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A particle swarm optimization for solving joint pricing and lot-sizing problem with fluctuating demand and unit purchasing cost. (English) Zbl 1205.90030
Summary: We extend the classical economic order quantity model to allow for not only a function of price-dependent and time-varying demand but also fluctuating unit purchasing cost. The joint replenishment problem is subject to continuous decay and a general partial backlogging rate. The objective is to find the optimal replenishment number, time scheduling and periodic selling price to maximize the discounted total profit. An effective search procedure is provided to find the optimal solution by employing the properties derived in this paper and particle swarm optimization algorithm. Several numerical examples are used to illustrate the features of the proposed model.

MSC:
 90B05 Inventory, storage, reservoirs 90C59 Approximation methods and heuristics in mathematical programming 90B06 Transportation, logistics and supply chain management 91B38 Production theory, theory of the firm
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 [1] Ghare, P.M.; Schrader, G.H., A model for exponentially decaying inventory system, International journal of production research, 14, 238-243, (1963) [2] Wu, K.S.; Ouyang, L.Y.; Yang, C.T., An optimal replenishment policy for non-instantaneous deteriorating items with stock-dependent demand and partial backlogging, International journal of production economics, 101, 369-384, (2006) [3] Huang, J.Y.; Yao, M.J., A new algorithm for optimally determining lot-sizing policies for a deteriorating item in an integrated production-inventory system, Computers & mathematics with applications, 51, 83-104, (2006) · Zbl 1125.90004 [4] Huang, K.N.; Liao, J.J., A simple method to locate the optimal solution for exponentially deteriorating items under trade credit financing, Computers & mathematics with applications, 56, 965-977, (2008) · Zbl 1155.90310 [5] Mishra, S.S.; Mishra, P.P., Price determination for an EOQ model for deteriorating items under perfect competition, Computers & mathematics with applications, 56, 1082-1101, (2008) · Zbl 1155.90313 [6] Maity, K.; Maiti, M., A numerical approach to a multi-objective optimal inventory control problem for deteriorating multi-items under fuzzy inflation and discounting, Computers & mathematics with applications, 55, 1794-1807, (2008) · Zbl 1145.90311 [7] Geetha, K.; Uthayakumar, R., Economic design of an inventory policy for non-instantaneous deteriorating items under permissible delay in payments, Journal of computational and applied mathematics, 233, 2492-2505, (2010) · Zbl 1183.90019 [8] Chang, C.T.; Teng, J.T.; Goyal, S.K., Optimal replenishment policies for non-instantaneous deteriorating items with stock-dependent demand, International journal of production economics, 123, 62-68, (2010) [9] Goyal, S.K.; Giri, B.C., Recent trends in modeling of deteriorating inventory, European journal of operational research, 134, 1-16, (2001) · Zbl 0978.90004 [10] Chen, K.C.; Liao, C.; Weng, T.C., Optimal replenishment policies for the case of a demand function with product-life-cycle shape in a finite planning horizon, Expert systems with applications, 32, 65-76, (2007) [11] Chen, C.K.; Hung, T.W.; Weng, T.C., A net present value approach in developing optimal replenishment policies for a product life cycle, Applied mathematics and computation, 184, 360-373, (2007) · Zbl 1162.90305 [12] Chen, C.K.; Hung, T.W.; Weng, T.C., Optimal replenishment policies with allowable shortages for a product life cycle, Computers & mathematics with applications, 53, 1582-1594, (2007) · Zbl 1152.90305 [13] Lee, H.L.; Padmanabhan, V.; Taylor, T.A.; Whang, S., Price protection in the personal computer industry, Management science, 46, 467-482, (2000) [14] Khouja, M.; Park, S., Optimal lot sizing under continuous price decrease, Omega: the international journal of management science, 31, 539-545, (2003) [15] Teunter, R., A note on khouja and park, optimal lot sizing under continuous price decrease. omega 31 (2003), Omega: the international journal of management science, 33, 467-471, (2005) [16] Khouja, M.; Goyal, S., Single item optimal lot sizing under continuous unit cost decrease, International journal of production economics, 102, 87-94, (2006) [17] Khouja, M.; Park, S.; Saydam, C., Joint replenishment problem under continuous unit cost change, International journal of production research, 43, 311-326, (2005) · Zbl 1060.90578 [18] Teng, J.T.; Yang, H.L., Deterministic economic order quantity models with partial backlogging when demand and cost are fluctuating with time, Journal of the operational research society, 55, 495-503, (2004) · Zbl 1060.90013 [19] Teng, J.T.; Chern, M.S.; Chan, Y.L., Deterministic inventory lot-size models with shortages for fluctuating demand and unit purchase cost, International transactions in operational research, 12, 83-100, (2005) · Zbl 1060.90014 [20] Teng, J.T.; Yang, H.L., Deterministic inventory lot-size models with time-varying demand and cost under generalized holding costs, International journal of information and management sciences, 18, 113-125, (2007) · Zbl 1171.90330 [21] Chen, J.M.; Chen, L.T., Pricing and lot-sizing for a deteriorating item in a periodic review inventory system with shortages, Journal of the operational research society, 55, 892-901, (2004) · Zbl 1060.90005 [22] Chang, H.J.; Teng, J.T.; Ouyang, L.Y.; Dye, C.Y., Retailerâ€™s optimal pricing and lot-sizing policies for deteriorating items with partial backlogging, European journal of operational research, 168, 51-64, (2006) · Zbl 1077.90002 [23] R.C. Eberhart, J. Kennedy, A new optimizer using particle swarm theory, in: Proceedings of the Sixth International Symposium on Micromachine and Human Science, Nagoya, Japan, 1995, pp. 39-43. [24] J. Kennedy, R.C. Eberhart, Particle swarm optimization, in: Proceedings of IEEE International Conference on Neural Networks, Piscataway, NJ, 1995, pp. 1942-1948.
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