• Previous Article
    Asymptotics for ruin probabilities of a non-standard renewal risk model with dependence structures and exponential Lévy process investment returns
  • JIMO Home
  • This Issue
  • Next Article
    The finite-time ruin probability for an inhomogeneous renewal risk model
January  2017, 13(1): 187-206. doi: 10.3934/jimo.2016011

Preservation of deteriorating seasonal products with stock-dependent consumption rate and shortages

1. 

Department of Industrial & Management Engineering, Hanyang University, Ansan Gyeonggi-do, 426 791, South Korea

2. 

Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore 721 102, India

* Corresponding author: ss.sumonsarkar@gmail.com, Office Ph. No. 031-436-8118

1Dr. Biswajit Sarkar is in leave on lien from Vidyasagar University.

Received  March 2015 Revised  December 2015 Published  March 2016

In literature, many inventory studies have been developed by assuming deterioration of items as either a variable or constant. But in real life situation, deterioration of goods can be reduced by adding some extra effective capital investment in preservation technology. In this paper, a deteriorating inventory model with ramp-type demand under stock-dependent consumption rate by assuming preservation technology cost as a decision variable is formulated. Shortages are allowed and the unsatisfied demand is partially backlogged at a negative exponential rate with the waiting time. The objective of this study is to obtain the optimal replenishment and preservation technology investment strategies so that the total profit per unit time is maximum. Further, the necessary and sufficient conditions are considered to prove the existence and uniqueness of the optimal solution. Some numerical examples along with graphical representations are provided to illustrate the proposed model. Sensitivity analysis of the optimal solution with respect to major parameters of the system has been carried out and the implications are discussed.

Citation: Biswajit Sarkar, Buddhadev Mandal, Sumon Sarkar. Preservation of deteriorating seasonal products with stock-dependent consumption rate and shortages. Journal of Industrial & Management Optimization, 2017, 13 (1) : 187-206. doi: 10.3934/jimo.2016011
References:
[1]

P. L. Abad, Optimal pricing and lot sizing under conditions of perishability and partial backordering, Management Science, 42 (1996), 1093-1104. doi: 10.1287/mnsc.42.8.1093.

[2]

H. K. Alfares, Inventory model with stock-level dependent demand rate and variable holding cost, International Journal of Production Economics, 108 (2007), 259-265. doi: 10.1016/j.ijpe.2006.12.013.

[3]

M. AsghariS. J. Abrishami and F. Mahdavi, Reverse logistics network design with incentive-dependent return, Industrial Engineering & Management Systems, 13 (2014), 383-397. doi: 10.7232/iems.2014.13.4.383.

[4]

A. Bouras and L. Tadj, Production planning in a three-stock reverse-logistics system with deteriorating items under a continuous review policy, Journal of Industrial and Management Optimization, 11 (2015), 1041-1058. doi: 10.3934/jimo.2015.11.1041.

[5]

H. J. Chang and C. Y. Dye, An EOQ model for deteriorating items with time-varying demand and partial backlogging, Journal of the Operational Research Society, 50 (1999), 1176-1182.

[6]

C. J. Chung and H. M. Wee, Short life-cycle deteriorating product remanufacturing in a green supply chain inventory control system, International Journal of Production Economics, 129 (2011), 195-203. doi: 10.1016/j.ijpe.2010.09.033.

[7]

C. J. Chung and H. M. Wee, An integrated production-inventory deteriorating model for pricing policy considering imperfect production, inspection planning and warranty-period and stock-level-dependant demand, International Journal of System Science, 39 (2008), 823-837. doi: 10.1080/00207720801902598.

[8]

C. J. Chung and H. M. Wee, Scheduling and replenishment plan for an integrated deteriorating inventory model with stock-dependent selling rate, International Journal of Advanced Manufacturing Technology, 35 (2007), 665-679. doi: 10.1007/s00170-006-0744-7.

[9]

R. P. Covert and G. C. Philip, An EOQ model for items with Weibull distribution deterioration, AIIE Transaction, 5 (1973), 323-326. doi: 10.1080/05695557308974918.

[10]

L. E. Cárdenas-Barrón, Economic production quantity with rework process at a single-stage manufacturing system with planned backorders, Computers & Industrial Engineering, 57 (2009), 1105-1113.

[11]

L. E. Cárdenas-Barrón, The derivation of EOQ/EPQ inventory models with two backorders costs using analytic geometry and algebra, Applied Mathematical Modelling, 35 (2011), 2394-2407. doi: 10.1016/j.apm.2010.11.053.

[12]

K. K. Damghani and A. Shahrokh, Solving a new multi-period multi-objective multi-product aggregate production planning problem using fuzzy goal programming, Industrial Engineering & Management Systems, 13 (2014), 369-382.

[13]

C. Y. DyeH. J. Chang and J. T. Teng, A deteriorating inventory model with time-varying demand and shortage-dependent partial backlogging, European Journal of Operational Research, 172 (2006), 417-429. doi: 10.1016/j.ejor.2004.10.025.

[14]

C. Y. Dye and T. P. Hsieh, An optimal replenishment policy for deteriorating items with effective investment in preservation technology, European Journal of Operational Research, 218 (2012), 106-112. doi: 10.1016/j.ejor.2011.10.016.

[15]

C. Y. Dye, The effect of preservation technology investment on a non-instantaneous deteriorating inventory model, Omega, 41 (2013), 872-880. doi: 10.1016/j.omega.2012.11.002.

[16]

C. Y. Dye and L. Y. Ouyang, An EOQ model for perishable items under stock-dependent selling rate and time-dependent partial backlogging, European Journal of Operational Research, 163 (2005), 776-783. doi: 10.1016/j.ejor.2003.09.027.

[17]

P. M. Ghare and G. F. Schrader, A model for exponentially decaying inventory, Journal of Industrial Engineering, 14 (1963), 238-243.

[18]

P. HsuH. M. Wee and H. Teng, Preservation technology investment for deteriorating inventory, International Journal of Production Economics, 124 (2010), 388-394. doi: 10.1016/j.ijpe.2009.11.034.

[19]

E. Kusukawa, Supply chain coordination in 2-stage-ordering-production system with update of demand information, Industrial Engineering & Management Systems, 13 (2014), 304-318. doi: 10.7232/iems.2014.13.3.304.

[20]

W. S. LeeB. S. Kim and P. F. Opit, A stock pre-positioning model to maximize the total expected relief demand of disaster areas, Industrial Engineering & Management Systems, 13 (2014), 297-303. doi: 10.7232/iems.2014.13.3.297.

[21]

R. I. Levin, C. P. McLaughlin, R. P. Lemone and J. F. Kottas, Production/Operations Management: Contemporary Policy for Managing Operating Systems, 2nd edition, McGraw Hill, New York, 1972.

[22]

H. C. LiaoC. H. Tsai and C. T. Su, An inventory model with deteriorating items under inflation when a delay in payment is permissible, International Journal of Production Economics, 63 (2000), 207-214. doi: 10.1016/S0925-5273(99)00015-8.

[23]

B. Mandal and A. K. Pal, Order level inventory system with ramp type demand rate for deteriorating items, Journal of Interdisciplinary Mathematics, 1 (1998), 49-66. doi: 10.1080/09720502.1998.10700243.

[24]

D. C. MontgomeryM. S. Bazaraa and A. K. Keswani, Inventory models with a mixture of backorders and lost sales, Naval Research Logistics Quarterly, 20 (1973), 255-263. doi: 10.1002/nav.3800200205.

[25]

B. Özyörük and N. Dönmeza, A fuzzy multi-objective linear programming model: A case study of an lpg distribution network, Industrial Engineering & Management Systems, 13 (2014), 319-329.

[26]

G. Padmanabhan and P. Vrat, EOQ models for perishable items under stock dependent selling rate, European Journal of Operational Research, 86 (1995), 281-292. doi: 10.1016/0377-2217(94)00103-J.

[27]

S. Papachristos and K. Skouri, An optimal replenishment policy for deteriorating items with time-varying demand and partial exponential type-backlogging, Operations Research Letters, 27 (2000), 175-184. doi: 10.1016/S0167-6377(00)00044-4.

[28]

K. S. Park, Inventory model with partial backorders, International Journal of System Science, 13 (1982), 1313-1317. doi: 10.1080/00207728208926430.

[29]

D. Rosenberg, A new analysis of a lot-size model with partial backordering, Naval Research Logistics Quarterly, 26 (1979), 349-353.

[30]

S. SanaS. K. Goyal and K. S. Chaudhuri, A production-inventory model for a deteriorating item with trended demand and shortages, European Journal of Operational Research, 157 (2004), 357-371. doi: 10.1016/S0377-2217(03)00222-4.

[31]

S. Sana, Optimal selling price and lotsize with time-varying deterioration and partial backlogging, Applied Mathematics and Computation, 217 (2010), 185-194. doi: 10.1016/j.amc.2010.05.040.

[32]

S. Sana and K. S. Chaudhuri, A deterministic EOQ model with delays in payments and price discount offers, European Journal of Operational Research, 184 (2008), 509-533. doi: 10.1016/j.ejor.2006.11.023.

[33]

S. Sana, An EOQ model for perishable item with stock-dependent demand and price discount rate, American Journal of Mathematical and Management, 30 (2012), 299-316. doi: 10.1080/01966324.2010.10737790.

[34]

B. Sarkar, An EOQ model with delay in payments and time varying deterioration rate, Mathematical and Computer Modelling, 55 (2012), 367-377. doi: 10.1016/j.mcm.2011.08.009.

[35]

B. Sarkar, An EOQ model with delay in payments and time-varying demand, Mathematical and Computer Modelling, 55 (2012), 367-377. doi: 10.1016/j.mcm.2011.08.009.

[36]

B. Sarkar, A production-inventory model with probabilistic deterioration in two-echelon supply chain management, Applied Mathematical Modelling, 37 (2013), 3138-3151. doi: 10.1016/j.apm.2012.07.026.

[37]

B. Sarkar, Supply chain coordination with variable backorder, inspections, and discount policy for fixed lifetime products, Mathematical Problems in Engineering, Available online, (2015).

[38]

B. Sarkar, An EOQ model with delay in payments and stock dependent demand in the presence of imperfect production, Applied Mathematics and Computation, 218 (2012), 8295-8308. doi: 10.1016/j.amc.2012.01.053.

[39]

B. SarkarB. Mandal and S. Sarkar, Quality improvement and backorder price discount under controllable lead time in an inventory model, Journal of Manufacturing Systems, 35 (2015), 26-36.

[40]

B. Sarkar and S. Sarkar, Variable deterioration and demand-An inventory model, Economic Modelling, 31 (2013), 548-556. doi: 10.1016/j.econmod.2012.11.045.

[41]

M. Sarkar and B. Sarkar, An economic manufacturing quantity model with probabilistic deterioration in a production system, Economic Modelling, 31 (2013), 245-252. doi: 10.1016/j.econmod.2012.11.019.

[42]

B. SarkarS. Sarkar and W. Y. Yun, Retailer's optimal strategy for fixed lifetime products, International Journal of Machine Learning and Cybernetics, 7 (2016), 121-133. doi: 10.1007/s13042-015-0393-y.

[43]

B. Sarkar and S. Sarkar, An improved inventory model with partial backlogging, time-varying deterioration and stock-dependent demand, Economic Modelling, 30 (2013), 924-932. doi: 10.1016/j.econmod.2012.09.049.

[44]

B. SarkarS. Saren and L. E. Cárdenas-Barrón, An inventory model with trade-credit policy and variable deterioration for fixed lifetime products, Annals of Operations Research, 229 (2015), 677-702. doi: 10.1007/s10479-014-1745-9.

[45]

B. SarkarB. K. SettA. Goswami and S. Sarkar, Mitigation of high-tech products with probabilistic deterioration and inflations, American Journal of Industrial and Business Management, 5 (2015), 73-89. doi: 10.4236/ajibm.2015.53009.

[46]

B. K. SettB. Sarkar and A. Goswami, A two-warehouse inventory model with increasing demand and time varying deterioration, Scientia Iranica, 19 (2012), 1969-1977.

[47]

E. A. Silver and R. Peterson, Decision Systems for Inventory Management and Production Planning, 2nd edition, Wiley, New York, 1985.

[48]

K. Skouri and S. Papachristos, A continuous review inventory model, with deteriorating items, time-varying demand, linear replenishment cost, partially time-varying backlogging, Applied Mathematical Modelling, 26 (2002), 603-617. doi: 10.1016/S0307-904X(01)00071-3.

[49]

K. SkouriI. KonstantarasS. Papachristos and I. Ganas, Inventory models with ramp-type demand rate, partial backlogging and weibull deterioration rate, European Journal of Operational Research, 192 (2009), 79-92. doi: 10.1016/j.ejor.2007.09.003.

[50]

T. Thongdee and R. Pitakaso, Differential evolution algorithms solving a multi-objective, source and stage location-allocation problem, Industrial Engineering & Management Systems, 14 (2015), 11-21. doi: 10.7232/iems.2015.14.1.011.

[51]

T. Watanabe and E. Kusukawa, Optimal operation for green supply chain considering demand information, collection incentive and quality of recycling parts, Industrial Engineering & Management Systems, 13 (2014), 129-147. doi: 10.7232/iems.2014.13.2.129.

[52]

H. M. WeeM. C. LeeJ. C. P. Yu and C. E. Wang, Optimal replenishment policy for a deteriorating green product:Lifecycle costing analysis, International Journal of Production Economics, 133 (2011), 603-611.

[53]

H. M. WeeY. D. HuangW. T. Wang and Y. L. Cheng, An EPQ model with partial backorders considering two backordering costs, Applied Mathematics and Computation, 232 (2014), 898-907. doi: 10.1016/j.amc.2014.01.106.

[54]

G. A. Widyadana and H. M. Wee, Optimal deteriorating items production inventory models with random machine breakdown and stochastic repair time, Applied Mathematical Modelling, 35 (2011), 3495-3508. doi: 10.1016/j.apm.2011.01.006.

[55]

G. A. WidyadanaL. E. Cárdenas-Barrón and H. M. Wee, Economics order quantity model for deteriorating items with planned backorder level, Mathematical and Computer Modelling, 54 (2011), 1569-1575. doi: 10.1016/j.mcm.2011.04.028.

[56]

K. S. Wu, An EOQ inventory model for items with Weibull distribution deterioration, ramp-type demand rate and partial backlogging, Production Planning & Control, 12 (2001), 787-793. doi: 10.1080/09537280110051819.

[57]

K. S. WuL. Y. Ouyang and C. T. Yang, Retailer's optimal ordering policy for deteriorating items with ramp-type demand under stock-dependent consumption rate, Information and Management Sciences, 19 (2008), 245-262.

[58]

J. ZhangZ. Bai and W. Tang, Optimal pricing policy for deteriorating items with preservation technology investment, Journal Of Industrial And Management Optimization, 10 (2014), 1261-1277. doi: 10.3934/jimo.2014.10.1261.

show all references

References:
[1]

P. L. Abad, Optimal pricing and lot sizing under conditions of perishability and partial backordering, Management Science, 42 (1996), 1093-1104. doi: 10.1287/mnsc.42.8.1093.

[2]

H. K. Alfares, Inventory model with stock-level dependent demand rate and variable holding cost, International Journal of Production Economics, 108 (2007), 259-265. doi: 10.1016/j.ijpe.2006.12.013.

[3]

M. AsghariS. J. Abrishami and F. Mahdavi, Reverse logistics network design with incentive-dependent return, Industrial Engineering & Management Systems, 13 (2014), 383-397. doi: 10.7232/iems.2014.13.4.383.

[4]

A. Bouras and L. Tadj, Production planning in a three-stock reverse-logistics system with deteriorating items under a continuous review policy, Journal of Industrial and Management Optimization, 11 (2015), 1041-1058. doi: 10.3934/jimo.2015.11.1041.

[5]

H. J. Chang and C. Y. Dye, An EOQ model for deteriorating items with time-varying demand and partial backlogging, Journal of the Operational Research Society, 50 (1999), 1176-1182.

[6]

C. J. Chung and H. M. Wee, Short life-cycle deteriorating product remanufacturing in a green supply chain inventory control system, International Journal of Production Economics, 129 (2011), 195-203. doi: 10.1016/j.ijpe.2010.09.033.

[7]

C. J. Chung and H. M. Wee, An integrated production-inventory deteriorating model for pricing policy considering imperfect production, inspection planning and warranty-period and stock-level-dependant demand, International Journal of System Science, 39 (2008), 823-837. doi: 10.1080/00207720801902598.

[8]

C. J. Chung and H. M. Wee, Scheduling and replenishment plan for an integrated deteriorating inventory model with stock-dependent selling rate, International Journal of Advanced Manufacturing Technology, 35 (2007), 665-679. doi: 10.1007/s00170-006-0744-7.

[9]

R. P. Covert and G. C. Philip, An EOQ model for items with Weibull distribution deterioration, AIIE Transaction, 5 (1973), 323-326. doi: 10.1080/05695557308974918.

[10]

L. E. Cárdenas-Barrón, Economic production quantity with rework process at a single-stage manufacturing system with planned backorders, Computers & Industrial Engineering, 57 (2009), 1105-1113.

[11]

L. E. Cárdenas-Barrón, The derivation of EOQ/EPQ inventory models with two backorders costs using analytic geometry and algebra, Applied Mathematical Modelling, 35 (2011), 2394-2407. doi: 10.1016/j.apm.2010.11.053.

[12]

K. K. Damghani and A. Shahrokh, Solving a new multi-period multi-objective multi-product aggregate production planning problem using fuzzy goal programming, Industrial Engineering & Management Systems, 13 (2014), 369-382.

[13]

C. Y. DyeH. J. Chang and J. T. Teng, A deteriorating inventory model with time-varying demand and shortage-dependent partial backlogging, European Journal of Operational Research, 172 (2006), 417-429. doi: 10.1016/j.ejor.2004.10.025.

[14]

C. Y. Dye and T. P. Hsieh, An optimal replenishment policy for deteriorating items with effective investment in preservation technology, European Journal of Operational Research, 218 (2012), 106-112. doi: 10.1016/j.ejor.2011.10.016.

[15]

C. Y. Dye, The effect of preservation technology investment on a non-instantaneous deteriorating inventory model, Omega, 41 (2013), 872-880. doi: 10.1016/j.omega.2012.11.002.

[16]

C. Y. Dye and L. Y. Ouyang, An EOQ model for perishable items under stock-dependent selling rate and time-dependent partial backlogging, European Journal of Operational Research, 163 (2005), 776-783. doi: 10.1016/j.ejor.2003.09.027.

[17]

P. M. Ghare and G. F. Schrader, A model for exponentially decaying inventory, Journal of Industrial Engineering, 14 (1963), 238-243.

[18]

P. HsuH. M. Wee and H. Teng, Preservation technology investment for deteriorating inventory, International Journal of Production Economics, 124 (2010), 388-394. doi: 10.1016/j.ijpe.2009.11.034.

[19]

E. Kusukawa, Supply chain coordination in 2-stage-ordering-production system with update of demand information, Industrial Engineering & Management Systems, 13 (2014), 304-318. doi: 10.7232/iems.2014.13.3.304.

[20]

W. S. LeeB. S. Kim and P. F. Opit, A stock pre-positioning model to maximize the total expected relief demand of disaster areas, Industrial Engineering & Management Systems, 13 (2014), 297-303. doi: 10.7232/iems.2014.13.3.297.

[21]

R. I. Levin, C. P. McLaughlin, R. P. Lemone and J. F. Kottas, Production/Operations Management: Contemporary Policy for Managing Operating Systems, 2nd edition, McGraw Hill, New York, 1972.

[22]

H. C. LiaoC. H. Tsai and C. T. Su, An inventory model with deteriorating items under inflation when a delay in payment is permissible, International Journal of Production Economics, 63 (2000), 207-214. doi: 10.1016/S0925-5273(99)00015-8.

[23]

B. Mandal and A. K. Pal, Order level inventory system with ramp type demand rate for deteriorating items, Journal of Interdisciplinary Mathematics, 1 (1998), 49-66. doi: 10.1080/09720502.1998.10700243.

[24]

D. C. MontgomeryM. S. Bazaraa and A. K. Keswani, Inventory models with a mixture of backorders and lost sales, Naval Research Logistics Quarterly, 20 (1973), 255-263. doi: 10.1002/nav.3800200205.

[25]

B. Özyörük and N. Dönmeza, A fuzzy multi-objective linear programming model: A case study of an lpg distribution network, Industrial Engineering & Management Systems, 13 (2014), 319-329.

[26]

G. Padmanabhan and P. Vrat, EOQ models for perishable items under stock dependent selling rate, European Journal of Operational Research, 86 (1995), 281-292. doi: 10.1016/0377-2217(94)00103-J.

[27]

S. Papachristos and K. Skouri, An optimal replenishment policy for deteriorating items with time-varying demand and partial exponential type-backlogging, Operations Research Letters, 27 (2000), 175-184. doi: 10.1016/S0167-6377(00)00044-4.

[28]

K. S. Park, Inventory model with partial backorders, International Journal of System Science, 13 (1982), 1313-1317. doi: 10.1080/00207728208926430.

[29]

D. Rosenberg, A new analysis of a lot-size model with partial backordering, Naval Research Logistics Quarterly, 26 (1979), 349-353.

[30]

S. SanaS. K. Goyal and K. S. Chaudhuri, A production-inventory model for a deteriorating item with trended demand and shortages, European Journal of Operational Research, 157 (2004), 357-371. doi: 10.1016/S0377-2217(03)00222-4.

[31]

S. Sana, Optimal selling price and lotsize with time-varying deterioration and partial backlogging, Applied Mathematics and Computation, 217 (2010), 185-194. doi: 10.1016/j.amc.2010.05.040.

[32]

S. Sana and K. S. Chaudhuri, A deterministic EOQ model with delays in payments and price discount offers, European Journal of Operational Research, 184 (2008), 509-533. doi: 10.1016/j.ejor.2006.11.023.

[33]

S. Sana, An EOQ model for perishable item with stock-dependent demand and price discount rate, American Journal of Mathematical and Management, 30 (2012), 299-316. doi: 10.1080/01966324.2010.10737790.

[34]

B. Sarkar, An EOQ model with delay in payments and time varying deterioration rate, Mathematical and Computer Modelling, 55 (2012), 367-377. doi: 10.1016/j.mcm.2011.08.009.

[35]

B. Sarkar, An EOQ model with delay in payments and time-varying demand, Mathematical and Computer Modelling, 55 (2012), 367-377. doi: 10.1016/j.mcm.2011.08.009.

[36]

B. Sarkar, A production-inventory model with probabilistic deterioration in two-echelon supply chain management, Applied Mathematical Modelling, 37 (2013), 3138-3151. doi: 10.1016/j.apm.2012.07.026.

[37]

B. Sarkar, Supply chain coordination with variable backorder, inspections, and discount policy for fixed lifetime products, Mathematical Problems in Engineering, Available online, (2015).

[38]

B. Sarkar, An EOQ model with delay in payments and stock dependent demand in the presence of imperfect production, Applied Mathematics and Computation, 218 (2012), 8295-8308. doi: 10.1016/j.amc.2012.01.053.

[39]

B. SarkarB. Mandal and S. Sarkar, Quality improvement and backorder price discount under controllable lead time in an inventory model, Journal of Manufacturing Systems, 35 (2015), 26-36.

[40]

B. Sarkar and S. Sarkar, Variable deterioration and demand-An inventory model, Economic Modelling, 31 (2013), 548-556. doi: 10.1016/j.econmod.2012.11.045.

[41]

M. Sarkar and B. Sarkar, An economic manufacturing quantity model with probabilistic deterioration in a production system, Economic Modelling, 31 (2013), 245-252. doi: 10.1016/j.econmod.2012.11.019.

[42]

B. SarkarS. Sarkar and W. Y. Yun, Retailer's optimal strategy for fixed lifetime products, International Journal of Machine Learning and Cybernetics, 7 (2016), 121-133. doi: 10.1007/s13042-015-0393-y.

[43]

B. Sarkar and S. Sarkar, An improved inventory model with partial backlogging, time-varying deterioration and stock-dependent demand, Economic Modelling, 30 (2013), 924-932. doi: 10.1016/j.econmod.2012.09.049.

[44]

B. SarkarS. Saren and L. E. Cárdenas-Barrón, An inventory model with trade-credit policy and variable deterioration for fixed lifetime products, Annals of Operations Research, 229 (2015), 677-702. doi: 10.1007/s10479-014-1745-9.

[45]

B. SarkarB. K. SettA. Goswami and S. Sarkar, Mitigation of high-tech products with probabilistic deterioration and inflations, American Journal of Industrial and Business Management, 5 (2015), 73-89. doi: 10.4236/ajibm.2015.53009.

[46]

B. K. SettB. Sarkar and A. Goswami, A two-warehouse inventory model with increasing demand and time varying deterioration, Scientia Iranica, 19 (2012), 1969-1977.

[47]

E. A. Silver and R. Peterson, Decision Systems for Inventory Management and Production Planning, 2nd edition, Wiley, New York, 1985.

[48]

K. Skouri and S. Papachristos, A continuous review inventory model, with deteriorating items, time-varying demand, linear replenishment cost, partially time-varying backlogging, Applied Mathematical Modelling, 26 (2002), 603-617. doi: 10.1016/S0307-904X(01)00071-3.

[49]

K. SkouriI. KonstantarasS. Papachristos and I. Ganas, Inventory models with ramp-type demand rate, partial backlogging and weibull deterioration rate, European Journal of Operational Research, 192 (2009), 79-92. doi: 10.1016/j.ejor.2007.09.003.

[50]

T. Thongdee and R. Pitakaso, Differential evolution algorithms solving a multi-objective, source and stage location-allocation problem, Industrial Engineering & Management Systems, 14 (2015), 11-21. doi: 10.7232/iems.2015.14.1.011.

[51]

T. Watanabe and E. Kusukawa, Optimal operation for green supply chain considering demand information, collection incentive and quality of recycling parts, Industrial Engineering & Management Systems, 13 (2014), 129-147. doi: 10.7232/iems.2014.13.2.129.

[52]

H. M. WeeM. C. LeeJ. C. P. Yu and C. E. Wang, Optimal replenishment policy for a deteriorating green product:Lifecycle costing analysis, International Journal of Production Economics, 133 (2011), 603-611.

[53]

H. M. WeeY. D. HuangW. T. Wang and Y. L. Cheng, An EPQ model with partial backorders considering two backordering costs, Applied Mathematics and Computation, 232 (2014), 898-907. doi: 10.1016/j.amc.2014.01.106.

[54]

G. A. Widyadana and H. M. Wee, Optimal deteriorating items production inventory models with random machine breakdown and stochastic repair time, Applied Mathematical Modelling, 35 (2011), 3495-3508. doi: 10.1016/j.apm.2011.01.006.

[55]

G. A. WidyadanaL. E. Cárdenas-Barrón and H. M. Wee, Economics order quantity model for deteriorating items with planned backorder level, Mathematical and Computer Modelling, 54 (2011), 1569-1575. doi: 10.1016/j.mcm.2011.04.028.

[56]

K. S. Wu, An EOQ inventory model for items with Weibull distribution deterioration, ramp-type demand rate and partial backlogging, Production Planning & Control, 12 (2001), 787-793. doi: 10.1080/09537280110051819.

[57]

K. S. WuL. Y. Ouyang and C. T. Yang, Retailer's optimal ordering policy for deteriorating items with ramp-type demand under stock-dependent consumption rate, Information and Management Sciences, 19 (2008), 245-262.

[58]

J. ZhangZ. Bai and W. Tang, Optimal pricing policy for deteriorating items with preservation technology investment, Journal Of Industrial And Management Optimization, 10 (2014), 1261-1277. doi: 10.3934/jimo.2014.10.1261.

Figure 1.  Graphical presentation of the inventory system (Case 1: μ>t1)
Figure 2.  Graphical presentation of the inventory system (Case 2: μ>t1)
Figure 3.  Graphical presentation of total profit function versus time and preservation technology cost (Example 1)
Figure 4.  Graphical presentation of total profit function versus time and preservation technology cost (Example 2)
Table 1.  Comparison between the contributions of different authors
Author (s) Ramp-type demand Deterio-ration Preser-vation Stock-dependent consumption rate Partial back-logging
Ghare and Schrader [17]
Covert and Philip [9]
Sana, Goyal, and Chaudhuri [30]
Dye, Chang, and Teng [13]
Chung and Wee [7]
Widyadana and Wee [54]
Chung and Wee [6]
Wee, Lee, Yu, and Wang [52]
Sarkar [34]
Sett, Sarkar, and Goswami [46]
Sarkar [35]
Sarkar and Sarkar [36]
Sarkar and Sarkar [40]
Sarkar, Sarkar, and Yun [41]
Sarkar [42]
Bouras and Tadj [4]
Sarkar, Saren, and
C$\acute{a}$rdenas-Barr$\acute{o}$n [44]
Hsu, Wee, and Teng [18]
Dye and Hsieh [14]
Dye [15]
Zhang, Bai, and Tang [58]
Montgomery, Bazaraa,
and Keswani [24]
Park [28]
Rosenberg [29]
Abad [1]
Chang and Dye [5]
Papachristos and Skouri [27]
Skouri and Papachristos [48]
C$\acute{a}$rdenas-Barr$\acute{o}$n [10]
Sana [31]
C$\acute{a}$rdenas-Barr$\acute{o}$n [11]
Widyadana, C$\acute{a}$rdenas-Barr$\acute{o}$n, and Wee [55]
Sarkar and Sarkar [43]
Wee, Huang,
Wang and Cheng [53]
Sarkar [37]
Sarkar, Mandal, and Sarkar [39]
Mandal and Pal [23]
Wu [56]
Wu, Ouyang, and Yang [57]
Skouri, Konstantaras,
Papachristos, and Ganas [49]
Sarkar, Sett, Goswami,
and Sarkar [45]
Levin, McLaughlin,
Lemone, and Kottas [21]
Silver and Peterson [47]
Padmanabhan and Vrat [26]
Liao, Tsai, and Su [22]
Dye and Ouyang [16]
Alfares [2]
Chung and Wee [8]
Sana and Chaudhuri [32]
Sana [33]
Sarkar [38]
Author (s) Ramp-type demand Deterio-ration Preser-vation Stock-dependent consumption rate Partial back-logging
Ghare and Schrader [17]
Covert and Philip [9]
Sana, Goyal, and Chaudhuri [30]
Dye, Chang, and Teng [13]
Chung and Wee [7]
Widyadana and Wee [54]
Chung and Wee [6]
Wee, Lee, Yu, and Wang [52]
Sarkar [34]
Sett, Sarkar, and Goswami [46]
Sarkar [35]
Sarkar and Sarkar [36]
Sarkar and Sarkar [40]
Sarkar, Sarkar, and Yun [41]
Sarkar [42]
Bouras and Tadj [4]
Sarkar, Saren, and
C$\acute{a}$rdenas-Barr$\acute{o}$n [44]
Hsu, Wee, and Teng [18]
Dye and Hsieh [14]
Dye [15]
Zhang, Bai, and Tang [58]
Montgomery, Bazaraa,
and Keswani [24]
Park [28]
Rosenberg [29]
Abad [1]
Chang and Dye [5]
Papachristos and Skouri [27]
Skouri and Papachristos [48]
C$\acute{a}$rdenas-Barr$\acute{o}$n [10]
Sana [31]
C$\acute{a}$rdenas-Barr$\acute{o}$n [11]
Widyadana, C$\acute{a}$rdenas-Barr$\acute{o}$n, and Wee [55]
Sarkar and Sarkar [43]
Wee, Huang,
Wang and Cheng [53]
Sarkar [37]
Sarkar, Mandal, and Sarkar [39]
Mandal and Pal [23]
Wu [56]
Wu, Ouyang, and Yang [57]
Skouri, Konstantaras,
Papachristos, and Ganas [49]
Sarkar, Sett, Goswami,
and Sarkar [45]
Levin, McLaughlin,
Lemone, and Kottas [21]
Silver and Peterson [47]
Padmanabhan and Vrat [26]
Liao, Tsai, and Su [22]
Dye and Ouyang [16]
Alfares [2]
Chung and Wee [8]
Sana and Chaudhuri [32]
Sana [33]
Sarkar [38]
Table 2.  Sensitivity analysis of the key parameters.
Parameters Changes (in %) Model 1 Model 2
-50% +00.27 +00.76
-25% +00.14 +00.38
A +25% -00.14 -00.38
+50% -00.27 -00.76
-50% -95.65 -97.17
-25% -48.39 -49.19
s +25% +49.34 +49.97
+50% +99.48 +100.52
-50% +42.97 +44.83
-25% +21.34 +22.18
p +25% -21.10 -21.84
+50% -41.96 -43.41
-50% +04.81 +03.57
-25% +02.12 +01.63
h +25% -01.69 -01.37
+50% -03.04 -02.53
-50% +00.22 +00.42
-25% +00.11 +00.18
b +25% -00.08 -00.14
+50% -00.15 -00.25
-50% +00.06 +00.11
-25% +00.03 +00.05
l +25% -00.03 -00.05
+50% -00.06 -00.09
Parameters Changes (in %) Model 1 Model 2
-50% +00.27 +00.76
-25% +00.14 +00.38
A +25% -00.14 -00.38
+50% -00.27 -00.76
-50% -95.65 -97.17
-25% -48.39 -49.19
s +25% +49.34 +49.97
+50% +99.48 +100.52
-50% +42.97 +44.83
-25% +21.34 +22.18
p +25% -21.10 -21.84
+50% -41.96 -43.41
-50% +04.81 +03.57
-25% +02.12 +01.63
h +25% -01.69 -01.37
+50% -03.04 -02.53
-50% +00.22 +00.42
-25% +00.11 +00.18
b +25% -00.08 -00.14
+50% -00.15 -00.25
-50% +00.06 +00.11
-25% +00.03 +00.05
l +25% -00.03 -00.05
+50% -00.06 -00.09
[1]

Magfura Pervin, Sankar Kumar Roy, Gerhard Wilhelm Weber. A two-echelon inventory model with stock-dependent demand and variable holding cost for deteriorating items. Numerical Algebra, Control & Optimization, 2017, 7 (1) : 21-50. doi: 10.3934/naco.2017002

[2]

Konstantina Skouri, Ioannis Konstantaras. Two-warehouse inventory models for deteriorating products with ramp type demand rate. Journal of Industrial & Management Optimization, 2013, 9 (4) : 855-883. doi: 10.3934/jimo.2013.9.855

[3]

Magfura Pervin, Sankar Kumar Roy, Gerhard Wilhelm Weber. Multi-item deteriorating two-echelon inventory model with price- and stock-dependent demand: A trade-credit policy. Journal of Industrial & Management Optimization, 2019, 15 (3) : 1345-1373. doi: 10.3934/jimo.2018098

[4]

Magfura Pervin, Sankar Kumar Roy, Gerhard Wilhelm Weber. Deteriorating inventory with preservation technology under price- and stock-sensitive demand. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-28. doi: 10.3934/jimo.2019019

[5]

Xing Huang, Chang Liu, Feng-Yu Wang. Order preservation for path-distribution dependent SDEs. Communications on Pure & Applied Analysis, 2018, 17 (5) : 2125-2133. doi: 10.3934/cpaa.2018100

[6]

Sung-Seok Ko, Jangha Kang, E-Yeon Kwon. An $(s,S)$ inventory model with level-dependent $G/M/1$-Type structure. Journal of Industrial & Management Optimization, 2016, 12 (2) : 609-624. doi: 10.3934/jimo.2016.12.609

[7]

Muhammad Waqas Iqbal, Biswajit Sarkar. Application of preservation technology for lifetime dependent products in an integrated production system. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-28. doi: 10.3934/jimo.2018144

[8]

Jia Shu, Zhengyi Li, Weijun Zhong. A market selection and inventory ordering problem under demand uncertainty. Journal of Industrial & Management Optimization, 2011, 7 (2) : 425-434. doi: 10.3934/jimo.2011.7.425

[9]

Chi Zhou, Wansheng Tang, Ruiqing Zhao. Optimal consumption with reference-dependent preferences in on-the-job search and savings. Journal of Industrial & Management Optimization, 2017, 13 (1) : 505-529. doi: 10.3934/jimo.2016029

[10]

Qi Feng, Suresh P. Sethi, Houmin Yan, Hanqin Zhang. Optimality and nonoptimality of the base-stock policy in inventory problems with multiple delivery modes. Journal of Industrial & Management Optimization, 2006, 2 (1) : 19-42. doi: 10.3934/jimo.2006.2.19

[11]

Shouyu Ma, Zied Jemai, Evren Sahin, Yves Dallery. Analysis of the Newsboy Problem subject to price dependent demand and multiple discounts. Journal of Industrial & Management Optimization, 2018, 14 (3) : 931-951. doi: 10.3934/jimo.2017083

[12]

Kjartan G. Magnússon, Sven Th. Sigurdsson, Petro Babak, Stefán F. Gudmundsson, Eva Hlín Dereksdóttir. A continuous density Kolmogorov type model for a migrating fish stock. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 695-704. doi: 10.3934/dcdsb.2004.4.695

[13]

Wei Liu, Shiji Song, Cheng Wu. Single-period inventory model with discrete stochastic demand based on prospect theory. Journal of Industrial & Management Optimization, 2012, 8 (3) : 577-590. doi: 10.3934/jimo.2012.8.577

[14]

Yanyi Xu, Arnab Bisi, Maqbool Dada. New structural properties of inventory models with Polya frequency distributed demand and fixed setup cost. Journal of Industrial & Management Optimization, 2017, 13 (2) : 931-945. doi: 10.3934/jimo.2016054

[15]

Lizhao Yan, Fei Xu, Yongzeng Lai, Mingyong Lai. Stability strategies of manufacturing-inventory systems with unknown time-varying demand. Journal of Industrial & Management Optimization, 2017, 13 (4) : 2033-2047. doi: 10.3934/jimo.2017030

[16]

Zhijie Sasha Dong, Wei Chen, Qing Zhao, Jingquan Li. Optimal pricing and inventory strategies for introducing a new product based on demand substitution effects. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-15. doi: 10.3934/jimo.2018175

[17]

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

[18]

Sankar Kumar Roy, Magfura Pervin, Gerhard Wilhelm Weber. Imperfection with inspection policy and variable demand under trade-credit: A deteriorating inventory model. Numerical Algebra, Control & Optimization, 2019, 0 (0) : 0-0. doi: 10.3934/naco.2019032

[19]

Andrei Korobeinikov. Global properties of a general predator-prey model with non-symmetric attack and consumption rate. Discrete & Continuous Dynamical Systems - B, 2010, 14 (3) : 1095-1103. doi: 10.3934/dcdsb.2010.14.1095

[20]

Roland Pulch. Stability preservation in Galerkin-type projection-based model order reduction. Numerical Algebra, Control & Optimization, 2019, 9 (1) : 23-44. doi: 10.3934/naco.2019003

2017 Impact Factor: 0.994

Metrics

  • PDF downloads (39)
  • HTML views (239)
  • Cited by (2)

Other articles
by authors

[Back to Top]