Abstract
In the real market, the item’s demand is substantially affected by the item’s selling price and frequency of advertising. This study focuses on an optimal ordering policy followed by advertising, pricing, and preservation policies. The present study incorporates the quantity-dependent ordering cost and time-dependent holding cost. A partial prepayment scheme is developed for inventory purchase decisions. The spoilage impact can be effectively reduced by an optimal investment in refrigeration. The optimal decision policy has been proposed by using three metaheuristic algorithms, namely particle swarm optimization, real-coded genetic algorithm, and differential evolution algorithm. A comparison is made for these metaheuristic schemes based on the numerical illustrations. The parameter sensitivity is performed to get insights of the variability in the indicators of the inventory model.
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The proposed article studies a mathematical inventory model for deteriorating items. It includes an illustrative data set for numerical results. No additional data set was used in this study.
References
Al-Amin Khan M, Shaikh AA, Konstantaras I, Bhunia AK, Cárdenas-Barrón LE (2020) Inventory models for perishable items with advanced payment, linearly time-dependent holding cost and demand dependent on advertisement and selling price. Int J Prod Econ 230:107804. https://doi.org/10.1016/j.ijpe.2020.107804
Alfares HK, Ghaithan AM (2016) Inventory and pricing model with price-dependent demand, time-varying holding cost, and quantity discounts. Comput Ind Eng 94:170–177. https://doi.org/10.1016/j.cie.2016.02.009
Baker RC, Urban TL (1988) A deterministic inventory system with an inventory-level-dependent demand rate. J Oper Res Soc 39:823–831. https://doi.org/10.1057/jors.1988.142
Bakker M, Riezebos J, Teunter RH (2012) Review of inventory systems with deterioration since 2001. Eur J Oper Res 221:275–284. https://doi.org/10.1016/j.ejor.2012.03.004
Bakkouri I, Afdel K (2020) Computer-aided diagnosis (CAD) system based on multi-layer feature fusion network for skin lesion recognition in dermoscopy images. Multimed Tools Appl 79:20483–20518. https://doi.org/10.1007/s11042-019-07988-1
Bakkouri I, Afdel K (2022) MLCA2F: Multi-level context attentional feature fusion for COVID-19 lesion segmentation from CT scans. Signal Image Video Process. https://doi.org/10.1007/s11760-022-02325-w
Barton DE, Abramovitz M, Stegun IA (1965) Handbook of mathematical functions with formulas, graphs and mathematical tables. Dover Publications Inc. https://doi.org/10.2307/2343473
Cárdenas-Barrón LE, Shaikh AA, Tiwari S, Treviño-Garza G (2020) An EOQ inventory model with nonlinear stock dependent holding cost, nonlinear stock dependent demand and trade credit. Comput Ind Eng 139:105557. https://doi.org/10.1016/j.cie.2018.12.004
Chandra Das S, Zidan AM, Manna AK, Shaikh AA, Bhunia AK (2020) An application of preservation technology in inventory control system with price dependent demand and partial backlogging. Alex Eng J 59:1359–1369. https://doi.org/10.1016/j.aej.2020.03.006
Chen L, Chen X, Keblis MF, Li G (2019a) Optimal pricing and replenishment policy for deteriorating inventory under stock-level-dependent, time-varying and price-dependent demand. Comput Ind Eng 135:1294–1299. https://doi.org/10.1016/j.cie.2018.06.005
Chen Y, Yang L, Jiang Y, Wahab MIM, Yang J (2019b) Joint replenishment decision considering shortages, partial demand substitution, and defective items. Comput Ind Eng 127:420–435. https://doi.org/10.1016/j.cie.2018.10.031
Clerc M, Kennedy J (2002) The particle swarm-explosion, stability, and convergence in a multidimensional complex space. IEEE Trans Evol Comput 6:58–73. https://doi.org/10.1109/4235.985692
Covert RP, Philip GC (1973) An EOQ model for items with Weibull distribution deterioration. AIIE Trans 5:323–326. https://doi.org/10.1080/05695557308974918
Cui L, Deng J, Zhang Y, Zhang Z, Xu M (2020) The bare-bones differential evolutionary for stochastic joint replenishment with random number of imperfect items. Knowl Based Syst 193:105416. https://doi.org/10.1016/j.knosys.2019.105416
De SK, Sana SS (2015) Backlogging EOQ model for promotional effort and selling price sensitive demand- an intuitionistic fuzzy approach. Ann Oper Res 233:57–76. https://doi.org/10.1007/s10479-013-1476-3
Deep K, Thakur M (2007a) A new crossover operator for real coded genetic algorithms. Appl Math Comput 188:895–911. https://doi.org/10.1016/j.amc.2006.10.047
Deep K, Thakur M (2007b) A new mutation operator for real coded genetic algorithms. Appl Math Comput 193:211–230. https://doi.org/10.1016/j.amc.2007.03.046
Deep K, Singh KP, Kansal ML, Mohan C (2009) A real coded genetic algorithm for solving integer and mixed integer optimization problems. Appl Math Comput 212:505–518. https://doi.org/10.1016/j.amc.2009.02.044
Dye C-Y, Yang C-T (2016) Optimal dynamic pricing and preservation technology investment for deteriorating products with reference price effects. Omega 62:52–67. https://doi.org/10.1016/j.omega.2015.08.009
Ghare MP, Schrader GF (1963) A model for an exponentially decaying inventory. J Ind Engng 14:238–243
Giri BC, Chaudhuri KS (1998) Deterministic models of perishable inventory with stock-dependent demand rate and nonlinear holding cost. Eur J Oper Res 105:467–474. https://doi.org/10.1016/S0377-2217(97)00086-6
Goyal SK, Giri BC (2001) Recent trends in modeling of deteriorating inventory. Eur J Oper Res 134:1–16. https://doi.org/10.1016/S0377-2217(00)00248-4
Holland JH (1975) Adaptation in natural and artificial systems. University of Michigan Press
Hsu PH, Wee HM, Teng HM (2010) Preservation technology investment for deteriorating inventory. Int J Prod Econ 124:388–394. https://doi.org/10.1016/j.ijpe.2009.11.034
Jain M, Singh P (2022) Optimal inspection and advance payment policy for deteriorating items using differential evolution metaheuristic. Appl Soft Comput 128:109475. https://doi.org/10.1016/j.asoc.2022.109475
Jain M, Sharma DK, Sharma N (2022) Artificial intelligence computing and nature-inspired optimization techniques for effective supply chain management. In: Data Analytics and artificial intelligence for inventory and supply chain management. Inventory Optimization, Springer, Singapore, pp 63–80. https://doi.org/10.1007/978-981-19-6337-7_4
Jain M, Sharma N, Singh P (2023) Sustainable inventory prediction with random defect and rework using bat algorithm. RAIRO Oper Res 57(2):481–501. https://doi.org/10.1051/ro/2023011
Kennedy J, Eberhart R (1995) Particle swarm optimization. In: IEEE Int Conf Neural Networks - Conf Proc, IEEE, pp 1942–1948. https://doi.org/10.4018/ijmfmp.2015010104
Khakzad A, Gholamian MR (2020) The effect of inspection on deterioration rate: an inventory model for deteriorating items with advanced payment. J Clean Prod 254:120117. https://doi.org/10.1016/j.jclepro.2020.120117
Li R, Teng J-T (2018) Pricing and lot-sizing decisions for perishable goods when demand depends on selling price, reference price, product freshness, and displayed stocks. Eur J Oper Res 270:1099–1108. https://doi.org/10.1016/j.ejor.2018.04.029
Li G, He X, Zhou J, Wu H (2019) Pricing, replenishment and preservation technology investment decisions for non-instantaneous deteriorating items. Omega 84:114–126. https://doi.org/10.1016/j.omega.2018.05.001
Mahata P, Mahata GC, Mukherjee A (2019) An ordering policy for deteriorating items with price-dependent iso-elastic demand under permissible delay in payments and price inflation. Math Comput Model Dyn Syst 25:575–601. https://doi.org/10.1080/13873954.2019.1677724
Manna AK, Khan MA-A, Rahman MS, Shaikh AA, Bhunia AK (2022) Interval valued demand and prepayment-based inventory model for perishable items via parametric approach of interval and meta-heuristic algorithms. Knowl Based Syst 242:108343. https://doi.org/10.1016/j.knosys.2022.108343
Mishra VK, Singh LS, Kumar R (2013) An inventory model for deteriorating items with time-dependent demand and time-varying holding cost under partial backlogging. J Ind Eng Int 9:4. https://doi.org/10.1186/2251-712X-9-4
Mishra U, Cárdenas-Barrón LE, Tiwari S, Shaikh AA, Treviño-Garza G (2017) An inventory model under price and stock dependent demand for controllable deterioration rate with shortages and preservation technology investment. Ann Oper Res 254:165–190. https://doi.org/10.1007/s10479-017-2419-1
Ouyang L-Y, Wu K-S, Yang C-T (2006) A study on an inventory model for non-instantaneous deteriorating items with permissible delay in payments. Comput Ind Eng 51:637–651. https://doi.org/10.1016/j.cie.2006.07.012
Pal H, Bardhan S, Giri BC (2018) Optimal replenishment policy for non-instantaneously perishable items with preservation technology and random deterioration start time. Int J Manag Sci Eng Manag 13:188–199. https://doi.org/10.1080/17509653.2017.1372228
Palanivel M, Uthayakumar R (2015) Finite horizon EOQ model for non-instantaneous deteriorating items with price and advertisement dependent demand and partial backlogging under inflation. Int J Syst Sci 46:1762–1773. https://doi.org/10.1080/00207721.2013.835001
Pando V, Garcı´a-Laguna J, San-José LA, Sicilia J (2012) Maximizing profits in an inventory model with both demand rate and holding cost per unit time dependent on the stock level. Comput Ind Eng 62:599–608. https://doi.org/10.1016/j.cie.2011.11.009
Parsopoulos KE, Konstantaras I, Skouri K (2015) Metaheuristic optimization for the single-item dynamic lot sizing problem with returns and remanufacturing. Comput Ind Eng 83:307–315. https://doi.org/10.1016/j.cie.2015.02.014
Sadikur Rahman M, Al-Amin Khan M, Abdul Halim M, Nofal TA, Akbar Shaikh A, Mahmoud EE (2021) Hybrid price and stock dependent inventory model for perishable goods with advance payment related discount facilities under preservation technology. Alex Eng J 60:3455–3465. https://doi.org/10.1016/j.aej.2021.01.045
Sana SS (2010) Optimal selling price and lotsize with time varying deterioration and partial backlogging. Appl Math Comput 217:185–194. https://doi.org/10.1016/j.amc.2010.05.040
San-José LA, Sicilia J, García-Laguna J (2015) Analysis of an EOQ inventory model with partial backordering and non-linear unit holding cost. Omega 54:147–157. https://doi.org/10.1016/j.omega.2015.01.007
San-José LA, Sicilia J, Cárdenas-Barrón LE, Gutiérrez JM (2019) Optimal price and quantity under power demand pattern and non-linear holding cost. Comput Ind Eng 129:426–434. https://doi.org/10.1016/j.cie.2019.01.054
Sanni S, O’Neill B (2019) Inventory optimisation in a three-parameter Weibull model under a prepayment system. Comput Ind Eng 128:298–304. https://doi.org/10.1016/j.cie.2018.12.045
Shah NH, Soni HN, Patel KA (2013) Optimizing inventory and marketing policy for non-instantaneous deteriorating items with generalized type deterioration and holding cost rates. Omega 41:421–430. https://doi.org/10.1016/j.omega.2012.03.002
Storn R, Price K (1995) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11:341–359. https://doi.org/10.1023/A:1008202821328
Taleizadeh AA (2014) An economic order quantity model for deteriorating item in a purchasing system with multiple prepayments. Appl Math Model 38:5357–5366. https://doi.org/10.1016/j.apm.2014.02.014
Teng J-T, Cárdenas-Barrón LE, Chang H-J, Wu J, Hu Y (2016) Inventory lot-size policies for deteriorating items with expiration dates and advance payments. Appl Math Model 40:8605–8616. https://doi.org/10.1016/j.apm.2016.05.022
Wang L, Fu Q-L, Zeng Y-R (2012) Continuous review inventory models with a mixture of backorders and lost sales under fuzzy demand and different decision situations. Expert Syst Appl 39:4181–4189. https://doi.org/10.1016/j.eswa.2011.09.116
Wang Y, Zhang J, Tang W (2015) Dynamic pricing for non-instantaneous deteriorating items. J Intell Manuf 26:629–640. https://doi.org/10.1007/s10845-013-0822-2
Yavari M, Zaker H, Emamzadeh ESM (2019) Joint dynamic pricing and inventory control for perishable products taking into account partial backlogging and inflation. Int J Appl Comput Math 5:1. https://doi.org/10.1007/s40819-018-0585-8
Acknowledgements
The authors thank the editor and anonymous referees for reviewing the manuscript and improving its quality. Additionally, the author (Praveendra Singh) wishes to acknowledge the support of the Council of Scientific and Industrial Research (CSIR), India, for his JRF/SRF (grant code 9013-12-061).
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Council for Scientific and Industrial Research (CSIR), India, 9013-12-061, Praveendra Singh
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It is declared that both the authors contributed towards conceptualization, write-up and computational work to the proposed study. The overall supervision and editing are performed by Dr Madhu Jain.
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Jain, M., Singh, P. Pricing, prepayment and preservation strategy for inventory model with deterioration using metaheuristic algorithms. Soft Comput 28, 3415–3430 (2024). https://doi.org/10.1007/s00500-023-08637-4
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DOI: https://doi.org/10.1007/s00500-023-08637-4