model for a three-echelon supply chain with multiple products considering the effect of marketing effort on demand. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-14. doi: 10.3934/jimo.2019020 [16] Ata Allah Taleizadeh, Leopoldo Eduardo Cárdenas-Barrón, Roya Sohani. Coordinating the supplier-retailer supply chain under noise effect with bundling and inventory strategies. Journal of Industrial & Management Optimization, 2019, 15 (4) : 1701-1727. doi: 10.3934/jimo.2018118 [17] P. C. Jha, Sugandha Aggarwal, Anshu Gupta, Ruhul Sarker. Multi-criteria media mix decision model for advertising a single product with segment specific and mass media. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1367-1389. doi: 10.3934/jimo.2016.12.1367 [18] Ming-Jong Yao, Tien-Cheng Hsu. An efficient search algorithm for obtaining the optimal replenishment strategies in multi-stage just-in-time supply chain systems. Journal of Industrial & Management Optimization, 2009, 5 (1) : 11-32. doi: 10.3934/jimo.2009.5.11 [19] T.C. Edwin Cheng, Yunan Wu. Henig efficiency of a multi-criterion supply-demand network equilibrium model. Journal of Industrial & Management Optimization, 2006, 2 (3) : 269-286. doi: 10.3934/jimo.2006.2.269 [20] Kar Hung Wong, Yu Chung Eugene Lee, Heung Wing Joseph Lee, Chi Kin Chan. Optimal production schedule in a single-supplier multi-manufacturer supply chain involving time delays in both levels. Journal of Industrial & Management Optimization, 2018, 14 (3) : 877-894. doi: 10.3934/jimo.2017080

2018 Impact Factor: 1.025