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doi: 10.3934/jimo.2020148

Effect of reliability on varying demand and holding cost on inventory system incorporating probabilistic deterioration

Sudip Adak and  G. S. Mahapatra ,

Department of Mathematics, National Institute of Technology Puducherry, Karaikal-609609, India

*Corresponding author: G. S. Mahapatra

Received  June 2020 Revised  August 2020 Published  September 2020

This paper presents a mathematical framework to derive an inventory model for time, reliability, and advertisement dependent demand. This paper considers the demand rate is high initially, and then the demand rate reduces later stage, which reflects the situation related to cash in hand. The uncertain deterioration of the product presents through Uniform, Triangular, and Double Triangular probability distributions. The holding cost of the proposed inventory system is dependent on the reliability of the item to make this study a more realistic one. This proposed inventory system allows the situation of shortage and partially backlogged at a fixed rate. Numerical examples, along with managerial implications and sensitivity analysis of the inventory parameters, discuss to examine the effect of changes on the optimal total inventory cost.

Keywords: Deterioration, Holding cost, Reliability, Shortage, Advertisement.
Mathematics Subject Classification: Primary: 90B05, 90B25 and Secondary: 90C31.
Citation: Sudip Adak, G. S. Mahapatra. Effect of reliability on varying demand and holding cost on inventory system incorporating probabilistic deterioration. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2020148
References:
[1]

B. Ahmad and L. Benkherouf, Economic-order-type inventory models for non-instantaneous deteriorating items and backlogging, RAIRO - Operations Research, 52 (2018), 895-901.  doi: 10.1051/ro/2018010.  Google Scholar

[2]

H. K. Alfares and A. M. Ghaithan, Inventory and pricing model with price-dependent demand, time-varying holding cost, and quantity discounts, Computers & Industrial Engineering, 94 (2016), 170-177.   Google Scholar

[3]

Z. T. Balkhi and L. Benkherouf, On an inventory model for deteriorating items with stock dependent and time-varying demand rates, Computers and Operations Research, 31 (2004), 223-240.  doi: 10.1016/S0305-0548(02)00182-X.  Google Scholar

[4]

H. Barman, M. Pervin, S. K. Roy and G. W. Weber, Back-ordered inventory model with inflation in a cloudy-fuzzy environment, Journal of Industrial and Management Optimization, 2020. doi: 10.3934/jimo.2020052.  Google Scholar

[5]

S. Barzegar, M. Seifbarghy, S.H. Pasandideh and M. Arjmand, Development of a joint economic lot size model with stochastic demand within non-equal shipments, Scientia Iranica, 23 (2016), 3026-3034.   Google Scholar

[6]

C. K. Chan, W. H. Wong, A. Langevin and Y. C. E. Lee, An integrated production-inventory model for deteriorating items with consideration of optimal production rate and deterioration during delivery, International Journal of Production Economics, 189 (2017), 1-13.   Google Scholar

[7]

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

[8]

C.T. Chang, Inventory model with stock-dependent demand and nonlinear holding costs for deteriorating items, Asia-Pacific Journal of Operational Research, 21 (2004), 435-446.  doi: 10.1142/S0217595904000321.  Google Scholar

[9]

U. Chanda and A. Kumar, Optimization of fuzzy EOQ model for advertising and price sensitive demand model under dynamic ceiling on potential adoption, International Journal of Systems Science, 4 (2016), 145-165.   Google Scholar

[10]

R. R. Chowdhury, S. K. Ghosh and K.S. Chaudhuri, An order-level inventory model for a deteriorating item with time-quadratic demand and time-dependent partial backlogging with shortages in all cycles, American Journal of Mathematical and Management Sciences, 33 (2014), 75-97.   Google Scholar

[11]

R. R. Chowdhury, S. K. Ghosh and K. S. Chaudhuri, An inventory model for perishable items with stock and advertisement sensitive demand, Int. J. Appl. Comput. Math., 1 (2015), 187-201.  doi: 10.1007/s40819-014-0011-9.  Google Scholar

[12]

P. S. Deng, R. Lin and P. P. Chu, A note on the inventory models for deteriorating items with ramp type demand rate, European Journal of Operational Research, 178 (2007), 112-120.  doi: 10.1016/j.ejor.2006.01.028.  Google Scholar

[13]

B. K. Dey, B. Sarkar, M. Sarkar and S. Pareek, An integrated inventory model involving discrete setup cost reduction, variable safety factor, selling price dependent demand, and investment, RAIRO - Operations Research, 53 (2019), 39-57.  doi: 10.1051/ro/2018009.  Google Scholar

[14]

T. K. Datta and A. K. Pal, Effects of inflation and time-value of money on an inventory model with linear time dependent demand rate and shortages, European Journal of Operational Research, 52 (1991), 326-333.   Google Scholar

[15]

K. V. Geetha and R. Udayakumar, Optimal replenishment policy for deteriorating items with time sensitive demand under trade credit financing., American Journal of Mathematical and Management Sciences, 34 (2015), 197-212.   Google Scholar

[16]

M. Ghoreishi, G. W. Weber and A. Mirzazadeh, An inventory model for non-instantaneous deteriorating items with partial backlogging, permissible delay in payments, inflation and selling price-dependent demand and customer returns, Annals of Operations Research, 226 (2014), 221-238.  doi: 10.1007/s10479-014-1739-7.  Google Scholar

[17]

S. K. Ghosh, T. Sarkar and K. Chaudhuri, A multi-item inventory model for deteriorating items in limited storage space with stock-dependent demand, American Journal of Mathematical and Management Sciences, 34 (2015), 147-161.   Google Scholar

[18]

R. Haji and H. Tayebi, Comparing four ordering policies in a lost sales inventory model with Poisson demand and zero ordering cost, Scientia Iranica, 22 (2015), 1294-1298.   Google Scholar

[19]

M. Hemmati, S. M. T. Fatemi Ghomi and M. S. Sajadieh, Inventory of complementary products with stock-dependent demand under vendor-managed inventory with consignment policy, Scientia Iranica, 25 (2018), 2347-2360.   Google Scholar

[20]

M. R. A. Jokar and M. S. Sajadieh, Optimizing a joint economic lot sizing problem with price-sensitive demand, Scientia Iranica, 16 (2009), 159-164.   Google Scholar

[21]

B. C. Giri and K. S. Chaudhuri, Deterministic models of perishable inventory with stock-dependent demand rate and nonlinear holding cost, European Journal of Operational Research, 105 (1998), 467-474.   Google Scholar

[22]

A. Goli, H. K. Zare, R. Sadeghieh and A. Tavakkoli-Moghaddam, Multiobjective fuzzy mathematical model for a financially constrained closed-loop supply chain with labor employment, Computational Intelligence, 36 (2020), 4-34.   Google Scholar

[23]

A. Goli, H. K. Zare, R. Tavakkoli-Moghaddam and A. Sadeghieh, Hybrid artificial intelligence and robust optimization for a multi-objective product portfolio problem Case study: The dairy products industry, Computers & Industrial Engineering, 37 (2019), 106090. Google Scholar

[24]

A. Goli and S. M. R. Davoodi, Coordination policy for production and delivery scheduling in the closed loop supply chain, Production Engineering, 12 (2018), 621-631.   Google Scholar

[25]

S. Khanra, S. K. Ghosh and K. S. Chaudhuri, An EOQ model for a deteriorating item with time dependent quadratic demand rate under permissible delay in payment, Applied Mathematics and Computation, 218 (2011), 1-9.  doi: 10.1016/j.amc.2011.04.062.  Google Scholar

[26]

I. P. Krommyda, K. Skouri and I. Konstantaras, Optimal ordering quantities for substitutable products with stock-dependent demand, Applied Mathematical Modelling, 39 (2015), 147-164.  doi: 10.1016/j.apm.2014.05.016.  Google Scholar

[27]

S. Kumar and U. S. Rajput, A probabilistic inventory model for deteriorating items with ramp type demand rate under inflation, American Journal of Operational Research, 6 (2016), 16-31.   Google Scholar

[28]

R. Lotfi, G. W. Weber, S. M. Sajadifar and N. Mardani, Interdependent demand in the two-period newsvendor problem, Journal of Industrial & Management Optimization, 16 (2018), 117-140.  doi: 10.3934/jimo.2018143.  Google Scholar

[29]

G. S. Mahapatra, S. Adak and K. Kaladhar, A fuzzy inventory model with three parameter Weibull deterioration with reliant holding cost and demand incorporating reliability, Journal of Intelligent and Fuzzy Systems, 36 (2019), 5731-5744.   Google Scholar

[30]

K. Maity and M. Maiti, Inventory of deteriorating complementary and substitute items with stock dependent demand, American Journal of Mathematical and Management Sciences, 25 (2005), 83-96.  doi: 10.1080/01966324.2005.10737644.  Google Scholar

[31]

U. Mishra, L. E. Cárdenas-Barrón, S. Tiwari, A. A. Shaikh and G. Trevi ño-Garza, An inventory model under price and stock dependent demand for controllable deterioration rate with shortages and preservation technology investment, Annals of Operations Research, 254 (2017), 165-190.  doi: 10.1007/s10479-017-2419-1.  Google Scholar

[32]

N. M. Modak and P. Kelle, Managing a dual-channel supply chain under price and delivery-time dependent stochastic demand, European Journal of Operational Research, 272 (2019), 147-161.  doi: 10.1016/j.ejor.2018.05.067.  Google Scholar

[33]

H. Mokhtari, A. Naimi-Sadigh and A. Salmasnia, A computational approach to economic production quantity model for perishable products with backordering shortage and stock-dependent demand, Scientia Iranica, 24 (2017), 2138-2151.   Google Scholar

[34]

U. Mishra, J. Tijerina-Aguilera, S. Tiwari and L. E. C árdenas-Barrón, Retailer's joint ordering, pricing, and preservation technology investment policies for a deteriorating item under permissible delay in payments, Mathematical Problems in Engineering, 2018 (2018), Art. ID 6962417, 14 pp. doi: 10.1155/2018/6962417.  Google Scholar

[35]

S. M. H. Molana, H. Davoudpour and S. Minner, An (r, nQ) inventory model for packaged deteriorating products with compound Poisson demand, Journal of the Operational Research Society, 63 (2012), 1499-1507.   Google Scholar

[36]

S. Pal and G. S. Mahapatra, A manufacturing-oriented supply chain model for imperfect quality with inspection errors, stochastic demand under rework and shortages, Computers & Industrial Engineering, 106 (2017), 299-314.  doi: 10.1016/j.cie.2017.02.003.  Google Scholar

[37]

S. Pal, G. S. Mahapatra and G. P. Samanta, A production inventory model for deteriorating item with ramp type demand allowing inflation and shortages under fuzziness, Economic Modelling, 46 (2015), 334-345.   Google Scholar

[38]

S. Pal, G. S. Mahapatra and G. P. Samanta, An EPQ model of ramp type demand with Weibull deterioration under inflation and finite horizon in crisp and fuzzy environment, International Journal of Production Economics, 156 (2014), 159-166.   Google Scholar

[39]

M. Palanivel and R. Uthayakumar, An inventory model with imperfect items, stock dependent demand and permissible delay in payments under inflation, RAIRO - Operations Research, 50 (2016), 473-489.  doi: 10.1051/ro/2015028.  Google Scholar

[40]

M. Palanivel and R. Uthayakumar, An EOQ model for non-instantaneous deteriorating items with partial backlogging and permissible delay in payments under inflation, International Journal of Industrial and Systems Engineering, 26 (2017), 63–89. Google Scholar

[41]

N. Pakhira, M. K. Maiti and M. Maiti, Two-level supply chain of a seasonal deteriorating item with time, price, and promotional cost dependent demand under finite time horizon, American Journal of Mathematical and Management Sciences, 36 (2017), 292-315.   Google Scholar

[42]

M. Pervin, G. C. Mahata and S. K. Roy, An inventory model with a declining demand market for deteriorating items under a trade credit policy, International Journal of Management Science and Engineering Management, 11 (2016), 243-251.   Google Scholar

[43]

M. Pervin, S. K. Roy and G. W. Weber, Multi-item deteriorating two-echelon inventory model with price- and stock-dependent demand: A trade-credit policy, Journal of Industrial & Management Optimization, 15 (2019), 1345-1373.  doi: 10.3934/jimo.2018098.  Google Scholar

[44]

M. Pervin, S. K. Roy and G. W. Weber, Deteriorating inventory with preservation technology under price and stock sensitive demand, Journal of Industrial and Management Optimization, 16 (2020), 1585-1612.  doi: 10.3934/jimo.2019019.  Google Scholar

[45]

M. Pervin, S. K. Roy and G. W. Weber, An integrated vendor-buyer model with quadratic demand under inspection policy and preservation technology, Hacettepe Journal of Mathematics and Statistics, 49 (2020), 1168-1189.   Google Scholar

[46]

M. Pervin, S. K. Roy and G. W. Weber, Analysis of inventory control model with shortage under time-dependent demand and time-varying holding cost including stochastic deterioration, Annals of Operations Research, 260 (2018), 437-460.  doi: 10.1007/s10479-016-2355-5.  Google Scholar

[47]

M. Pervin, S. K. Roy and G. W. Weber, A Two-echelon inventory model with stock-dependent demand and variable holding cost for deteriorating items, Numerical Algebra, Control and Optimization, 7 (2017), 21-50.  doi: 10.3934/naco.2017002.  Google Scholar

[48]

M. Pervin, S. K. Roy and G. W. Weber, An integrated inventory model with variable holding cost under two levels of trade-credit policy, Numerical Algebra, Control and Optimization, 8 (2018), 169-191.  doi: 10.3934/naco.2018010.  Google Scholar

[49]

S. K. Roy, M. Pervin and G. W. Weber, Imperfection with inspection policy and variable demand under trade-credit: A deteriorating inventory model, Numerical Algebra, Control and Optimization, 10 (2020), 45-74.   Google Scholar

[50]

S. K. Roy, M. Pervin and G. W. Weber, A two-warehouse probabilistic model with price discount on backorders under two levels of trade-credit policy, Journal of Industrial and Management Optimization, 16 (2020), 553-578.   Google Scholar

[51]

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

[52]

S. S. Sanni and W. I. E. Chukwu, An Economic order quantity model for Items with three-parameter Weibull distribution deterioration, ramp-type demand and shortages, Applied Mathematical Modelling, 37 (2013), 9698-9706.  doi: 10.1016/j.apm.2013.05.017.  Google Scholar

[53]

S. Sanni, Z. Jovanoski and H. S. Sidhu, An economic order quantity model with reverse logistics program, Operations Research Perspectives, 7 (2020), 100133, 8pp. doi: 10.1016/j.orp.2019.100133.  Google Scholar

[54]

L. A. San-José, J. Sicilia and J. Garcia-Laguna, Analysis of an EOQ inventory model with partial backordering and non linear unit holding cost, Omega, 54 (2015), 147-157.   Google Scholar

[55]

L. A. San-José, J. Sicilia, L. E. Cárdenas-Barr ón and J. M. Gutiérrez, Optimal price and quantity under power demand pattern and non-linear holding cost, Computers & Industrial Engineering, 129 (2019), 426-434.   Google Scholar

[56]

M. Sarkar and B. Sarkar, An economic manufacturing quantity model with probabilistic deterioration in a production system, Economic Modelling, 31 (2013), 245-252.   Google Scholar

[57]

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

[58]

S. Shabani, A. Mirzazadeh and E. Sharifi, A two-warehouse inventory model with fuzzy deterioration rate and fuzzy demand rate under conditionally permissible delay in payment, Journal of Industrial and Production Engineering, 33 (2016), 134-142.   Google Scholar

[59]

N. H. Shah and C. R. Vaghela, Imperfect production inventory model for time and effort dependent demand under inflation and maximum reliability, International Journal of Systems Science: Operations & Logistics, 5 (2016), 60-68.   Google Scholar

[60]

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.   Google Scholar

[61]

K. Skouri and S. Papachristos, Four inventory models for deteriorating items with time varying demand and partial backlogging: a cost comparison, Optimal Control Applications and Methods, 24 (2003), 315-330.  doi: 10.1002/oca.734.  Google Scholar

[62]

K. Skouri, I. Konstantaras, S. 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.  Google Scholar

[63]

R. Sundararajan and R. Uthayakumar, Optimal pricing and replenishment policies for instantaneous deteriorating Items with backlogging and permissible delay in payment under inflation, American Journal of Mathematical and Management Sciences, 37 (2018), 307-323.   Google Scholar

[64]

A. A. Taleizadeh and A. Rasuli-Baghban, Pricing and lot sizing of a decaying item under group dispatching with time-dependent demand and decay rates, Scientia Iranica, 25 (2018), 1656–1670. Google Scholar

[65]

A. A. Taleizadeh, L. E. Cárdenas-Barron and R. Sohani, Coordinating the supplier-retailer supply chain under noise effect with bundling and inventory strategies, Journal of Industrial & Management Optimization, 15 (2019), 1701-1727.  doi: 10.3934/jimo.2018118.  Google Scholar

[66]

J. T. Teng, I. P. Krommyda, K. Skouri and K. R. Lou, A comprehensive extension of optimal ordering policy for stock-dependent demand under progressive payment scheme, European Journal of Operational Research, 215 (2011), 97-104.  doi: 10.1016/j.ejor.2011.05.056.  Google Scholar

[67]

E. B. Tirkolaee, A. Goli and G. W. Weber, Multi-objective aggregate production planning model considering overtime and outsourcing options under fuzzy seasonal demand, Advances in Manufacturing, (2019), 81–96. Google Scholar

[68]

S. Tiwari, L. E. Cárdenas-Barrón, M. Goh and A. A. Shaikh, Joint pricing and inventory model for deteriorating items with expiration dates and partial backlogging under two-level partial trade credits in supply chain, International Journal of Production Economics, 200 (2018), 16-36.   Google Scholar

[69]

C. Wang and L. Jiang, Inventory policy for deteriorating seasonal products with price and ramp-type time dependent demand, RAIRO - Operations Research, 49 (2015), 865–878. doi: 10.1051/ro/2015033.  Google Scholar

[70]

C. F. Wu and Q. H. Zhao, An inventory model for deteriorating items with inventory-dependent and linear trend demand under trade credit, Scientia Iranica, 22 (2015), 2558-2570.   Google Scholar

show all references

References:
[1]

B. Ahmad and L. Benkherouf, Economic-order-type inventory models for non-instantaneous deteriorating items and backlogging, RAIRO - Operations Research, 52 (2018), 895-901.  doi: 10.1051/ro/2018010.  Google Scholar

[2]

H. K. Alfares and A. M. Ghaithan, Inventory and pricing model with price-dependent demand, time-varying holding cost, and quantity discounts, Computers & Industrial Engineering, 94 (2016), 170-177.   Google Scholar

[3]

Z. T. Balkhi and L. Benkherouf, On an inventory model for deteriorating items with stock dependent and time-varying demand rates, Computers and Operations Research, 31 (2004), 223-240.  doi: 10.1016/S0305-0548(02)00182-X.  Google Scholar

[4]

H. Barman, M. Pervin, S. K. Roy and G. W. Weber, Back-ordered inventory model with inflation in a cloudy-fuzzy environment, Journal of Industrial and Management Optimization, 2020. doi: 10.3934/jimo.2020052.  Google Scholar

[5]

S. Barzegar, M. Seifbarghy, S.H. Pasandideh and M. Arjmand, Development of a joint economic lot size model with stochastic demand within non-equal shipments, Scientia Iranica, 23 (2016), 3026-3034.   Google Scholar

[6]

C. K. Chan, W. H. Wong, A. Langevin and Y. C. E. Lee, An integrated production-inventory model for deteriorating items with consideration of optimal production rate and deterioration during delivery, International Journal of Production Economics, 189 (2017), 1-13.   Google Scholar

[7]

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

[8]

C.T. Chang, Inventory model with stock-dependent demand and nonlinear holding costs for deteriorating items, Asia-Pacific Journal of Operational Research, 21 (2004), 435-446.  doi: 10.1142/S0217595904000321.  Google Scholar

[9]

U. Chanda and A. Kumar, Optimization of fuzzy EOQ model for advertising and price sensitive demand model under dynamic ceiling on potential adoption, International Journal of Systems Science, 4 (2016), 145-165.   Google Scholar

[10]

R. R. Chowdhury, S. K. Ghosh and K.S. Chaudhuri, An order-level inventory model for a deteriorating item with time-quadratic demand and time-dependent partial backlogging with shortages in all cycles, American Journal of Mathematical and Management Sciences, 33 (2014), 75-97.   Google Scholar

[11]

R. R. Chowdhury, S. K. Ghosh and K. S. Chaudhuri, An inventory model for perishable items with stock and advertisement sensitive demand, Int. J. Appl. Comput. Math., 1 (2015), 187-201.  doi: 10.1007/s40819-014-0011-9.  Google Scholar

[12]

P. S. Deng, R. Lin and P. P. Chu, A note on the inventory models for deteriorating items with ramp type demand rate, European Journal of Operational Research, 178 (2007), 112-120.  doi: 10.1016/j.ejor.2006.01.028.  Google Scholar

[13]

B. K. Dey, B. Sarkar, M. Sarkar and S. Pareek, An integrated inventory model involving discrete setup cost reduction, variable safety factor, selling price dependent demand, and investment, RAIRO - Operations Research, 53 (2019), 39-57.  doi: 10.1051/ro/2018009.  Google Scholar

[14]

T. K. Datta and A. K. Pal, Effects of inflation and time-value of money on an inventory model with linear time dependent demand rate and shortages, European Journal of Operational Research, 52 (1991), 326-333.   Google Scholar

[15]

K. V. Geetha and R. Udayakumar, Optimal replenishment policy for deteriorating items with time sensitive demand under trade credit financing., American Journal of Mathematical and Management Sciences, 34 (2015), 197-212.   Google Scholar

[16]

M. Ghoreishi, G. W. Weber and A. Mirzazadeh, An inventory model for non-instantaneous deteriorating items with partial backlogging, permissible delay in payments, inflation and selling price-dependent demand and customer returns, Annals of Operations Research, 226 (2014), 221-238.  doi: 10.1007/s10479-014-1739-7.  Google Scholar

[17]

S. K. Ghosh, T. Sarkar and K. Chaudhuri, A multi-item inventory model for deteriorating items in limited storage space with stock-dependent demand, American Journal of Mathematical and Management Sciences, 34 (2015), 147-161.   Google Scholar

[18]

R. Haji and H. Tayebi, Comparing four ordering policies in a lost sales inventory model with Poisson demand and zero ordering cost, Scientia Iranica, 22 (2015), 1294-1298.   Google Scholar

[19]

M. Hemmati, S. M. T. Fatemi Ghomi and M. S. Sajadieh, Inventory of complementary products with stock-dependent demand under vendor-managed inventory with consignment policy, Scientia Iranica, 25 (2018), 2347-2360.   Google Scholar

[20]

M. R. A. Jokar and M. S. Sajadieh, Optimizing a joint economic lot sizing problem with price-sensitive demand, Scientia Iranica, 16 (2009), 159-164.   Google Scholar

[21]

B. C. Giri and K. S. Chaudhuri, Deterministic models of perishable inventory with stock-dependent demand rate and nonlinear holding cost, European Journal of Operational Research, 105 (1998), 467-474.   Google Scholar

[22]

A. Goli, H. K. Zare, R. Sadeghieh and A. Tavakkoli-Moghaddam, Multiobjective fuzzy mathematical model for a financially constrained closed-loop supply chain with labor employment, Computational Intelligence, 36 (2020), 4-34.   Google Scholar

[23]

A. Goli, H. K. Zare, R. Tavakkoli-Moghaddam and A. Sadeghieh, Hybrid artificial intelligence and robust optimization for a multi-objective product portfolio problem Case study: The dairy products industry, Computers & Industrial Engineering, 37 (2019), 106090. Google Scholar

[24]

A. Goli and S. M. R. Davoodi, Coordination policy for production and delivery scheduling in the closed loop supply chain, Production Engineering, 12 (2018), 621-631.   Google Scholar

[25]

S. Khanra, S. K. Ghosh and K. S. Chaudhuri, An EOQ model for a deteriorating item with time dependent quadratic demand rate under permissible delay in payment, Applied Mathematics and Computation, 218 (2011), 1-9.  doi: 10.1016/j.amc.2011.04.062.  Google Scholar

[26]

I. P. Krommyda, K. Skouri and I. Konstantaras, Optimal ordering quantities for substitutable products with stock-dependent demand, Applied Mathematical Modelling, 39 (2015), 147-164.  doi: 10.1016/j.apm.2014.05.016.  Google Scholar

[27]

S. Kumar and U. S. Rajput, A probabilistic inventory model for deteriorating items with ramp type demand rate under inflation, American Journal of Operational Research, 6 (2016), 16-31.   Google Scholar

[28]

R. Lotfi, G. W. Weber, S. M. Sajadifar and N. Mardani, Interdependent demand in the two-period newsvendor problem, Journal of Industrial & Management Optimization, 16 (2018), 117-140.  doi: 10.3934/jimo.2018143.  Google Scholar

[29]

G. S. Mahapatra, S. Adak and K. Kaladhar, A fuzzy inventory model with three parameter Weibull deterioration with reliant holding cost and demand incorporating reliability, Journal of Intelligent and Fuzzy Systems, 36 (2019), 5731-5744.   Google Scholar

[30]

K. Maity and M. Maiti, Inventory of deteriorating complementary and substitute items with stock dependent demand, American Journal of Mathematical and Management Sciences, 25 (2005), 83-96.  doi: 10.1080/01966324.2005.10737644.  Google Scholar

[31]

U. Mishra, L. E. Cárdenas-Barrón, S. Tiwari, A. A. Shaikh and G. Trevi ño-Garza, An inventory model under price and stock dependent demand for controllable deterioration rate with shortages and preservation technology investment, Annals of Operations Research, 254 (2017), 165-190.  doi: 10.1007/s10479-017-2419-1.  Google Scholar

[32]

N. M. Modak and P. Kelle, Managing a dual-channel supply chain under price and delivery-time dependent stochastic demand, European Journal of Operational Research, 272 (2019), 147-161.  doi: 10.1016/j.ejor.2018.05.067.  Google Scholar

[33]

H. Mokhtari, A. Naimi-Sadigh and A. Salmasnia, A computational approach to economic production quantity model for perishable products with backordering shortage and stock-dependent demand, Scientia Iranica, 24 (2017), 2138-2151.   Google Scholar

[34]

U. Mishra, J. Tijerina-Aguilera, S. Tiwari and L. E. C árdenas-Barrón, Retailer's joint ordering, pricing, and preservation technology investment policies for a deteriorating item under permissible delay in payments, Mathematical Problems in Engineering, 2018 (2018), Art. ID 6962417, 14 pp. doi: 10.1155/2018/6962417.  Google Scholar

[35]

S. M. H. Molana, H. Davoudpour and S. Minner, An (r, nQ) inventory model for packaged deteriorating products with compound Poisson demand, Journal of the Operational Research Society, 63 (2012), 1499-1507.   Google Scholar

[36]

S. Pal and G. S. Mahapatra, A manufacturing-oriented supply chain model for imperfect quality with inspection errors, stochastic demand under rework and shortages, Computers & Industrial Engineering, 106 (2017), 299-314.  doi: 10.1016/j.cie.2017.02.003.  Google Scholar

[37]

S. Pal, G. S. Mahapatra and G. P. Samanta, A production inventory model for deteriorating item with ramp type demand allowing inflation and shortages under fuzziness, Economic Modelling, 46 (2015), 334-345.   Google Scholar

[38]

S. Pal, G. S. Mahapatra and G. P. Samanta, An EPQ model of ramp type demand with Weibull deterioration under inflation and finite horizon in crisp and fuzzy environment, International Journal of Production Economics, 156 (2014), 159-166.   Google Scholar

[39]

M. Palanivel and R. Uthayakumar, An inventory model with imperfect items, stock dependent demand and permissible delay in payments under inflation, RAIRO - Operations Research, 50 (2016), 473-489.  doi: 10.1051/ro/2015028.  Google Scholar

[40]

M. Palanivel and R. Uthayakumar, An EOQ model for non-instantaneous deteriorating items with partial backlogging and permissible delay in payments under inflation, International Journal of Industrial and Systems Engineering, 26 (2017), 63–89. Google Scholar

[41]

N. Pakhira, M. K. Maiti and M. Maiti, Two-level supply chain of a seasonal deteriorating item with time, price, and promotional cost dependent demand under finite time horizon, American Journal of Mathematical and Management Sciences, 36 (2017), 292-315.   Google Scholar

[42]

M. Pervin, G. C. Mahata and S. K. Roy, An inventory model with a declining demand market for deteriorating items under a trade credit policy, International Journal of Management Science and Engineering Management, 11 (2016), 243-251.   Google Scholar

[43]

M. Pervin, S. K. Roy and G. W. Weber, Multi-item deteriorating two-echelon inventory model with price- and stock-dependent demand: A trade-credit policy, Journal of Industrial & Management Optimization, 15 (2019), 1345-1373.  doi: 10.3934/jimo.2018098.  Google Scholar

[44]

M. Pervin, S. K. Roy and G. W. Weber, Deteriorating inventory with preservation technology under price and stock sensitive demand, Journal of Industrial and Management Optimization, 16 (2020), 1585-1612.  doi: 10.3934/jimo.2019019.  Google Scholar

[45]

M. Pervin, S. K. Roy and G. W. Weber, An integrated vendor-buyer model with quadratic demand under inspection policy and preservation technology, Hacettepe Journal of Mathematics and Statistics, 49 (2020), 1168-1189.   Google Scholar

[46]

M. Pervin, S. K. Roy and G. W. Weber, Analysis of inventory control model with shortage under time-dependent demand and time-varying holding cost including stochastic deterioration, Annals of Operations Research, 260 (2018), 437-460.  doi: 10.1007/s10479-016-2355-5.  Google Scholar

[47]

M. Pervin, S. K. Roy and G. W. Weber, A Two-echelon inventory model with stock-dependent demand and variable holding cost for deteriorating items, Numerical Algebra, Control and Optimization, 7 (2017), 21-50.  doi: 10.3934/naco.2017002.  Google Scholar

[48]

M. Pervin, S. K. Roy and G. W. Weber, An integrated inventory model with variable holding cost under two levels of trade-credit policy, Numerical Algebra, Control and Optimization, 8 (2018), 169-191.  doi: 10.3934/naco.2018010.  Google Scholar

[49]

S. K. Roy, M. Pervin and G. W. Weber, Imperfection with inspection policy and variable demand under trade-credit: A deteriorating inventory model, Numerical Algebra, Control and Optimization, 10 (2020), 45-74.   Google Scholar

[50]

S. K. Roy, M. Pervin and G. W. Weber, A two-warehouse probabilistic model with price discount on backorders under two levels of trade-credit policy, Journal of Industrial and Management Optimization, 16 (2020), 553-578.   Google Scholar

[51]

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

[52]

S. S. Sanni and W. I. E. Chukwu, An Economic order quantity model for Items with three-parameter Weibull distribution deterioration, ramp-type demand and shortages, Applied Mathematical Modelling, 37 (2013), 9698-9706.  doi: 10.1016/j.apm.2013.05.017.  Google Scholar

[53]

S. Sanni, Z. Jovanoski and H. S. Sidhu, An economic order quantity model with reverse logistics program, Operations Research Perspectives, 7 (2020), 100133, 8pp. doi: 10.1016/j.orp.2019.100133.  Google Scholar

[54]

L. A. San-José, J. Sicilia and J. Garcia-Laguna, Analysis of an EOQ inventory model with partial backordering and non linear unit holding cost, Omega, 54 (2015), 147-157.   Google Scholar

[55]

L. A. San-José, J. Sicilia, L. E. Cárdenas-Barr ón and J. M. Gutiérrez, Optimal price and quantity under power demand pattern and non-linear holding cost, Computers & Industrial Engineering, 129 (2019), 426-434.   Google Scholar

[56]

M. Sarkar and B. Sarkar, An economic manufacturing quantity model with probabilistic deterioration in a production system, Economic Modelling, 31 (2013), 245-252.   Google Scholar

[57]

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

[58]

S. Shabani, A. Mirzazadeh and E. Sharifi, A two-warehouse inventory model with fuzzy deterioration rate and fuzzy demand rate under conditionally permissible delay in payment, Journal of Industrial and Production Engineering, 33 (2016), 134-142.   Google Scholar

[59]

N. H. Shah and C. R. Vaghela, Imperfect production inventory model for time and effort dependent demand under inflation and maximum reliability, International Journal of Systems Science: Operations & Logistics, 5 (2016), 60-68.   Google Scholar

[60]

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.   Google Scholar

[61]

K. Skouri and S. Papachristos, Four inventory models for deteriorating items with time varying demand and partial backlogging: a cost comparison, Optimal Control Applications and Methods, 24 (2003), 315-330.  doi: 10.1002/oca.734.  Google Scholar

[62]

K. Skouri, I. Konstantaras, S. 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.  Google Scholar

[63]

R. Sundararajan and R. Uthayakumar, Optimal pricing and replenishment policies for instantaneous deteriorating Items with backlogging and permissible delay in payment under inflation, American Journal of Mathematical and Management Sciences, 37 (2018), 307-323.   Google Scholar

[64]

A. A. Taleizadeh and A. Rasuli-Baghban, Pricing and lot sizing of a decaying item under group dispatching with time-dependent demand and decay rates, Scientia Iranica, 25 (2018), 1656–1670. Google Scholar

[65]

A. A. Taleizadeh, L. E. Cárdenas-Barron and R. Sohani, Coordinating the supplier-retailer supply chain under noise effect with bundling and inventory strategies, Journal of Industrial & Management Optimization, 15 (2019), 1701-1727.  doi: 10.3934/jimo.2018118.  Google Scholar

[66]

J. T. Teng, I. P. Krommyda, K. Skouri and K. R. Lou, A comprehensive extension of optimal ordering policy for stock-dependent demand under progressive payment scheme, European Journal of Operational Research, 215 (2011), 97-104.  doi: 10.1016/j.ejor.2011.05.056.  Google Scholar

[67]

E. B. Tirkolaee, A. Goli and G. W. Weber, Multi-objective aggregate production planning model considering overtime and outsourcing options under fuzzy seasonal demand, Advances in Manufacturing, (2019), 81–96. Google Scholar

[68]

S. Tiwari, L. E. Cárdenas-Barrón, M. Goh and A. A. Shaikh, Joint pricing and inventory model for deteriorating items with expiration dates and partial backlogging under two-level partial trade credits in supply chain, International Journal of Production Economics, 200 (2018), 16-36.   Google Scholar

[69]

C. Wang and L. Jiang, Inventory policy for deteriorating seasonal products with price and ramp-type time dependent demand, RAIRO - Operations Research, 49 (2015), 865–878. doi: 10.1051/ro/2015033.  Google Scholar

[70]

C. F. Wu and Q. H. Zhao, An inventory model for deteriorating items with inventory-dependent and linear trend demand under trade credit, Scientia Iranica, 22 (2015), 2558-2570.   Google Scholar

Figure 1.  Proposed inventory model with inventory vs time
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Figure 2.  Total cost vs. $ T_{1} $ vs. $ T_{2} $ for Uniformly distributed deterioration
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Figure 3.  Total cost vs. $ T_{1} $ vs. $ T_{2} $ for Triangular distribution deterioration
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Figure 4.  Total cost vs. $ T_{1} $ vs. $ T_{2} $ for Triangular distribution deterioration
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Figure 5.  Percentage change of total profit vs change of parameter
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Figure 6.  Percentage change of total profit vs change of parameter
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Figure 7.  Percentage change of total profit vs change of parameter
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Figure 8.  Percentage change of total profit vs change of parameter
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Table 1.  Contributions of the proposed model with compare to previous studies
Author's Cash in hand Demand depend on Holding Cost depend on Deterioration Backlog
Giri & Chaudhuri (1998) NA stock Non linear NA No
Chang (2004) NA stock Non linear constant No
Skouri et al. (2009) NA ramp type NA Weibull Yes
Sana (2010) NA stock NA probabilistic No
Sett et al. (2012) NA time demand NA NA No
Sarkar & Sarkar (2013) NA time NA probabilistic No
Chowdhury et al. (2014) NA time-quadratic NA time demand Yes
Ghoreishi et al. (2014) NA price & time NA non-instantaneous Yes
Ghosh et al. (2015) NA stock Constant constant No
Wu & Zhao (2015) NA inventory & time NA constant No
Bhunia et al. (2015) NA time, advertisement NA constant Yes
Alfares & Ghaithan (2016) NA price time NA No
Chanda & Kumar (2016) NA advertising & price NA NA No
Sanni & Chukwu (2016) NA deterministic NA Weibull Yes
Shah & Vaghela (2016) NA time & advertisement NA constant No
Mahapatra et al. (2017) NA time & reliability NA constant Yes
Mokhtari et al. (2017) NA stochastic NA constant Yes
Pervin et al. (2018) NA time time Weibull Yes
Lotfi et al. (2018) NA interdependent NA NA Yes
Dey et al. (2019) NA selling price NA NA Yes
Pervin et al. (2019) NA price and stock purchasing cost constant Yes
Pervin et al. (2020) NA time & price NA constant Yes
Roy et al. (2020) NA probabilistic Constant Weibull Yes
This paper Consider time, reliability, advertisement reliability probabilistic Yes
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Author's Cash in hand Demand depend on Holding Cost depend on Deterioration Backlog
Giri & Chaudhuri (1998) NA stock Non linear NA No
Chang (2004) NA stock Non linear constant No
Skouri et al. (2009) NA ramp type NA Weibull Yes
Sana (2010) NA stock NA probabilistic No
Sett et al. (2012) NA time demand NA NA No
Sarkar & Sarkar (2013) NA time NA probabilistic No
Chowdhury et al. (2014) NA time-quadratic NA time demand Yes
Ghoreishi et al. (2014) NA price & time NA non-instantaneous Yes
Ghosh et al. (2015) NA stock Constant constant No
Wu & Zhao (2015) NA inventory & time NA constant No
Bhunia et al. (2015) NA time, advertisement NA constant Yes
Alfares & Ghaithan (2016) NA price time NA No
Chanda & Kumar (2016) NA advertising & price NA NA No
Sanni & Chukwu (2016) NA deterministic NA Weibull Yes
Shah & Vaghela (2016) NA time & advertisement NA constant No
Mahapatra et al. (2017) NA time & reliability NA constant Yes
Mokhtari et al. (2017) NA stochastic NA constant Yes
Pervin et al. (2018) NA time time Weibull Yes
Lotfi et al. (2018) NA interdependent NA NA Yes
Dey et al. (2019) NA selling price NA NA Yes
Pervin et al. (2019) NA price and stock purchasing cost constant Yes
Pervin et al. (2020) NA time & price NA constant Yes
Roy et al. (2020) NA probabilistic Constant Weibull Yes
This paper Consider time, reliability, advertisement reliability probabilistic Yes
Table 2.  Comparison of the proposed model for deterioration
Range of $ \theta $ Distribution $ \theta $ $ \mathbf{T} _{1}^{\ast } $ $ \mathbf{T}_{2}^{\ast } $ $ \mathbf{TC}\left( T_{1}^{\ast }, \text{ }T_{2}^{\ast }\right) \mathbf{(＄)} $
$ \mathbf{0.7\leq 0.9} $ Uniform $ \mathbf{0.8} $ $ \mathbf{0.166} $ $ \mathbf{0.418} $ $ \mathbf{151.144} $
$ \mathbf{0.7\leq 0.85\leq 0.9} $ Triangular $ \mathbf{0.82} $ $ \mathbf{\ 0.142} $ $ \mathbf{0.418} $ $ \mathbf{151.615} $
$ \mathbf{0.7\leq 0.85\leq 0.9} $ Double Triangular $ \mathbf{0.83} $ $ \mathbf{0.13} $ $ \mathbf{0.418} $ $ \mathbf{151.795} $
$ \mathbf{0.8\leq 0.9} $ Uniform $ \mathbf{0.85} $ $ \mathbf{0.108} $ $ \mathbf{0.418} $ $ \mathbf{152.07} $
$ \mathbf{0.8\leq 0.83\leq 0.9} $ Triangular $ \mathbf{0.84} $ $ \mathbf{\ 0.119} $ $ \mathbf{0.418} $ $ \mathbf{151.946} $
$ \mathbf{0.8\leq 0.83\leq 0.9} $ Double Triangular $ \mathbf{0.83} $ $ \mathbf{0.13} $ $ \mathbf{0.418} $ $ \mathbf{151.795} $
$ \mathbf{0.76\leq 0.96} $ Uniform $ \mathbf{0.86} $ $ \mathbf{0.098} $ $ \mathbf{0.418} $ $ \mathbf{152.171} $
$ \mathbf{0.76\leq 0.83\leq 0.96} $ Triangular $ \mathbf{0.85} $ $ \mathbf{\ 0.108} $ $ \mathbf{0.418} $ $ \mathbf{152.07} $
$ \mathbf{0.76\leq 0.83\leq 0.96} $ Double Triangular $ \mathbf{0.84} $ $ \mathbf{0.119} $ $ \mathbf{0.418} $ $ \mathbf{151.946} $
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Range of $ \theta $ Distribution $ \theta $ $ \mathbf{T} _{1}^{\ast } $ $ \mathbf{T}_{2}^{\ast } $ $ \mathbf{TC}\left( T_{1}^{\ast }, \text{ }T_{2}^{\ast }\right) \mathbf{(＄)} $
$ \mathbf{0.7\leq 0.9} $ Uniform $ \mathbf{0.8} $ $ \mathbf{0.166} $ $ \mathbf{0.418} $ $ \mathbf{151.144} $
$ \mathbf{0.7\leq 0.85\leq 0.9} $ Triangular $ \mathbf{0.82} $ $ \mathbf{\ 0.142} $ $ \mathbf{0.418} $ $ \mathbf{151.615} $
$ \mathbf{0.7\leq 0.85\leq 0.9} $ Double Triangular $ \mathbf{0.83} $ $ \mathbf{0.13} $ $ \mathbf{0.418} $ $ \mathbf{151.795} $
$ \mathbf{0.8\leq 0.9} $ Uniform $ \mathbf{0.85} $ $ \mathbf{0.108} $ $ \mathbf{0.418} $ $ \mathbf{152.07} $
$ \mathbf{0.8\leq 0.83\leq 0.9} $ Triangular $ \mathbf{0.84} $ $ \mathbf{\ 0.119} $ $ \mathbf{0.418} $ $ \mathbf{151.946} $
$ \mathbf{0.8\leq 0.83\leq 0.9} $ Double Triangular $ \mathbf{0.83} $ $ \mathbf{0.13} $ $ \mathbf{0.418} $ $ \mathbf{151.795} $
$ \mathbf{0.76\leq 0.96} $ Uniform $ \mathbf{0.86} $ $ \mathbf{0.098} $ $ \mathbf{0.418} $ $ \mathbf{152.171} $
$ \mathbf{0.76\leq 0.83\leq 0.96} $ Triangular $ \mathbf{0.85} $ $ \mathbf{\ 0.108} $ $ \mathbf{0.418} $ $ \mathbf{152.07} $
$ \mathbf{0.76\leq 0.83\leq 0.96} $ Double Triangular $ \mathbf{0.84} $ $ \mathbf{0.119} $ $ \mathbf{0.418} $ $ \mathbf{151.946} $
Table 3.  Sensitivity analysis of the proposed inventory system for parameters
Parameter Change(%) $ T_{1} $ $ T_{2} $ $ TC $ Change $ TC(\%) $
$ -20 $ $ 0.166 $ $ 0.334 $ $ 143.064 $ $ -5.346 $
$ T $ $ -10 $ $ 0.166 $ $ 0.376 $ $ 146.444 $ $ -3.110 $
$ 10 $ $ 0.166 $ $ 0.459 $ $ 156.796 $ $ 3.739 $
$ 20 $ $ 0.166 $ $ 0.501 $ $ 163.153 $ $ 7.946 $
$ -20 $ $ 0.166 $ $ 0.418 $ $ 96.319 $ $ -36.274 $
$ A $ $ -10 $ $ 0.166 $ $ 0.418 $ $ 119.950 $ $ -20.639 $
$ 10 $ $ 0.166 $ $ 0.418 $ $ 191.193 $ $ 26.498 $
$ 20 $ $ 0.166 $ $ 0.418 $ $ 241.458 $ $ 59.754 $
$ -20 $ $ 0.085 $ $ 0.442 $ $ 140.954 $ $ -6.742 $
$ C_{d} $ $ -10 $ $ 0.127 $ $ 0.430 $ $ 146.384 $ $ -3.149 $
$ 10 $ $ 0.201 $ $ 0.406 $ $ 155.207 $ $ 2.688 $
$ 20 $ $ 0.235 $ $ 0.396 $ $ 158.566 $ $ 4.911 $
$ -20 $ $ 0.250 $ $ 0.431 $ $ 142.313 $ $ -5.843 $
$ C_{h} $ $ -10 $ $ 0.205 $ $ 0.424 $ $ 147.077 $ $ -2.691 $
$ 10 $ $ 0.131 $ $ 0.411 $ $ 154.715 $ $ 2.363 $
$ 20 $ $ 0.099 $ $ 0.405 $ $ 157.929 $ $ 4.489 $
$ -20 $ $ 0.166 $ $ 0.365 $ $ 116.975 $ $ -22.607 $
$ C_{s} $ $ -10 $ $ 0.166 $ $ 0.392 $ $ 134.803 $ $ -10.812 $
$ 10 $ $ 0.166 $ $ 0.441 $ $ 166.178 $ $ 9.947 $
$ 20 $ $ 0.166 $ $ 0.462 $ $ 180.055 $ $ 19.128 $
$ -20 $ $ 0.166 $ $ 0.430 $ $ 178.469 $ $ 18.079 $
$ C_{l} $ $ -10 $ $ 0.166 $ $ 0.424 $ $ 164.852 $ $ 9.069 $
$ 10 $ $ 0.166 $ $ 0.411 $ $ 137.350 $ $ -9.126 $
$ 20 $ $ 0.166 $ $ 0.405 $ $ 123.473 $ $ -18.308 $
$ -10 $ $ 0.074 $ $ 0.400 $ $ 151.598 $ $ 0.300 $
$ r $ $ -5 $ $ 0.121 $ $ 0.409 $ $ 151.493 $ $ 0.231 $
$ 5 $ $ 0.210 $ $ 0.425 $ $ 150.459 $ $ -0.453 $
$ 10 $ $ 0.252 $ $ 0.431 $ $ 149.375 $ $ -1.171 $
$ -10 $ $ 0.283 $ $ 0.418 $ $ 146.868 $ $ -2.829 $
$ \theta $ $ -5 $ $ 0.220 $ $ 0.418 $ $ 149.608 $ $ -1.016 $
$ 5 $ $ 0.119 $ $ 0.418 $ $ 151.946 $ $ 0.530 $
$ 10 $ $ 0.079 $ $ 0.418 $ $ 152.317 $ $ 0.776 $
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Parameter Change(%) $ T_{1} $ $ T_{2} $ $ TC $ Change $ TC(\%) $
$ -20 $ $ 0.166 $ $ 0.334 $ $ 143.064 $ $ -5.346 $
$ T $ $ -10 $ $ 0.166 $ $ 0.376 $ $ 146.444 $ $ -3.110 $
$ 10 $ $ 0.166 $ $ 0.459 $ $ 156.796 $ $ 3.739 $
$ 20 $ $ 0.166 $ $ 0.501 $ $ 163.153 $ $ 7.946 $
$ -20 $ $ 0.166 $ $ 0.418 $ $ 96.319 $ $ -36.274 $
$ A $ $ -10 $ $ 0.166 $ $ 0.418 $ $ 119.950 $ $ -20.639 $
$ 10 $ $ 0.166 $ $ 0.418 $ $ 191.193 $ $ 26.498 $
$ 20 $ $ 0.166 $ $ 0.418 $ $ 241.458 $ $ 59.754 $
$ -20 $ $ 0.085 $ $ 0.442 $ $ 140.954 $ $ -6.742 $
$ C_{d} $ $ -10 $ $ 0.127 $ $ 0.430 $ $ 146.384 $ $ -3.149 $
$ 10 $ $ 0.201 $ $ 0.406 $ $ 155.207 $ $ 2.688 $
$ 20 $ $ 0.235 $ $ 0.396 $ $ 158.566 $ $ 4.911 $
$ -20 $ $ 0.250 $ $ 0.431 $ $ 142.313 $ $ -5.843 $
$ C_{h} $ $ -10 $ $ 0.205 $ $ 0.424 $ $ 147.077 $ $ -2.691 $
$ 10 $ $ 0.131 $ $ 0.411 $ $ 154.715 $ $ 2.363 $
$ 20 $ $ 0.099 $ $ 0.405 $ $ 157.929 $ $ 4.489 $
$ -20 $ $ 0.166 $ $ 0.365 $ $ 116.975 $ $ -22.607 $
$ C_{s} $ $ -10 $ $ 0.166 $ $ 0.392 $ $ 134.803 $ $ -10.812 $
$ 10 $ $ 0.166 $ $ 0.441 $ $ 166.178 $ $ 9.947 $
$ 20 $ $ 0.166 $ $ 0.462 $ $ 180.055 $ $ 19.128 $
$ -20 $ $ 0.166 $ $ 0.430 $ $ 178.469 $ $ 18.079 $
$ C_{l} $ $ -10 $ $ 0.166 $ $ 0.424 $ $ 164.852 $ $ 9.069 $
$ 10 $ $ 0.166 $ $ 0.411 $ $ 137.350 $ $ -9.126 $
$ 20 $ $ 0.166 $ $ 0.405 $ $ 123.473 $ $ -18.308 $
$ -10 $ $ 0.074 $ $ 0.400 $ $ 151.598 $ $ 0.300 $
$ r $ $ -5 $ $ 0.121 $ $ 0.409 $ $ 151.493 $ $ 0.231 $
$ 5 $ $ 0.210 $ $ 0.425 $ $ 150.459 $ $ -0.453 $
$ 10 $ $ 0.252 $ $ 0.431 $ $ 149.375 $ $ -1.171 $
$ -10 $ $ 0.283 $ $ 0.418 $ $ 146.868 $ $ -2.829 $
$ \theta $ $ -5 $ $ 0.220 $ $ 0.418 $ $ 149.608 $ $ -1.016 $
$ 5 $ $ 0.119 $ $ 0.418 $ $ 151.946 $ $ 0.530 $
$ 10 $ $ 0.079 $ $ 0.418 $ $ 152.317 $ $ 0.776 $
Table 4.  Sensitivity analysis of the proposed inventory model for parameters
ParameterChange(%) $ T_{1} $ $ T_{2} $ $ TC $ Change $ TC(\%) $
$ -20 $ $ 0.306 $ $ 0.418 $ $ 145.956 $ $ -3.432 $
$ a $ $ -10 $ $ 0.227 $ $ 0.418 $ $ 149.419 $ $ -1.141 $
$ 10 $ $ 0.116 $ $ 0.418 $ $ 151.970 $ $ 0.547 $
$ 20 $ $ 0.076 $ $ 0.418 $ $ 152.329 $ $ 0.784 $
$ -10 $ $ 0.047 $ $ 0.436 $ $ 160.574 $ $ 6.239 $
$ b $ $ -5 $ $ 0.106 $ $ 0.427 $ $ 156.287 $ $ 3.403 $
$ 5 $ $ 0.227 $ $ 0.409 $ $ 144.764 $ $ -4.221 $
$ 10 $ $ 0.289 $ $ 0.400 $ $ 136.737 $ $ -9.532 $
$ -20 $ $ 0.058 $ $ 0.418 $ $ 131.929 $ $ -12.713 $
$ c $ $ -10 $ $ 0.111 $ $ 0.418 $ $ 141.825 $ $ -6.166 $
$ 10 $ $ 0.221 $ $ 0.418 $ $ 159.594 $ $ 5.591 $
$ 20 $ $ 0.278 $ $ 0.418 $ $ 166.861 $ $ 10.399 $
$ -20 $ $ 0.166 $ $ 0.418 $ $ 82.784 $ $ -45.784 $
$ \nu $ $ -10 $ $ 0.166 $ $ 0.418 $ $ 107.584 $ $ -28.820 $
$ 10 $ $ 0.166 $ $ 0.418 $ $ 227.656 $ $ 50.622 $
$ 20 $ $ 0.166 $ $ 0.418 $ $ 362.046 $ $ 139.537 $
$ -20 $ $ 0.166 $ $ 0.418 $ $ 155.908 $ $ 3.152 $
$ k $ $ -10 $ $ 0.166 $ $ 0.418 $ $ 153.499 $ $ 1.558 $
$ 10 $ $ 0.166 $ $ 0.418 $ $ 148.843 $ $ -1.523 $
$ 20 $ $ 0.166 $ $ 0.418 $ $ 146.594 $ $ -3.010 $
$ -20 $ $ 0.166 $ $ 0.418 $ $ 151.242 $ $ 0.065 $
$ \lambda $ $ -10 $ $ 0.166 $ $ 0.418 $ $ 151.193 $ $ 0.032 $
$ 10 $ $ 0.166 $ $ 0.417 $ $ 151.095 $ $ -0.032 $
$ 20 $ $ 0.166 $ $ 0.417 $ $ 151.046 $ $ -0.065 $
$ -20 $ $ 0.218 $ $ 0.426 $ $ 145.779 $ $ -3.550 $
$ u $ $ -10 $ $ 0.192 $ $ 0.422 $ $ 148.496 $ $ -1.752 $
$ 10 $ $ 0.140 $ $ 0.413 $ $ 153.738 $ $ 1.716 $
$ 20 $ $ 0.115 $ $ 0.408 $ $ 156.298 $ $ 3.410 $
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ParameterChange(%) $ T_{1} $ $ T_{2} $ $ TC $ Change $ TC(\%) $
$ -20 $ $ 0.306 $ $ 0.418 $ $ 145.956 $ $ -3.432 $
$ a $ $ -10 $ $ 0.227 $ $ 0.418 $ $ 149.419 $ $ -1.141 $
$ 10 $ $ 0.116 $ $ 0.418 $ $ 151.970 $ $ 0.547 $
$ 20 $ $ 0.076 $ $ 0.418 $ $ 152.329 $ $ 0.784 $
$ -10 $ $ 0.047 $ $ 0.436 $ $ 160.574 $ $ 6.239 $
$ b $ $ -5 $ $ 0.106 $ $ 0.427 $ $ 156.287 $ $ 3.403 $
$ 5 $ $ 0.227 $ $ 0.409 $ $ 144.764 $ $ -4.221 $
$ 10 $ $ 0.289 $ $ 0.400 $ $ 136.737 $ $ -9.532 $
$ -20 $ $ 0.058 $ $ 0.418 $ $ 131.929 $ $ -12.713 $
$ c $ $ -10 $ $ 0.111 $ $ 0.418 $ $ 141.825 $ $ -6.166 $
$ 10 $ $ 0.221 $ $ 0.418 $ $ 159.594 $ $ 5.591 $
$ 20 $ $ 0.278 $ $ 0.418 $ $ 166.861 $ $ 10.399 $
$ -20 $ $ 0.166 $ $ 0.418 $ $ 82.784 $ $ -45.784 $
$ \nu $ $ -10 $ $ 0.166 $ $ 0.418 $ $ 107.584 $ $ -28.820 $
$ 10 $ $ 0.166 $ $ 0.418 $ $ 227.656 $ $ 50.622 $
$ 20 $ $ 0.166 $ $ 0.418 $ $ 362.046 $ $ 139.537 $
$ -20 $ $ 0.166 $ $ 0.418 $ $ 155.908 $ $ 3.152 $
$ k $ $ -10 $ $ 0.166 $ $ 0.418 $ $ 153.499 $ $ 1.558 $
$ 10 $ $ 0.166 $ $ 0.418 $ $ 148.843 $ $ -1.523 $
$ 20 $ $ 0.166 $ $ 0.418 $ $ 146.594 $ $ -3.010 $
$ -20 $ $ 0.166 $ $ 0.418 $ $ 151.242 $ $ 0.065 $
$ \lambda $ $ -10 $ $ 0.166 $ $ 0.418 $ $ 151.193 $ $ 0.032 $
$ 10 $ $ 0.166 $ $ 0.417 $ $ 151.095 $ $ -0.032 $
$ 20 $ $ 0.166 $ $ 0.417 $ $ 151.046 $ $ -0.065 $
$ -20 $ $ 0.218 $ $ 0.426 $ $ 145.779 $ $ -3.550 $
$ u $ $ -10 $ $ 0.192 $ $ 0.422 $ $ 148.496 $ $ -1.752 $
$ 10 $ $ 0.140 $ $ 0.413 $ $ 153.738 $ $ 1.716 $
$ 20 $ $ 0.115 $ $ 0.408 $ $ 156.298 $ $ 3.410 $
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