Two-storage inventory model for deteriorating items with price dependent demand and shortages under partial backlogged in fuzzy approach

Fuzzy inventory model of seasonal deteriorating products with time and price sensitive demand and holding cost under partial backlogged

“…Continuous review inventory model of deteriorating items was developed by Roy and Samanta (2009). Most of the research have been carried out in time to time on the necessity of society by Jaggi et al (2012), Ranganathan and Thirunavukarsu (2014), De and Sana (2015), Indrajitsingha et al (2019aIndrajitsingha et al ( , 2019b, Sahoo et al (2021). Kuppulakshmi et al(2023) proposed an inventory method of imperfect items in which deterioration taken as triangular fuzzy number.…”

Cost optimization inventory model for deteriorating items with trapezoidal demand rate under completely backlogged shortages in crisp and fuzzy environment

“…However, the stock, price and time-dependent demand having constant deteriorating inventory problems were examined by Chen et al [8]. Furthermore, Banerjee and Agarwal [5], Singh and Kumar [47], Jaggi et al [16], and Indrajitsingha et al [14] found optimal results for constant deteriorating items having selling price dependent demand. Nevertheless, the selling price dependent demand assumed by Sahoo et al [40] for linear deteriorating items, and Khanna et al [21] for imperfect quality and constant deteriorating items in their proposed problems.…”

“…Thus, many researchers in the present era have considered the impreciseness of the parameters for the inventory requirements in the fuzzy environment. For some developments in this direction, see the recent works of Chanda and Kumar [7], Sharma et al [46], Indrajitsingha et al [12][13][14], Mishra et al [32], Shaikh et al [43], Kumar et al [23][24][25], Nayak et al [35], Routray et al [39] and Shabani et al [42]. Apart from these, the government and various companies are changing their policies from time to time, which also lead to fuzziness in inventory models.…”

“…The values of the parameters involved in demand function are 𝑐 1 = 450, 𝑑 1 = 5, 𝑐 2 = 522.5, 𝑑 2 = 15, and 𝐷 = 462.5, the time at which demand pattern changes in the cycle are 𝜈 1 = 2.5, and 𝜈 2 = 4, the total cycle time is 𝑇 = 5, the ordering cost is 𝐶0 = 1800, the rate of deterioration of items in the inventory is 𝜂 = 0.25, and the fuzzy deterioration, holding and shortage costs are 𝑘 1 = (𝑘 11 , 𝑘 12 , 𝑘 13 , 𝑘 14 ) = (12,13,14,15), 𝑘 2 = (𝑘 21 , 𝑘 22 , 𝑘 23 , 𝑘 24 ) = (6, 7, 8, 9), and 𝑘 3 = (𝑘 31 , 𝑘 32 , 𝑘 33 , 𝑘 34 ) = (9,10,11,12) respectively.…”

“…But, there will be no change in positive inventory time (refer Figs. [13][14][15][16][17][18]. This means that when the length of increasing demand or stable demand increases, retailers will need to order more inventory and have to spend more money on inventory upkeep to match the demand.…”