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Optimal dynamic pricing and replenishment policy for perishable items with inventory-level-dependent demand. (English) Zbl 1336.49048

Summary: An inventory system for perishable items with limited replenishment capacity is introduced in this paper. The demand rate depends on the stock quantity displayed in the store as well as the sales price. With the goal to realise profit maximization, an optimization problem is addressed to seek for the optimal joint dynamic pricing and replenishment policy which is obtained by solving the optimization problem with Pontryagin’s maximum principle. A joint mixed policy, in which the sales price is a static decision variable and the replenishment rate remains to be a dynamic decision variable, is presented to compare with the joint dynamic policy. Numerical results demonstrate the advantages of the joint dynamic one, and further show the effects of different system parameters on the optimal joint dynamic policy and the maximal total profit.

MSC:

49N90 Applications of optimal control and differential games
49K15 Optimality conditions for problems involving ordinary differential equations
49M05 Numerical methods based on necessary conditions
90B05 Inventory, storage, reservoirs
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[1] DOI: 10.1057/jors.1988.142 · Zbl 0659.90040 · doi:10.1057/jors.1988.142
[2] Bakker M., European Journal of Operational Research, 134 (1) pp 1– (2012)
[3] Bounkhel M., Applied Mathematics E-Notes, 5 pp 36– (2005)
[4] DOI: 10.1016/j.ejor.2005.04.024 · Zbl 1109.90002 · doi:10.1016/j.ejor.2005.04.024
[5] DOI: 10.1016/j.ejor.2007.08.012 · Zbl 1144.90003 · doi:10.1016/j.ejor.2007.08.012
[6] DOI: 10.1080/07408170500371848 · doi:10.1080/07408170500371848
[7] DOI: 10.1016/S0377-2217(99)00203-9 · Zbl 0969.90003 · doi:10.1016/S0377-2217(99)00203-9
[8] DOI: 10.1057/jors.1990.149 · Zbl 0725.90028 · doi:10.1057/jors.1990.149
[9] DOI: 10.1016/j.orl.2012.06.010 · Zbl 1258.90006 · doi:10.1016/j.orl.2012.06.010
[10] DOI: 10.1016/j.ejor.2003.09.027 · Zbl 1071.90505 · doi:10.1016/j.ejor.2003.09.027
[11] DOI: 10.1287/mnsc.49.10.1287.17315 · Zbl 1232.90042 · doi:10.1287/mnsc.49.10.1287.17315
[12] DOI: 10.1287/opre.47.3.454 · Zbl 0979.90004 · doi:10.1287/opre.47.3.454
[13] DOI: 10.1016/0377-2217(85)90307-8 · Zbl 0551.90017 · doi:10.1016/0377-2217(85)90307-8
[14] DOI: 10.1515/9783110856149 · doi:10.1515/9783110856149
[15] Feng L., Information-An International Interdisciplinary Journal, 15 (8) pp 3323– (2012)
[16] DOI: 10.1016/S0377-2217(00)00248-4 · Zbl 0978.90004 · doi:10.1016/S0377-2217(00)00248-4
[17] Gupta R., Opsearch, 23 (1) pp 19– (1986)
[18] DOI: 10.1016/j.ejor.2004.05.011 · Zbl 1101.90006 · doi:10.1016/j.ejor.2004.05.011
[19] DOI: 10.1080/00207720601014206 · Zbl 1284.90017 · doi:10.1080/00207720601014206
[20] DOI: 10.1016/j.mcm.2009.07.017 · Zbl 1190.90018 · doi:10.1016/j.mcm.2009.07.017
[21] DOI: 10.1016/S0377-2217(01)00170-9 · Zbl 1007.90006 · doi:10.1016/S0377-2217(01)00170-9
[22] DOI: 10.1109/9.983360 · Zbl 1364.90141 · doi:10.1109/9.983360
[23] Levin R.I., Production operations management: Contemporary policy for managing operating systems (1972)
[24] DOI: 10.1016/j.ejor.2009.05.010 · Zbl 1173.90313 · doi:10.1016/j.ejor.2009.05.010
[25] DOI: 10.1016/0377-2217(94)00103-J · Zbl 0906.90054 · doi:10.1016/0377-2217(94)00103-J
[26] DOI: 10.1080/00207721.2011.565134 · Zbl 1304.90019 · doi:10.1080/00207721.2011.565134
[27] DOI: 10.1287/opre.22.4.788 · Zbl 0284.90038 · doi:10.1287/opre.22.4.788
[28] DOI: 10.1080/00207729808929518 · doi:10.1080/00207729808929518
[29] DOI: 10.1016/j.tre.2010.01.007 · doi:10.1016/j.tre.2010.01.007
[30] DOI: 10.1016/j.ejor.2006.10.048 · Zbl 1152.90321 · doi:10.1016/j.ejor.2006.10.048
[31] DOI: 10.1504/IJSOI.2012.048790 · doi:10.1504/IJSOI.2012.048790
[32] DOI: 10.1080/00207721.2012.659692 · Zbl 1277.93050 · doi:10.1080/00207721.2012.659692
[33] DOI: 10.1016/j.ejor.2011.05.056 · Zbl 1237.90031 · doi:10.1016/j.ejor.2011.05.056
[34] DOI: 10.1080/00207720701431144 · Zbl 1148.90316 · doi:10.1080/00207720701431144
[35] DOI: 10.1016/j.ejor.2003.08.065 · Zbl 1067.90009 · doi:10.1016/j.ejor.2003.08.065
[36] DOI: 10.1016/j.ijpe.2007.10.024 · doi:10.1016/j.ijpe.2007.10.024
[37] DOI: 10.1016/j.ejor.2011.07.024 · Zbl 1237.90033 · doi:10.1016/j.ejor.2011.07.024
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