Analysis of a Two-Storage System for Advance Payment Policies with the Partial Backlogged Shortage

       [1]        Deighton, J., Henderson, C. M. and Neslin, S. A. (1994), “The effects of advertising on brand switching and repeat purchasing”,  Journal of marketing research, Vol. 31 No. 1, pp. 28-43.

       [2]        Bronnenberg, B. J. (1998), “Advertising frequency decisions in a discrete Markov process under a budget constraint”, Journal of Marketing Research, Vol. 35 No. 3, pp. 399-406.

       [3]        Datta, T. K. and Paul, K. (2001), “An inventory system with stock-dependent, price-sensitive demand rate”,  Production planning and control, Vol. 12 No. 1, pp. 13-20.

       [4]        Bhunia, A. K. and Shaikh, A. A. (2011), “A two warehouse inventory model for deteriorating items with time dependent partial backlogging and variable demand dependent on marketing strategy and time”, International Journal of Inventory Control and Management, Vol. 1 No. 2, pp. 95-110.

       [5]        Fordyce III, E. W., Winters, M. E., Siegel, K. P., Amaro, L., Byce, C. R. and Savas, N. (2016), U.S. Patent No. 9,342,835. Washington, DC: U.S. Patent and Trademark Office.

       [6]        Razniewski, S. (2016), “Optimizing update frequencies for decaying information”, In Proceedings of the 25th ACM International on Conference on Information and Knowledge Management  pp. 1191-1200.

       [7]        Pervin, M., Roy, S. K. and Weber, G. W. (2019), “Multi-item deteriorating two-echelon inventory model with price-and stock-dependent demand: A trade-credit policy”, Journal of Industrial and Management Optimization, Vol. 15 No. 3, pp. 1345.

       [8]        Shaikh, A. A., Cárdenas–Barrón, L. E., Bhunia, A. K. and Tiwari, S. (2019), “An inventory model of a three parameter Weibull distributed deteriorating item with variable demand dependent on price and frequency of advertisement under trade credit”, RAIRO-Operations Research, Vol. 53 No. 3, pp. 903-916.

       [9]        Rahman, M. S., Duary, A., Shaikh, A. A. and Bhunia, A. K. (2020),  “An application of parametric approach for interval differential equation in inventory model for deteriorating items with selling-price-dependent demand”, Neural Computing and Applications, pp. 1-17.

     [10]      Khan, M. A. A., Shaikh, A. A., Konstantaras, I., Bhunia, A. K. and Cárdenas-Barrón, L. E. (2020), “Inventory models for perishable items with advanced payment, linearly time-dependent holding cost and demand dependent on advertisement and selling price”, International Journal of Production Economics, pp. 107804.

     [11]      Mirzazadeh, A., Seyyed Esfahani, M. M. and FatemiGhomi, S. M. T. (2009), “An inventory model under uncertain inflationary conditions, finite production rate and inflation-dependent demand rate for deteriorating items with shortages”, International Journal of Systems Science, Vol. 40 No. 1, pp. 21-31.

     [12]      Chang, C. T., Teng, J. T. and Goyal, S. K. (2010), “Optimal replenishment policies for non-instantaneous deteriorating items with stock-dependent demand”, International Journal of Production Economics, Vol. 123 No. 1, pp. 62-68.

     [13]      Mandal, B. (2010), “An EOQ inventory model for weibull distributed deteriorating items under ramp type demand and shortages”, Opsearch, Vol. 47 No. 2, pp. 158-165.

     [14]      Mishra, V. K. (2010), “Deteriorating inventory model with time dependent demand and partial backlogging”, Applied Mathematical Sciences, Vol. 4 No. 72, pp. 3611-3619.

     [15]      Das, D., Roy, A. and Kar, S. (2015), “A multi-warehouse partial backlogging inventory model for deteriorating items under inflation when a delay in payment is permissible”, Annals of Operations Research, Vol. 226 No. 1, pp. 133-162.

     [16]      Hung, K. C. (2011), “An inventory model with generalized type demand, deterioration and backorder rates” European Journal of Operational Research, Vol. 208 No. 3, pp. 239-242.

     [17]      Jolai, F., Gheisariha, E., and Nojavan, F. (2011). Inventory Control of Perishable Items in a Two-Echelon Supply Chain. Advances in Industrial Engineering, 45(Special Issue), 69-77.

     [18]      Lee, Y. P. and Dye, C. Y. (2012), “An inventory model for deteriorating items under stock-dependent demand and controllable deterioration rate”, Computers and Industrial Engineering, Vol. 63 No. 2, pp. 474-482.

     [19]      Sarkar, B. (2012), “An inventory model with reliability in an imperfect production process”, Applied Mathematics and Computation, Vol. 218 No. 9, pp. 4881-4891.

     [20]      Sarkar, B., Saren, S. and Wee, H. M. (2013), “An inventory model with variable demand, component cost and selling price for deteriorating items”, Economic Modelling, Vol. 30, pp. 306-310.

     [21]      Bhunia, A. and Shaikh, A. (2014), “A deterministic inventory model for deteriorating items with selling price dependent demand and three-parameter Weibull distributed deterioration”, International Journal of Industrial Engineering Computations,  Vol. 5 No. 3, pp.  497-510.

     [22]      Taleizadeh, A. A., Noori-daryan, M. and Cárdenas-Barrón, L. E. (2015), “Joint optimization of price, replenishment frequency, replenishment cycle and production rate in vendor managed inventory system with deteriorating items”, International Journal of Production Economics, Vol. 159, pp.  285-295.

     [23]      Teimoury, E., and Kazemi, S. M. M. (2015). Development of pricing model for deteriorating items with constant deterioration rate considering replacement. Advances in Industrial Engineering, 49(1), 1-9.

     [24]      Gholami, M., and Honarvar, M. (2015). Developing a Mathematical Model for Vendor Managed Inventory Considering Deterioration and Amelioration Items in a Three-Level Supply Chain. Advances in Industrial Engineering, 49(2), 237-256.

     [25]      Pallanivel, M. and Uthayakumar , R., (2015), “An EPQ model for deteriorating items variable production cost , timed dependent holding cost and partial backlogging under inflation”, Opsearch, Vol. 52 No. 1, pp. 1-17,

     [26]      Ghoreishi, M., Weber, G. W. and Mirzazadeh, A. (2015), “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, Vol. 226 No. 1, pp. 221-238.

     [27]      Duong, L. N., Wood, L. C. and Wang, W. Y. (2015), “A multi-criteria inventory management system for perishable and substitutable products”, Procedia Manufacturing, Vol. 2, pp. 66-76.

     [28]      Alfares, H. K. and Ghaithan, A. M. (2016), “Inventory and pricing model with price-dependent demand, time-varying holding cost, and quantity discounts”, Computers and Industrial Engineering, Vol. 94, pp. 170-177.

     [29]      Hasanpour Rodbaraki, J., and Sharifi, E. (2016). Economic Order Quantity for Deteriorating Items with Imperfect Quality, Destructive Testing Acceptance Sampling, and Inspection Errors. Advances in Industrial Engineering, 50(2), 235-246.

     [30]      Rabbani, M., Pourmohammad-Zia, N., and Rafiei, H. (2016). Developing an Integrated Approach for Inventory Control, Pricing and Advertisement of Deteriorating Items. Advances in Industrial Engineering, 50(3), 407-4016.

     [31]      Zohoori, S., Karimi, B., and Maihami, R. (2016). Inventory Control for Deteriorating Items in Closed-loop Supply Chain with Stochastic Demand. Advances in Industrial Engineering, 50(3), 429-439.

     [32]      Li, R. and 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”, European Journal of Operational Research, Vol. 270 No. 3, pp. 1099-1108.

     [33]      Duong, L. N., Wood, L. C. and Wang, W. Y. (2018), “Effects of Consumer Demand, Product Lifetime, and Substitution Ratio on Perishable Inventory Management. Sustainability, Vol. 10 No 5, pp. 1559.

     [34]      Khan, M. A. A., Shaikh, A. A., Panda, G. C. and Konstantaras, I. (2019), “Two-warehouse inventory model for deteriorating items with partial backlogging and advance payment scheme”, RAIRO-Operations Research, Vol. 53 No. 5, pp. 1691-1708.

     [35]      Li, R., Liu, Y., Teng, J. T. and Tsao, Y. C. (2019), “Optimal pricing, lot-sizing and backordering decisions when a seller demands for an advance-cash-credit payment scheme”, European Journal of Operational Research,  Vol. 278 No. 1, pp. 283-295.

     [36]      Das, S. C., Zidan, A. M., Manna, A. K., Shaikh, A. A. and Bhunia, A. K. (2020), “An application of preservation technology in inventory control system with price dependent demand and partial backlogging”,  Alexandria Engineering Journal, Vol. 59 No. 3, pp. 1359-1369.

     [37]      Rahaman, M., Mondal, S. P., Shaikh, A. A., Ahmadian, A., Senu, N. and Salahshour, S. (2020), “Arbitrary-order economic production quantity model with and without deterioration: generalized point of view”, Advances in Difference Equations, Vol. 2020 No. 1, pp. 16.

     [38]      Xu, C., Liu, X., Wu, C. and Yuan, B. (2020a), “Optimal Inventory Control Strategies for Deteriorating Items with a General Time-Varying Demand under Carbon Emission Regulations”,  Energies, Vol. 13 No. 4, pp. 999.

     [39]      Xu, C., Zhao, D., Min, J. and Hao, J. (2020b), “An inventory model for nonperishable items with warehouse mode selection and partial backlogging under trapezoidal-type demand”, Journal of the Operational Research Society, pp. 1-20.

     [40]      Liang, Y. and Zhou, F. (2011), “A two-warehouse inventory model for deteriorating items under conditionally permissible delay in payment”, Applied Mathematical Modelling, Vol. 35 No. 5, pp. 2221-2231.

     [41]      Liao, J. J., Huang, K. N. and Ting, P. S. (2014), “Optimal strategy of deteriorating items with capacity constraints under two-levels of trade credit policy”, Applied Mathematics and Computation, Vol. 233, pp. 647-658.

     [42]      Bhunia, A. K., Shaikh, A. A., Sharma, G. and Pareek, S. (2015), “A two storage inventory model for deteriorating items with variable demand and partial backlogging”, Journal of Industrial and Production Engineering, Vol. 32 No. 4, pp. 263-272.

     [43]      Khanna, A., Gautam, P., and Jaggi, C. K. (2016, March). Coordinating vendor-buyer decisions for imperfect quality items considering trade credit and fully backlogged shortages. In AIP Conference Proceedings (Vol. 1715, No. 1, p. 020065). AIP Publishing LLC.

     [44]      Khanna, A., Gautam, P., and Jaggi, C. K. (2017). Inventory modeling for deteriorating imperfect quality items with selling price dependent demand and shortage backordering under credit financing. International Journal of Mathematical, Engineering and Management Sciences, Vol. 2 No 2, pp. 110-124.

     [45]      Khanna, A., Mittal, M., Gautam, P., and Jaggi, C. (2016). Credit financing for deteriorating imperfect quality items with allowable shortages. Decision Science Letters, Vol. 5 No. 1, pp. 45-60.

     [46]      Shaikh, A. A., Mashud, A. H. M., Uddin, M. S. and Khan, M. A. A. (2017), “Non-instantaneous deterioration inventory model with price and stock dependent demand for fully backlogged shortages under inflation”, International Journal of Business Forecasting and Marketing Intelligence, Vol. 3 No. 2, pp. 152-164.

     [47]      Tiwari, S., Jaggi, C. K., Bhunia, A. K., Shaikh, A. A. and Goh, M. (2017), “Two-warehouse inventory model for non-instantaneous deteriorating items with stock-dependent demand and inflation using particle swarm optimization”,  Annals of Operations Research, Vol. 254 No. 1-2, pp. 401-423.

     [48]      Pervin, M., Roy, S. K. and Weber, G. W. (2018), “Analysis of inventory control model with shortage under time-dependent demand and time-varying holding cost including stochastic deterioration”,  Annals of Operations Research, Vol. 260 No. 1-2, pp. 437-460.

     [49]      Gautam, P., and Khanna, A. (2018). An imperfect production inventory model with setup cost reduction and carbon emission for an integrated supply chain. Uncertain Supply Chain Management, Vol 6 No 3, pp. 271-286.

     [50]      Jaggi, C. K., Gautam, P., and Khanna, A. (2018). Inventory decisions for imperfect quality deteriorating items with exponential declining demand under trade credit and partially backlogged shortages. In Quality, IT and Business Operations (pp. 213-229). Springer, Singapore.

     [51]      Panda, G. C., Khan, M. A. A. and Shaikh, A. A. (2019), “A credit policy approach in a two-warehouse inventory model for deteriorating items with price-and stock-dependent demand under partial backlogging”, Journal of Industrial Engineering International, Vol. 15 No. 1, pp. 147-170.

     [52]      Manna, A. K., Das, B. and Tiwari, S. (2020), “Impact of carbon emission on imperfect production inventory system with advance payment base free transportation”, RAIRO-Operations Research, Vol. 54 No. 4, pp. 1103-1117.

     [53]      Manna, A. K., Akhtar, M., Shaikh, A. A., and Bhunia, A. K. (2021). Optimization of a deteriorated two-warehouse inventory problem with all-unit discount and shortages via tournament differential evolution. Applied Soft Computing, 107, 107388.

     [54]      Taleizadeh, A. A., Moghadasi, H., Niaki, S. T. A. and Eftekhari, A. (2008), “An economic order quantity under joint replenishment policy to supply expensive imported raw materials with payment in advance”, Journal of Applied Sciences, Vol. 8 No. 23, pp. 4263-4273.

     [55]      Maiti, A. K., Maiti, M. K. and Maiti, M. (2009), “Inventory model with stochastic lead-time and price dependent demand incorporating advance payment”, Applied Mathematical Modelling, Vol. 33 No. 5, pp. 2433-2443.

     [56]      Gupta, R. K., Bhunia, A. K. and Goyal, S. K. (2009), “An application of genetic algorithm in solving an inventory model with advance payment and interval valued inventory costs”, Mathematical and Computer Modelling, Vol. 49 No. 4-6, pp. 893-905.

     [57]      Tsao, Y. C. (2009), “Retailer’s optimal ordering and discounting policies under advance sales discount and trade credits”, Computers and Industrial Engineering, Vol. 56 No. 1, pp. 208-215.

     [58]      Thangam, A. (2011), “Dominant retailer’s optimal policy in a supply chain under Advance Payment scheme and trade credit”, International Journal of Mathematics in Operational Research, Vol. 3 No. 6, 658-679.

     [59]      Thangam, A. (2012), “Optimal price discounting and lot-sizing policies for perishable items in a supply chain under advance payment scheme and two-echelon trade credits”, International Journal of Production Economics, Vol. 139 No. 2, pp. 459-472.

     [60]      Taleizadeh, A. A., Pentico, D. W., Jabalameli, M. S. and Aryanezhad, M. (2013), “An economic order quantity model with multiple partial prepayments and partial backordering”, Mathematical and Computer Modelling, Vol. 57 No. 3-4, pp. 311-323.

     [61]      Taleizadeh, A. A. (2014a), “An economic order quantity model for deteriorating item in a purchasing system with multiple prepayments”, “Applied Mathematical Modelling”, Vol.38 No. 23, pp. 5357-5366.

     [62]      Taleizadeh, A. A. (2014b), “An EOQ model with partial backordering and advance payments for an evaporating item”,  International Journal of Production Economics, Vol. 155, No. 185-193.

     [63]      Zia, N. P. and Taleizadeh, A. A. (2015), “A lot-sizing model with backordering under hybrid linked-to-order multiple advance payments and delayed payment”, Transportation Research Part E: Logistics and Transportation Review, Vol. 82, pp. 19-37.

     [64]      Lashgari, M., Taleizadeh, A. A. and Ahmadi, A. (2016), “Partial up-stream advanced payment and partial down-stream delayed payment in a three-level supply chain”, Annals of Operations Research, Vol. 238 No. 1-2, pp. 329-354.

     [65]      Teng, J. T., Cárdenas-Barrón, L. E., Chang, H. J., Wu, J. and  Hu, Y. (2016), “Inventory lot-size policies for deteriorating items with expiration dates and advance payments”, Applied Mathematical Modelling, Vol. 40 No. 19-20, pp. 8605-8616.

     [66]      Tavakoli, S. and Taleizadeh, A. A. (2017), “An EOQ model for decaying item with full advanced payment and conditional discount”,  Annals of Operations Research, Vol. 259 No. 1-2, pp. 415-436.

     [67]      Taleizadeh, A. A., Tavakoli, S. and San-José, L. A. (2018), “A lot sizing model with advance payment and planned backordering”,  Annals of Operations Research, Vol. 271 No. 2, pp. 1001-1022.

     [68]      Shah, N. H. and Naik, M. K. (2018), “EOQ model for deteriorating item under full advance payment availing of discount when demand is price-sensitive”, International Journal of Supply Chain and Operations Resilience, Vol. 3 No. 2, pp. 163-197.

     [69]      Chang, C. T., Ouyang, L. Y., Teng, J. T., Lai, K. K. and Cárdenas-Barrón, L. E. (2019), “Manufacturer's pricing and lot-sizing decisions for perishable goods under various payment terms by a discounted cash flow analysis”, International Journal of Production Economics, Vol. 218, pp83-95.

     [70]      Li, R., Teng, J. T. and Zheng, Y. (2019), “Optimal credit term, order quantity and pricing policies for perishable products when demand depends on price, expiration date, and credit period”, Annals of Operations Research Vol. 280 No. 1-2, pp. 377-405.

     [71]      Shaikh, A. A., Das, S. C., Bhunia, A. K., Panda, G. C. and Khan, M. A. A. (2019), “A two-warehouse EOQ model with interval-valued inventory cost and advance payment for deteriorating item under particle swarm optimization”, Soft Computing, Vol. 23 No. 24, pp. 13531-13546.

     [72]      Khan, M. A. A., Shaikh, A. A., Panda, G. C., Konstantaras, I. and Taleizadeh, A. A. (2019), “Inventory system with expiration date: Pricing and replenishment decisions”, Computers and Industrial Engineering, Vol. 132, pp. 232-247.

     [73]      Khan, M. A. A., Shaikh, A. A., Panda, G. C., Bhunia, A. K. and Konstantaras, I. (2020), “Non-instantaneous deterioration effect in ordering decisions for a two-warehouse inventory system under advance payment and backlogging”, Annals of Operations Research, pp. 1-33.

     [74]      Khan, M. A. A., Shaikh, A. A., Panda, G. C., Konstantaras, I. and Cárdenas‐Barrón, L. E. (2020), “The effect of advance payment with discount facility on supply decisions of deteriorating products whose demand is both price and stock dependent”, International Transactions in Operational Research, Vol. 27 No. 3, pp. 1343-1367.

     [75]      Khakzad, A. and Gholamian, M. R. (2020), “The effect of inspection on deterioration rate: An inventory model for deteriorating items with advanced payment”, Journal of Cleaner Production, Vol. 254, pp. 120-117.

     [76]      Das, S. C., Manna, A. K., Rahman, M. S., Shaikh, A. A., and Bhunia, A. K. (2021). An inventory model for non-instantaneous deteriorating items with preservation technology and multiple credit periods-based trade credit financing via particle swarm optimization. Soft Computing, 25(7), 5365-5384.

     [77]      Ghosh, P. K., Manna, A. K., Dey, J. K., and Kar, S. (2021). An EOQ model with backordering for perishable items under multiple advanced and delayed payments policies. Journal of Management Analytics, 1-32.

     [78]      Ghosh, P. K., Manna, A. K., Dey, J. K., and Kar, S. (2021). Supply chain coordination model for green product with different payment strategies: a game theoretic approach. Journal of Cleaner Production, 290, 125734.