Particle swarm optimization for bi-level pricing problems in supply chains. (English) Zbl 1230.90179

Summary: With rapid technological innovation and strong competition in hi-tech industries such as computer and communication organizations, the upstream component price and the downstream product cost usually decline significantly with time. As a result, an effective pricing supply chain model is very important. This paper first establishes two bi-level pricing models for pricing problems with the buyer and the vendor in a supply chain designated as the leader and the follower, respectively. A particle swarm optimization (PSO) based algorithm is developed to solve problems defined by these bi-level pricing models. Experiments illustrate that this PSO based algorithm can achieve a profit increase for buyers or vendors if they are treated as the leaders under some situations, compared with the existing methods.


90C30 Nonlinear programming
91B24 Microeconomic theory (price theory and economic markets)
90C59 Approximation methods and heuristics in mathematical programming
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[1] Yang P.C., Wee H.M., Yu J.: Collaborative pricing and replenishment policy for hi-tech industry. J. Oper. Res. Soc. 58, 894–909 (2007) · Zbl 1178.90173
[2] Sern, L.C.: Present and future of supply chain in information and electronic industry. Supply Chain Management Conference for Electronic Industry, pp. 6–27 (2003)
[3] Lev B., Weiss H.: Inventory models with cost changes. Oper. Res. 38, 53–63 (1990) · Zbl 0715.90042
[4] Goyal S.K.: A note on inventory models with cost changes. Oper. Res. 40, 414–415 (1992) · Zbl 0825.90343
[5] Gascon A.: On the finite horizon eoq model with cost changes. Oper. Res. 43, 716–717 (1995) · Zbl 0860.90048
[6] Buzacott J.A.: Economic order quantities with inflation. Oper. Res. 26, 553–558 (1975)
[7] Erel E.: The effect of continuous price change in the eoq. Omega 20, 523–527 (1992)
[8] Yang P.C., Wee H.M.: A quick response production strategy to market demand. Prod. Plan. Control 12, 326–334 (2001)
[9] Khouja M., Park S.: Optimal lot sizing under continuous price decrease. Omega 31, 539–545 (2003)
[10] Tsoukalas A., Rustem B., Pistikopoulos E.N.: A global optimization algorithm for generalized semi-infinite, continuous minimax with coupled constraints and bi-level problems. J. Glob. Optim. 44, 235–250 (2009) · Zbl 1178.90329
[11] Lu J., Shi C., Zhang G.: On bilevel multi-follower decision making: general framework and solutions. Inf. Sci. 176, 1607–1627 (2006) · Zbl 1086.90032
[12] Panagiotopoulos P.D., Mistakidis E.S., Stavroulakis G.E., Panagouli O.K.: Multilevel optimization methods in mechanics. In: Migdalas, A., Pardalos, P.M., Varbrand, P. (eds) Multilevel Optimization: Algorithms and Applications, pp. 51–90. Kluwer Academic Publishers, Dordrecht (1997) · Zbl 0896.90177
[13] Yu H., Dang C., Wang S.: Game theoretical analysis of buy-it-now price Auctions. Int. J. Inf. Technol. Decis. Mak. 5, 557–581 (2006)
[14] Hobbs B.F., Metzler B., Pang J.S.: Strategic gaming analysis for electric power system: an mpec approach. IEEE Trans. Power Syst. 15, 637–645 (2000)
[15] Zhang G., Lu J.: Model and approach of fuzzy bilevel decision making for logistics planning problem. J. Enterp. Inf. Manag. 20, 178–197 (2007)
[16] Fortuny-Amat J., McCarl B.: A representation and economic interpretation of a two-level programming problem. J. Oper. Res. Soc. 32, 783–792 (1981) · Zbl 0459.90067
[17] Feng C., Wen C.: Bi-level and multi-objective model to control traffic flow into the disaster area post earthquake. J. East. Asia Soc. Transp. Stud. 6, 4253–4268 (2005)
[18] Gao, Y., Zhang, G., Lu, J., Gao, S.: A bilevel model for railway train set organizing optimization. 2007 International Conference on Intelligent Systems and Knowledge Engineering (ISKE2007), pp. 777–782 (2007)
[19] Chinchuluun A., Pardalos P.M., Huang H-X.: Multilevel (Hierarchical) optimization: complexity issues, optimality conditions, algorithms. In: Gao, D., Sherali, H. (eds) Advances in Applied Mathematics and Global Optimization, pp. 197–221. Springer, Berlin (2009) · Zbl 1193.49035
[20] White D.J., Anandalinga G.: A penalty function approach for solving bi-level linear programs. J. Glob. Optim. 3, 397–419 (1993) · Zbl 0791.90047
[21] Wen U.P., Hsu S.T.: Linear bilevel programming problems-a review. J. Oper. Res. Soc. 42, 123–133 (1991)
[22] Bard J.: Practical bilevel optimization. Kluwer Academic Publishers, Dordrecht, The Netherlands (1998) · Zbl 0943.90078
[23] Lu J., Zhang G., Dillon T.: Fuzzy multi-objective bilevel decision making by an approximation kth-best approach. Multi-Valued Log. Soft Comput. 14, 205–232 (2007) · Zbl 1236.90115
[24] Calvete H.I., Gale C., Mateo P.M.: A new approach for solving linear bilevel problems using genetic algorithms. Eur. J. Oper. Res. 188, 14–28 (2008) · Zbl 1135.90023
[25] Zhang, G., Zhang G., Gao, Y., Lu, J.: Competitive strategic bidding optimization in electricity markets using bi-level programming and swarm technique. Accepted by IEEE Transactions on Industrial Electronics. (2009)
[26] Zhang G., Lu J.: Fuzzy bilevel programming with multiple objectives and cooperative multiple followers. J. Glob. Optim. 47, 403–419 (2010) · Zbl 1222.90058
[27] Gao, Y., Zhang, G., Lu, J.: A {\(\lambda\)}-cut and goal programming based algorithm for fuzzy linear multiple objective bi-level optimization. Accepted by IEEE Transactions on Fuzzy Systems (2009)
[28] Lu H., Chen W.: Self-adaptive velocity particle swarm optimization for solving constrained optimization problems. J. Glob. Optim. 41, 427–445 (2008) · Zbl 1152.90670
[29] Jiang Y., Hu T., Huang C., Wu X.: An improved particle swarm optimization algorithm. Appl. Math. Comput. 193, 231–239 (2007) · Zbl 1193.90220
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