International Journal of Nonlinear Analysis and Applications
Production planning for controllable deteriorating items with price and stock dependent demand rate
Document Type : Research Paper
Authors
Department of Mathematics and Statistics, Dr. Harisingh Gour Vishwavidyalaya, A Central University, Sagar M.P., India
Abstract
In this paper, an Economic Production Quantity (EPQ) inventory model for deteriorating items with price-stock dependent demand rate under complete and partial backlog is developed, in which the deterioration rate is controlled by investment in preservation technology. To fulfil the demand and to reduce the shortage we have considered the production rate proportional to the selling price of the product. This study is to maximize the total profit for seasonal deteriorating items by simultaneously determining the optimal selling price, the optimal production and the optimal preservation technology cost when the producer invests in the preservation technology to reduce the deterioration rate. We first show that for any given number of the production cycle, optimal selling price and preservation technology cost exists and are unique. Next, we show that the total profit is a jointly concave function of selling price and preservation technology cost. We provide some conditions to determine an optimal solution that maximizes profits for the EPQ model. We then provide a simple algorithm to figure out the optimality of total profit for the proposed model. Mathematical theorems are developed to determine optimal inventory policy. Numerical results demonstrate the advantages of the preservation technology, and further show the effects of different system parameters on the optimal variables and the maximal total profit. Finally, some managerial implications are provided.
Keywords
[1] P.L. Abad, Optimal pricing and lot-sizing under conditions of perishability and partial backordering, Manag. Sci.
42 (1996), no. 8, 1093–1104.
[2] P.L. Abad, Optimal lot size for a perishable good under conditions of finite production and partial backordering
and lost sale, Comput. Ind. Eng. 38 (2000), no. 4, 457–465.
[3] L.E. C´ardenas-Barr´on, H.M. Wee and J.T. Teng, A supplement to ‘using the EPQ to coordinated planning of a
product with partial backordering and its components’, Math. Comput. Model. 54 (2011), no. 1–2, 852–857.
[4] S. Chandra Das, A.M. Zidan, A.K. Manna, A.A. Shaikh and A.K. Bhunia, An application of preservation
technology in inventory control system with price dependent demand and partial backlogging, Alexandria Eng. J.
59 (2020), no. 3, 1359–1369.
[5] T. Chakrabarti and K.S. Chaudhuri, An EOQ model for deteriorating items with a linear trend in demand and
shortages in all cycles, Internat. J. Prod. Econ. 49(3) (1997) 205–213.[6] J.M. Chen and L.T. Chen, Pricing and production lot-size/scheduling with finite capacity for a deteriorating item
over a finite horizon, Comput. Oper. Res. 32 (2005), no. 11, 2801–2819.
[7] T.H. Chen and J.M. Chen, Optimal pricing and replenishment policy for a deteriorating item in a two-echelon
supply chain, J. Stat. Manag. Syst. 9 (2006), no. 2, 285–299.
[8] K.J. Chung, L.E. C´ardenas-Barr´on and P.S. Ting, An inventory model with non-instantaneous receipt and exponentially deteriorating items for an integrated three layer supply chain system under two levels of trade credit,
Internat. J. Prod. Econ. 155 (2014), 310–317.
[9] C.Y. Dye, Joint pricing and ordering policy for a deteriorating inventory with partial backlogging, Omega 35
(2007), no. 2, 184–189.
[10] C.Y. Dye and T.P. Hsieh, An optimal replenishment policy for deteriorating items with effective investment in
preservation technology, Eur. J. Oper. Res. 218 (2012), no. 1, 106–112.
[11] C.Y. Dye, The effect of preservation technology investment on a non-instantaneous deteriorating inventory model,
Omega 41 (2013), no. 5, 872–880.
[12] P.M. Ghare and G.H. Schrader, A model for exponentially decaying inventory system, J. Ind. Eng. 14 (1963),
238–243.
[13] B.C. Giri and S. Bardhan, Supply chain coordination for a deteriorating item with stock and price-dependent
demand under revenue sharing contract, Internat. Trans. Oper. Res. 19 (2012), no. 5, 753–768.
[14] R. Goel, P.S. Singh and S. Sharma, Supply chain model with stock dependent demand, quadratic rate of deterioration with allowable shortage, Internat. J. Math. Oper. Res. 7 (2015), no. 2, 156–177.
[15] T.P. Hsieh and C.Y. Dye, A production-inventory model incorporating the effect of preservation technology investment when demand is fluctuating with time, J. Comput. Appl. Math. 239 (2013), 25–36.
[16] P.H. Hsu, H.M. Wee and H.M. Teng, Preservation technology investment for deteriorating inventory, Internat. J.
Prod. Econ. 124 (2010), no. 2, 388–394.
[17] A. Kabirian, The economic production and pricing model with lot-size-dependent production cost, J. Glob. Optim.
54 (2012), 1–15.
[18] S. Karray, Cooperative promotions in the distribution channel, Omega 51 (2015), 49–58.
[19] U.K. Khedlekar, A. Namdeo and A. Nigwal, Production inventory model with disruption considering shortage and
time proportional demand, Yugosl. J. Oper. Res. 28 (2018), no. 1, 123–139.
[20] U.K. Khedlekar and P. Singh, Three-layer supply chain policy under sharing recycling responsibility, J. Adv.
Manag. Res. 16 (2019), no. 5, 734–762.
[21] U.K. Khedlekar, P. Singh and N. Gupta, Dynamic pricing policy using preservation technology with stock and
price sensitive demand, J. Indones. Math. Soc. 2020 (2020), 266–274.
[22] Y.P. Lee and C.Y. Dye, An inventory model for deteriorating items under stock-dependent demand and controllable
deterioration rate, Comput. Ind. Eng. 63 (2012), no. 2, 474–482.
[23] G. Li, X. He, J. Zhou and H. Wu, Pricing, replenishment and preservation technology investment decisions for
non-instantaneous deteriorating items, Omega 2018 (2018), 1–33.
[24] L. Liu, L. Zhao and X. Ren, Optimal preservation technology investment and pricing policy for fresh food, Comput.
Ind. Eng. 135 (2019), 746–756.
[25] C. Liuxin, C. Xian, M.F. Keblis and L. Gen, Optimal pricing and replenishment policy for deteriorating inventory
under stock-level-dependent, time-varying and price-dependent demand, Comput. Ind. Eng. 2018 (2018), 1–15.
[26] L. Lu, J. Zhang and W. Tang, Optimal dynamic pricing and replenishment policy for perishable items with
inventory-level-dependent demand, Internat. J. Syst. Sci. 47 (2014), no. 6, 1480–1494.
[27] P. Mahata, A. Gupta and G.C. Mahata, Optimal pricing and ordering policy for an EPQ inventory system with
perishable items under partial trade credit financing, Internat. J. Oper. Res. 21 (2014), no. 2, 221–251.
[28] G.C. Mahata, An integrated production-inventory model with back order and lot for lot policy in fuzzy sense,Internat. J. Math. Oper. Res. 7 (2015), no. 1, 69–102.
[29] R. Maihami and I.N. Kamalabadi, Joint pricing and inventory control for non-instantaneous deteriorating items
with partial backlogging and time and price dependent demand, Internat. J. Prod. Econ. 136 (2012), no. 1, 116–122.
[30] S.K. Manna and K.S. Chaudhuri, An EOQ model with ramp type demand rate, time dependent deterioration rate,
unit production cost and shortages, Eur. J. Oper. Res. 171 (2006), no. 2, 557-566.
[31] V.K. Mishra, An inventory model of instantaneous deteriorating items with controllable deterioration rate for time
dependent demand and holding cost, J. Ind. Eng. Manag. 6 (2013), no. 2, 496–506.
[32] V.K. Mishra, Inventory model of deteriorating items with revenue sharing on preservation technology investment
under price sensitive stock dependent demand, Internat. J. Math. Model. Comput. 21 (2016), no. 6, 37–48.
[33] U. Mishra, L.E. C´ardenas-Barr´on, S. Tiwari, A.A. Shaikh and G. Trevi˜no-Garza, An inventory model under
price and stock dependent demand for controllable deterioration rate with shortages and preservation technology
investment, Ann. Oper. Res. 254 (2017), no. 1–2, 165–190.
[34] D.P. Murr and L.L. Morris, Effect of storage temperature on post change in mushrooms, J. Amer. Soc. Horticul.
Sci. 100 (1975), 16–19.
[35] M. Onal, A. Yenipazarli and O. Erhun Kundakcioglu, A mathematical model for perishable products with priceand displayed-stock-dependent demand, Comput. Ind. Eng. 102 (2016), 1–32.
[36] M. Palanivel and R. Uthayakumar, An EPQ model with variable production probabilistic deterioration and partial
backlogging under inflation, J. Manag. Anal. 1 (2014), no. 3, 200–223.
[37] V. Pando, L.A. San-Jos´e, J. Garc´ıa-Laguna and J. Sicilia, Optimal lot-size policy for deteriorating items with
stock-dependent demand considering profit maximization, Comput. Ind. Engin. 117 (2018), 81–93.
[38] S. Papachristos and K. Skouri, An inventory model with deteriorating items, quantity discount, pricing and timedependent partial backlogging, Internat. J. Prod. Econ. 83 (2003), no. 3, 247–256.
[39] J. Ray and K.S. Chaudhuri, An EOQ model with stock-dependent demand, shortage, inflation and time discounting, Internat. J. Prod. Econ. 53 (1997), no. 2, 171–180.
[40] D.D. Salookolaeia, P. Babaeia and S. Heydari Gorjib, Prediction of Renewable Energy Production Using Grey
Systems Theory, Int. J. Nonlinear Anal. Appl. 10 (2019), 39–51.
[41] S. Sana, S.K. Goyal and K.S. Chaudhuri, A production-inventory model for a deteriorating item with trended
demand and shortages, Eur. J. Oper. Res. 157 (2004), no. 2, 357–371.
[42] B. Sarkar, A production-inventory model with probabilistic deterioration in two-echelon supply chain management,
Appl. Math. Model. 37 (2013), no. 5, 3138–3151.
[43] M. Sarkar and B. Sarkar, An economic manufacturing quantity model with probabilistic deterioration in a production system, Econ. Model. 31 (2013), no. 2, 245–252.
[44] B. Sarkar, B. Mandal and S. Sarkar, Preservation of deteriorating seasonal products with stock-dependent consumption rate and shortages, J. Ind. Manag. Optim. 13 (2017), no. 1, 187–206.
[45] N.H. Shah, D.B. Shah and D.G. Patel, Optimal preservation technology investment, retail price and ordering policies for deteriorating items under trended demand and two-level trade credit financing, J. Math. Model. Algorithms
Oper. Res. 14 (2015), no. 1. 1–12.
[46] S. Singh, S. R. Singh and S. Sharma, A partially backlogged EPQ model with demand dependent production and
non-instantaneous deterioration, Internat. J. Math. Oper. Res. 10 (2017), no. 2, 211–228.
[47] K. Skouri, I. Konstantaras, S. K. Manna and K. S. Chaudhuri, Inventory models with ramp type demand rate,
time dependent deterioration rate, unit production cost and shortages, Ann. Oper. Res. 191 (2011), no. 1, 73–95.
[48] N. Tashakkor, S. H. Mirmohammadi and M. Iranpoor, Joint optimization of dynamic pricing and replenishment
cycle considering variable non-instantaneous deterioration and stock-dependent demand, Comput. Ind. Eng. 123
(2018), 232–241.
[49] J.T. Teng and C.T. Chang, Economic production quantity models for deteriorating items with price- and stock-dependent demand, Comput. Oper. Res. 32 (2005), no. 2, 297–308.
[50] X. Wang and D. Li, A dynamic product quality evaluation based pricing model for perishable food supply chains,
Omega 40 (2012), no. 6, 906–917.
[51] H.M. Wee, Economic production lot size model for deteriorating items with partial back-ordering, Comput. Ind.
Eng. 24 (1993), no. 3, 449–458.
[52] H.M. Wee and W.T. Wang, A variable production scheduling policy for deteriorating items with time-varying
demand, Comput. Oper. Res. 26 (1999), 237–254.
[53] K.S. Wu, L.Y. Ouyang and C.T. Yang, An optimal replenishment policy for non-instantaneous deteriorating items
with stock-dependent demand and partial backlogging, Internat. J. Prod. Econ. 101 (2006), no. 2, 369–384.
[54] Y. Yang, H. Chi, W. Zhou, T. Fan and S. Piramuthu, Deterioration control decision support for perishable
inventory management, Decis. Supp. Syst. 2020 (2020), 1–9.
[55] J.X. Zhang, Z.Y. Bai and W.S. Tang, Optimal pricing policy for deteriorating items with preservation technology
investment, J. Ind. Manag. Optim. 10 (2014), no. 4, 1261–1277.
[56] J. Zhang, G. Liu, Q. Zhang and Z. Bai, Coordinating a supply chain for deteriorating items with a revenue sharing
and cooperative investment contract, Omega 56 (2015) 37–49.
[57] L. Zhang, J. Wang and J. You, Consumer environmental awareness and channel coordination with two substitutable
products, Eur. J. Oper. Res. 241 (2015), no.1, 63–73.
[58] Y.W. Zhou, H.S. Laub and S.L. Yang, A new variable production scheduling strategy for deteriorating items with
time-varying demand and partial lost sale, Comput. Oper. Res. 30 (2003), 1753–1776.
42 (1996), no. 8, 1093–1104.
[2] P.L. Abad, Optimal lot size for a perishable good under conditions of finite production and partial backordering
and lost sale, Comput. Ind. Eng. 38 (2000), no. 4, 457–465.
[3] L.E. C´ardenas-Barr´on, H.M. Wee and J.T. Teng, A supplement to ‘using the EPQ to coordinated planning of a
product with partial backordering and its components’, Math. Comput. Model. 54 (2011), no. 1–2, 852–857.
[4] S. Chandra Das, A.M. Zidan, A.K. Manna, A.A. Shaikh and A.K. Bhunia, An application of preservation
technology in inventory control system with price dependent demand and partial backlogging, Alexandria Eng. J.
59 (2020), no. 3, 1359–1369.
[5] T. Chakrabarti and K.S. Chaudhuri, An EOQ model for deteriorating items with a linear trend in demand and
shortages in all cycles, Internat. J. Prod. Econ. 49(3) (1997) 205–213.[6] J.M. Chen and L.T. Chen, Pricing and production lot-size/scheduling with finite capacity for a deteriorating item
over a finite horizon, Comput. Oper. Res. 32 (2005), no. 11, 2801–2819.
[7] T.H. Chen and J.M. Chen, Optimal pricing and replenishment policy for a deteriorating item in a two-echelon
supply chain, J. Stat. Manag. Syst. 9 (2006), no. 2, 285–299.
[8] K.J. Chung, L.E. C´ardenas-Barr´on and P.S. Ting, An inventory model with non-instantaneous receipt and exponentially deteriorating items for an integrated three layer supply chain system under two levels of trade credit,
Internat. J. Prod. Econ. 155 (2014), 310–317.
[9] C.Y. Dye, Joint pricing and ordering policy for a deteriorating inventory with partial backlogging, Omega 35
(2007), no. 2, 184–189.
[10] C.Y. Dye and T.P. Hsieh, An optimal replenishment policy for deteriorating items with effective investment in
preservation technology, Eur. J. Oper. Res. 218 (2012), no. 1, 106–112.
[11] C.Y. Dye, The effect of preservation technology investment on a non-instantaneous deteriorating inventory model,
Omega 41 (2013), no. 5, 872–880.
[12] P.M. Ghare and G.H. Schrader, A model for exponentially decaying inventory system, J. Ind. Eng. 14 (1963),
238–243.
[13] B.C. Giri and S. Bardhan, Supply chain coordination for a deteriorating item with stock and price-dependent
demand under revenue sharing contract, Internat. Trans. Oper. Res. 19 (2012), no. 5, 753–768.
[14] R. Goel, P.S. Singh and S. Sharma, Supply chain model with stock dependent demand, quadratic rate of deterioration with allowable shortage, Internat. J. Math. Oper. Res. 7 (2015), no. 2, 156–177.
[15] T.P. Hsieh and C.Y. Dye, A production-inventory model incorporating the effect of preservation technology investment when demand is fluctuating with time, J. Comput. Appl. Math. 239 (2013), 25–36.
[16] P.H. Hsu, H.M. Wee and H.M. Teng, Preservation technology investment for deteriorating inventory, Internat. J.
Prod. Econ. 124 (2010), no. 2, 388–394.
[17] A. Kabirian, The economic production and pricing model with lot-size-dependent production cost, J. Glob. Optim.
54 (2012), 1–15.
[18] S. Karray, Cooperative promotions in the distribution channel, Omega 51 (2015), 49–58.
[19] U.K. Khedlekar, A. Namdeo and A. Nigwal, Production inventory model with disruption considering shortage and
time proportional demand, Yugosl. J. Oper. Res. 28 (2018), no. 1, 123–139.
[20] U.K. Khedlekar and P. Singh, Three-layer supply chain policy under sharing recycling responsibility, J. Adv.
Manag. Res. 16 (2019), no. 5, 734–762.
[21] U.K. Khedlekar, P. Singh and N. Gupta, Dynamic pricing policy using preservation technology with stock and
price sensitive demand, J. Indones. Math. Soc. 2020 (2020), 266–274.
[22] Y.P. Lee and C.Y. Dye, An inventory model for deteriorating items under stock-dependent demand and controllable
deterioration rate, Comput. Ind. Eng. 63 (2012), no. 2, 474–482.
[23] G. Li, X. He, J. Zhou and H. Wu, Pricing, replenishment and preservation technology investment decisions for
non-instantaneous deteriorating items, Omega 2018 (2018), 1–33.
[24] L. Liu, L. Zhao and X. Ren, Optimal preservation technology investment and pricing policy for fresh food, Comput.
Ind. Eng. 135 (2019), 746–756.
[25] C. Liuxin, C. Xian, M.F. Keblis and L. Gen, Optimal pricing and replenishment policy for deteriorating inventory
under stock-level-dependent, time-varying and price-dependent demand, Comput. Ind. Eng. 2018 (2018), 1–15.
[26] L. Lu, J. Zhang and W. Tang, Optimal dynamic pricing and replenishment policy for perishable items with
inventory-level-dependent demand, Internat. J. Syst. Sci. 47 (2014), no. 6, 1480–1494.
[27] P. Mahata, A. Gupta and G.C. Mahata, Optimal pricing and ordering policy for an EPQ inventory system with
perishable items under partial trade credit financing, Internat. J. Oper. Res. 21 (2014), no. 2, 221–251.
[28] G.C. Mahata, An integrated production-inventory model with back order and lot for lot policy in fuzzy sense,Internat. J. Math. Oper. Res. 7 (2015), no. 1, 69–102.
[29] R. Maihami and I.N. Kamalabadi, Joint pricing and inventory control for non-instantaneous deteriorating items
with partial backlogging and time and price dependent demand, Internat. J. Prod. Econ. 136 (2012), no. 1, 116–122.
[30] S.K. Manna and K.S. Chaudhuri, An EOQ model with ramp type demand rate, time dependent deterioration rate,
unit production cost and shortages, Eur. J. Oper. Res. 171 (2006), no. 2, 557-566.
[31] V.K. Mishra, An inventory model of instantaneous deteriorating items with controllable deterioration rate for time
dependent demand and holding cost, J. Ind. Eng. Manag. 6 (2013), no. 2, 496–506.
[32] V.K. Mishra, Inventory model of deteriorating items with revenue sharing on preservation technology investment
under price sensitive stock dependent demand, Internat. J. Math. Model. Comput. 21 (2016), no. 6, 37–48.
[33] U. Mishra, L.E. C´ardenas-Barr´on, S. Tiwari, A.A. Shaikh and G. Trevi˜no-Garza, An inventory model under
price and stock dependent demand for controllable deterioration rate with shortages and preservation technology
investment, Ann. Oper. Res. 254 (2017), no. 1–2, 165–190.
[34] D.P. Murr and L.L. Morris, Effect of storage temperature on post change in mushrooms, J. Amer. Soc. Horticul.
Sci. 100 (1975), 16–19.
[35] M. Onal, A. Yenipazarli and O. Erhun Kundakcioglu, A mathematical model for perishable products with priceand displayed-stock-dependent demand, Comput. Ind. Eng. 102 (2016), 1–32.
[36] M. Palanivel and R. Uthayakumar, An EPQ model with variable production probabilistic deterioration and partial
backlogging under inflation, J. Manag. Anal. 1 (2014), no. 3, 200–223.
[37] V. Pando, L.A. San-Jos´e, J. Garc´ıa-Laguna and J. Sicilia, Optimal lot-size policy for deteriorating items with
stock-dependent demand considering profit maximization, Comput. Ind. Engin. 117 (2018), 81–93.
[38] S. Papachristos and K. Skouri, An inventory model with deteriorating items, quantity discount, pricing and timedependent partial backlogging, Internat. J. Prod. Econ. 83 (2003), no. 3, 247–256.
[39] J. Ray and K.S. Chaudhuri, An EOQ model with stock-dependent demand, shortage, inflation and time discounting, Internat. J. Prod. Econ. 53 (1997), no. 2, 171–180.
[40] D.D. Salookolaeia, P. Babaeia and S. Heydari Gorjib, Prediction of Renewable Energy Production Using Grey
Systems Theory, Int. J. Nonlinear Anal. Appl. 10 (2019), 39–51.
[41] S. Sana, S.K. Goyal and K.S. Chaudhuri, A production-inventory model for a deteriorating item with trended
demand and shortages, Eur. J. Oper. Res. 157 (2004), no. 2, 357–371.
[42] B. Sarkar, A production-inventory model with probabilistic deterioration in two-echelon supply chain management,
Appl. Math. Model. 37 (2013), no. 5, 3138–3151.
[43] M. Sarkar and B. Sarkar, An economic manufacturing quantity model with probabilistic deterioration in a production system, Econ. Model. 31 (2013), no. 2, 245–252.
[44] B. Sarkar, B. Mandal and S. Sarkar, Preservation of deteriorating seasonal products with stock-dependent consumption rate and shortages, J. Ind. Manag. Optim. 13 (2017), no. 1, 187–206.
[45] N.H. Shah, D.B. Shah and D.G. Patel, Optimal preservation technology investment, retail price and ordering policies for deteriorating items under trended demand and two-level trade credit financing, J. Math. Model. Algorithms
Oper. Res. 14 (2015), no. 1. 1–12.
[46] S. Singh, S. R. Singh and S. Sharma, A partially backlogged EPQ model with demand dependent production and
non-instantaneous deterioration, Internat. J. Math. Oper. Res. 10 (2017), no. 2, 211–228.
[47] K. Skouri, I. Konstantaras, S. K. Manna and K. S. Chaudhuri, Inventory models with ramp type demand rate,
time dependent deterioration rate, unit production cost and shortages, Ann. Oper. Res. 191 (2011), no. 1, 73–95.
[48] N. Tashakkor, S. H. Mirmohammadi and M. Iranpoor, Joint optimization of dynamic pricing and replenishment
cycle considering variable non-instantaneous deterioration and stock-dependent demand, Comput. Ind. Eng. 123
(2018), 232–241.
[49] J.T. Teng and C.T. Chang, Economic production quantity models for deteriorating items with price- and stock-dependent demand, Comput. Oper. Res. 32 (2005), no. 2, 297–308.
[50] X. Wang and D. Li, A dynamic product quality evaluation based pricing model for perishable food supply chains,
Omega 40 (2012), no. 6, 906–917.
[51] H.M. Wee, Economic production lot size model for deteriorating items with partial back-ordering, Comput. Ind.
Eng. 24 (1993), no. 3, 449–458.
[52] H.M. Wee and W.T. Wang, A variable production scheduling policy for deteriorating items with time-varying
demand, Comput. Oper. Res. 26 (1999), 237–254.
[53] K.S. Wu, L.Y. Ouyang and C.T. Yang, An optimal replenishment policy for non-instantaneous deteriorating items
with stock-dependent demand and partial backlogging, Internat. J. Prod. Econ. 101 (2006), no. 2, 369–384.
[54] Y. Yang, H. Chi, W. Zhou, T. Fan and S. Piramuthu, Deterioration control decision support for perishable
inventory management, Decis. Supp. Syst. 2020 (2020), 1–9.
[55] J.X. Zhang, Z.Y. Bai and W.S. Tang, Optimal pricing policy for deteriorating items with preservation technology
investment, J. Ind. Manag. Optim. 10 (2014), no. 4, 1261–1277.
[56] J. Zhang, G. Liu, Q. Zhang and Z. Bai, Coordinating a supply chain for deteriorating items with a revenue sharing
and cooperative investment contract, Omega 56 (2015) 37–49.
[57] L. Zhang, J. Wang and J. You, Consumer environmental awareness and channel coordination with two substitutable
products, Eur. J. Oper. Res. 241 (2015), no.1, 63–73.
[58] Y.W. Zhou, H.S. Laub and S.L. Yang, A new variable production scheduling strategy for deteriorating items with
time-varying demand and partial lost sale, Comput. Oper. Res. 30 (2003), 1753–1776.
)
Volume 13, Issue 2
July 2022Pages 1419-1446
- Receive Date: 09 April 2020
- Revise Date: 11 August 2020
- Accept Date: 28 September 2020