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Optimal selling price and lotsize with time varying deterioration and partial backlogging. (English) Zbl 1231.90055
Summary: The article deals with an EOQ (economic order quantity) model over an infinite time horizon for perishable items where demand is price dependent and partial backorder is permitted. The rate of deterioration is taken to be time proportional and it is assumed that shortage occurs at starting of the inventory cycle. Based on the partial backlogging and lost sale cases, the author develops the criterion for the optimal solution for the replenishment schedule, and proves the optimal ordering policy is unique. Moreover, the article suggests to new functions regarding price-dependent demand and time varying deterioration rate. Finally, numerical examples are illustrated to test the model in various issues.

90B05 Inventory, storage, reservoirs
Full Text: DOI
[1] Rakesh, A.R.; Steinberg, R., Dynamic pricing and ordering decisions by a monopolist, Manag. sci., 38, 240-262, (1992) · Zbl 0763.90016
[2] Chun, Y.H., Optimal pricing and ordering policies for perishable commodities, Eur. oper. res., 144, 68-82, (2003) · Zbl 1066.91030
[3] Weatherford, L.R.; Bodily, S.E., A taxonomy research overview of perishable-asset revenue management: yield management, overbooking, and pricing, Oper. res., 40, 831-844, (1992)
[4] Petruzzi, N.C.; Dada, M., Pricing and the news vendor problem: a review with extension, Oper. res., 47, 183-194, (1999) · Zbl 1005.90546
[5] Elmaghraby, W.; Keskinocak, P., Dynamic pricing in the presence of inventory considerations research overview, Manag. sci., 49, 1287-1309, (2003) · Zbl 1232.90042
[6] You, P.S., Ordering and pricing of service products in an advance sales system with price-dependent demand, Eur. oper. res., 170, 57-71, (2006) · Zbl 1079.90015
[7] You, P.S.; Chen, T.C., Dynamic pricing of seasonal goods with spot and forward purchase demands, Comput. math. appl., 54, 490-498, (2007) · Zbl 1126.90305
[8] Haugen, K.K.; Obstad, A.; Pettersen, B.I., The profit maximizing capacitated lot-size (PCLSP) problem, Eur. oper. res., 176, 165-176, (2007) · Zbl 1137.90619
[9] Chen, J.M.; Chen, L.T., Periodic pricing and replenishment policy for continuously decaying inventory with multivariate demand, Appl. math. model., 31, 1819-1828, (2007) · Zbl 1167.90316
[10] Tsao, Y.C.; Sheen, G.J., Dynamic pricing, promotion and replenishment policies for a deteriorating item under permissible delay in payment, Comput. oper. res., 35, 3562-3580, (2008) · Zbl 1140.91358
[11] Abad, P.L., Optimal price order size under partial backordering incorporating shortage, backorder and lost Sale costs, Int. prod. eco., 114, 179-186, (2008)
[12] Salvietti, L.; Smith, N.R., A profit-maximizing economic lot scheduling problem with price optimization, Eur. oper. res., 184, 900-914, (2008) · Zbl 1141.90007
[13] Mishra, S.S.; Mishra, P.P., Price determination for an EOQ model for deteriorating items under perfect competition, Comput. math. appl., 56, 1082-1101, (2008) · Zbl 1155.90313
[14] Mo, J.; Mi, F.; Zhou, F.; Pan, H., A note on an EOQ model with stock and price sensitive demand, Math. comput. model., 49, 2029-2036, (2009) · Zbl 1171.90314
[15] Thangam, A.; Uthayakumar, R., Two-echelon trade credit financing for perishable items in a supply chain when demand depends on both selling price and credit period, Comput. ind. eng., 57, 773-786, (2009)
[16] Ghare, P.M.; Schrader, G.F., A model for exponentially decaying inventory, J. ind. eng., 14, 238-243, (1963)
[17] Covert, R.P.; Philip, G.C., An EOQ model for items with Weibull distribution deterioration, AIIE trans., 5, 323-326, (1973)
[18] Philip, G.C., A generalized EOQ model for items with Weibull distribution, AIIE trans., 16, 159-162, (1974)
[19] Tadikamalla, P.R., An EOQ inventory model for items with gamma distribution, AIIE trans., 9, 108-112, (1978)
[20] Sachan, R.S., On (T,si) policy inventory model for deteriorating items with time proportional demand, J. oper. res. soc., 35, 1013-1019, (1984) · Zbl 0563.90035
[21] Shah, Y.K.; Jaiswal, M.C., An order-level model for a system with constant rate of deterioration, Opsearch, 14, 174-184, (1997)
[22] Hwang, H.; Shinn, S.W., Retailer’s pricing and lotsizing policy for exponentially deteriorating items under conditions of permissible delay in payments, Comput. oper. res., 24, 539-547, (1997) · Zbl 0882.90029
[23] Goswami, A.; Chaudhuri, K.S., An EOQ model for deteriorating items with shortages and a linear trend in demand, J. oper. res. soc., 42, 1105-1110, (1991) · Zbl 0741.90015
[24] Goswami, A.; Chaudhuri, K.S., Variation of order-level inventory models for deteriorating items, Int. prod. eco., 27, 111-117, (1992)
[25] Chung, K.; Ting, P., An heuristic for replenishment of deteriorating items with a linear trend in demand, J. oper. res. soc., 44, 1235-1241, (1993) · Zbl 0797.90016
[26] Fujiwara, O., EOQ models for continuously deteriorating products using linear and exponential penalty costs, Eur. oper. res., 70, 104-114, (1993) · Zbl 0783.90031
[27] Hariga, M., The inventory replenishment problem with a linear trend in demand, Comput. oper. res., 24, 143-150, (1993)
[28] Hariga, M., Optimal EOQ models for deteriorating items with time-varying demand, J. oper. res. soc., 47, 1228-1246, (1996) · Zbl 0871.90028
[29] Wee, H.M., A deterministic lot-size inventory model for deteriorating items with shortages and a declining market, Comput. oper. res., 22, 345-356, (1995) · Zbl 0827.90050
[30] Cohen, M.A., Joint pricing and ordering policy for exponentially decay inventory with known demand, Nav. res. log. qua., 24, 257-268, (1997) · Zbl 0374.90026
[31] Su, C.T.; Tong, L.I.; Liao, H.C., An inventory model under inflation for stock-dependent consumption rate and exponential decay, Opsearch, 33, 72-82, (1996) · Zbl 0879.90076
[32] Chakrabarty, T.; Chaudhuri, K.S., An EOQ model for deteriorating items with a linear trend in demand and shortages in all cycles, Int. prod. eco., 49, 205-213, (1997)
[33] Manna, S.K.; Chaudhuri, K.S., An economic order quantity model for deteriorating items with time-dependent deterioration rate, demand rate, unit production cost and shortages, Int. J. syst. sci., 32, 1003-1009, (2001) · Zbl 1005.90029
[34] Khanra, S.; Chaudhuri, K.S., A note on an order-level inventory model for a deteriorating item with time-dependent quadratic demand, Comput. oper. res., 30, 1901-1916, (2003) · Zbl 1047.90002
[35] Ghosh, S.K.; Chaudhuri, K.S., An EOQ model with a quadratic demand, time-proportional deterioration and shortages in all cycles, Int. syst. sci., 37, 663-672, (2006) · Zbl 1116.90006
[36] Silver, E.A., Operations research in inventory management: a review and critique, Oper. res., 29, 628-645, (1981)
[37] Nahmias, S., Perishable inventory theory – a review, Oper. res., 30, 680-708, (1982) · Zbl 0486.90033
[38] Raafat, F., Survey of literature on continuously deteriorating inventory model, J. oper. res. soc., 42, 27-37, (1991) · Zbl 0718.90025
[39] Khouja, M., The single-period (news-vendor) problem: literature review and suggestions for future research, Omega, 27, 537-553, (1999)
[40] Chung, C.J.; Wee, H.M., Scheduling and replenishment plan for an integrated deteriorating inventory model with stock-dependent selling rate, Int. adv. manuf. technol., 35, 665-679, (2008)
[41] Chang, C.T.; Teng, J.T.; Goyal, S.K., Optimal replenishment policies for non-instantaneous deteriorating items with stock-dependent demand, Int. prod. eco., 123, 62-68, (2010)
[42] Park, K.S., Inventory model with partial backorders, Int. syst. sci., 13, 1313-1317, (1982) · Zbl 0503.90035
[43] Abad, P.L., Optimal pricing and lot sizing under conditions of perishability and partial backordering, Manag. sci., 42, 1093-1104, (1996) · Zbl 0879.90069
[44] Ouyang, L.Y.; Yen, N.C.; Wu, K.S., Mixture inventory model with backorders and lost sales for variable lead time, J. oper. res. soc., 47, 829-832, (1996) · Zbl 0856.90041
[45] Moon, I.; Choi, S., Distribution free procedures for make-to-order (MITO) make-in-advance (MIA) and composite policies, Int. prod. eco., 48, 21-28, (1997)
[46] Abad, P.L., Optimal lotsize for a perishable good under conditions of finite production and partial backordering and lost Sale, Comput. ind. eng., 38, 457-465, (2000)
[47] Melchiors, P.; Dekker, R.; Kleijn, M.J., Inventory rationing in an (S,Q) inventory model with cost sales and two demand classes, J. oper. res. soc., 51, 111-122, (2000) · Zbl 1107.90311
[48] Papachristos, S.; Skouri, K., An inventory model with deteriorating items, quantity discount, pricing and time-dependent partial backlogging, Int. prod. eco., 83, 247-256, (2003) · Zbl 1073.90511
[49] Abad, P.L., Optimal pricing and lot-sizing under conditions of perishability, finite production and partial backordering and lost Sale, Eur. oper. res, 144, 677-685, (2003) · Zbl 1012.90002
[50] Goyal, S.K., The production inventory problem of a product with time varying demand, production and deterioration rates, Eur. oper. res., 147, 549-557, (2003) · Zbl 1026.90001
[51] Chu, P.; Chung, K.J., The sensitivity of the inventory model with partial backorders, Eur. oper. res., 152, 289-295, (2004) · Zbl 1044.90003
[52] Pan, J.C.H.; Lo, M.C.; Hsiao, Y.C., Optimal reorder point inventory models with variable lead time and backorder discount considerations, Eur. oper. res., 158, 488-505, (2004) · Zbl 1067.90005
[53] Yang, H.L., Two-warehouse inventory models for deteriorating items with shortages under inflation, Eur. oper. res., 157, 344-356, (2004) · Zbl 1103.90312
[54] Chiu, S.W.; Chiu, Y.S.P., Mathematical modelling for production system with backlogging and failure in repair, J. sci. ind. res., 65, 499-506, (2006)
[55] Teng, J.T.; Ouyang, L.Y.; Chen, L.H., A comparison between two pricing and lot-sizing models with partial backlogging and deteriorated items, Int. prod. eco., 105, 190-203, (2007)
[56] Chiu, S.W., Optimal replenishment policy for imperfect quality EMQ model with rework and backlogging, Appl. stoch. models bus. ind., 23, 65-178, (2007) · Zbl 1164.90010
[57] Lin, H.D.; Chiu, Y.S.P.; Ting, C.K., A note on optimal replenishment policy for imperfect quality EMQ model with rework and backlogging, Comput. math. appl., 56, 2819-2824, (2008) · Zbl 1165.90328
[58] Chiu, S.W., Production lot sizing problem with failure in repair and backlogging derived without derivatives, Eur. J. oper. res., 188, 610-615, (2008) · Zbl 1129.90018
[59] Emmett, J.L., Advanced supply chain planning with mixtures of backorders, lost sales, and lost contract, Eur. J. oper. res., 181, 168-183, (2007) · Zbl 1121.90013
[60] Dye, C.Y.; Hsieh, T.P.; Ouyang, L.Y., Determining optimal selling price and lotsize with a varying rate of deterioration and exponential partial backlogging, Eur. J. oper. res., 181, 668-678, (2007) · Zbl 1131.90003
[61] Chen, M.S.; Yang, H.L.; Teng, J.T.; Papachristos, S., Partial backlogging inventory lot-size models for deteriorating items with fluctuating demand under inflation, Eur. J. oper. res., 191, 127-141, (2010) · Zbl 1144.90004
[62] Hsieh, T.P.; Dye, C.Y.; Ouyang, L.Y., Optimal lot size for an item with partial backlogging rate when demand is stimulated by inventory above a certain stock level, Math. comput. model., 51, 13-32, (2010) · Zbl 1190.90018
[63] Yang, H.L.; Teng, J.S.; Chern, M.S., An inventory model under inflation for deteriorating items with stock-dependent consumption rate and partial backlogging shortages, Int. J. prod. eco., 123, 8-19, (2010)
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