Demand is a business or enterprise’s most important component. Over the past few years, scholars have examined the many types of demand. As an outcome, the investigators have built inventory models that account for diverse types of demand. For instance, Shah et al. [15] introduced a deteriorating economic order quantity model for non-instantaneous products in which the demand function is nonlinear and dependent on the unit selling price and frequency of advertisement simultaneously. Bhunia et al. [16] introduced a worsening inventory model that considers demand as a function of the selling price, advertisement frequency, and time. An EOQ model for a production system that produces defective items, considering that the demand function decreases exponentially with time, was investigated by Jaggi et al. [17], who found that this model is suitable for business environments where new products are introduced every day. Tripathi [18] developed an EOQ model by using a quadratic time-dependent demand as a variable. Namdeo et al. [19] presented a deteriorating pricing model whose demand is simultaneously dependent on the items’ prices and on-hand stock level. Shaikh et al. [20] prepared an EOQ model with a time-dependent ramp-type demand rate. Handa et al. [21] examined the inflation effect in their production inventory policy, in which they considered that the market demand depends on the time and selling price. An EOQ model for perishable products was examined by Mishra [22], taking stock and time-dependent demand as variables. Recently, Khan et al. [23] presented an inventory model whose demand is nonlinear and dependent on stock. After this, Shah and Shroff [24] proposed a pricing model with time-dependent trapezoidal-type demand.

Hadley and Whitin [25] first incorporated the notion of a quantity discount in an economic order quantity model. Suppliers sometimes provide quantity discounts to motivate retailers or buyers to order more. In control theory, suppliers typically provide mainly one or two discount policies, such as incremental and all-unit discounts. Researchers have recently been quite interested in inventory control theory, considering an all-unit price discount strategy. For instance, Shi et al. [26] established an inventory policy in which the demand function is price-dependent and additive stochastic by considering that the supplier provides all-unit quantity discounts to buyers or retailers through a mixed integer nonlinear programming model and a generalized disjunctive programming model. An inventory model with an all-unit discount was presented by Taleizadeh and Pentico [27], and they illustrated the model by comparing the EOQ models without a discount and with an all-unit discount. An EPQ model where the demand function is dependent on the stock level of the product was addressed by Alfares [28], considering the all-unit quantity discount. Shaikh et al. [29] discussed an EOQ model while assuming that the all-unit price discount policy and demand rate are dependent on the stock level and unit selling price. After that, this work was explored by Khan et al. [30], taking the holding cost as being linearly dependent on time and assuming that the unit carrying charge is directly proportional to the unit purchase cost. Rahman et al. [31] added an EOQ model while considering deterioration, demand patterns, purchasing cost, etc., as interval-valued numbers by considering two scenarios: one with shortages and one without shortages in all-unit quantity discount environments. A decision support framework for installment prepayments in an inventory system with a power demand rate was investigated by Khan et al. [32], incorporating all-unit discounts from the manufacturer or supplier to the retailer. They explored that when the total capital cost of a prepayment is less than the transaction cost of a single installment, the retailer should prefer a single installment prepayment policy. Recently, Momena et al. [33] presented a learning-based EOQ model while considering an all-unit price discount facility in a fuzzy environment. Khan et al. [34] examined how applying an all-unit discount impacts the total average profit of an inventory model with power demand patterns.

A holding cost is typically seen as a constant in inventory control policy [10]. However, this presumption about deteriorating goods is only sometimes true. Therefore, it is vital to linearly consider that the holding cost is time-dependent when making inventory decisions. In this regard, Ferguson et al. [35] first introduced an inventory policy for perishable products, nonlinearly considering the holding cost rate per unit as a function of time. By taking cost as a linear function of time, Mishra [36] incorporated an EOQ model. A partial back-ordering inventory strategy for perishable products was studied by Dutta and Kumar [37]. In this article, they assumed that the carrying cost depends on time and found that low stock levels should be maintained to avoid high holding costs. Pervin et al. [38] explored an integrated supply chain design by considering that time is dependent on the holding cost. Garai et al. [39] discussed a pricing model by analyzing the time-varying carrying cost in a fuzzy environment through trapezoidal fuzzy numbers. Pando et al. [40] formulated an inventory model by assuming a linear and nonlinear price-dependent demand in both time and stock levels. Furthermore, Swain et al. [41] investigated the EOQ design for perishable items by taking the holding cost as a function of time under consideration. A green pricing strategy was developed by Paul et al. [42], taking variable holding costs into account. Recently, Kumar et al. [43] discussed the combined effect of advertisement and selling price on customers in the inventory model by considering time-dependent carrying costs. The holding cost for this current article is taken as a linear function of time and is directly proportional to the unit purchasing cost.

Numerous research articles have been published in the previous few decades incorporating the two-warehouse concept into different inventory models. Hartley [44] suggested the first two-warehouse model for the inventory system in his book, Operations Research: A Managerial Emphasis. Other researchers also tried to create issues with the two-warehouse arrangement. In this area, Yang and Chang [45] introduced a two-storage inventory design for perishable products with an allowed payment delay, considering that the inflation effect and shortages are partially back-ordered. After that, Bhunia et al. [46] explored the study by Yang and Chang [45] by considering that time depends on the partial backlogging rate and analyzing different cases on the trade credit time. Xu et al. [47] discussed a two-storage inventory model by comparing other dispatching policies such as last-in-first-out, modified last-in-first-out, and first-in-first-out policies. Tiwari et al. [48] analyzed a two-warehouse inventory model using particle swarm optimization’s meta-heuristic algorithm. Chakraborty et al. [49] investigated a two-warehouse inventory setup with three-parameter Weibull distributed deterioration and the ramp type time-varying demand curve under the permitted payment delay. Jonas [50] studied a two-layer supply chain containing one distributor and one buyer in a two-warehouse setup, where the holding cost per unit for storing the item in an R.W. decreases over time. Ghiami and Beullens [51] developed a two-echelon supply chain in a two-warehouse setup considering a continuous resupply policy, i.e., the items in an R.W. are regularly relocated to an O.W. to keep their total capacity as demand depends on stock. A two-warehouse inventory model for perishable products was introduced by Khan et al. [52], considering that the rate of deterioration in an R.W. is lower than that of an O.W. since an R.W. has superior preservation services compared to an O.W. Xu et al. [53] explored a deteriorating inventory model by considering the selection of an item that can be stored in an O.W. or an R.W. or both an O.W. and R.W. Thilagavathi et al. [54] discussed a two-storage inventory problem, where the supplier offers three slots of payment to the retailer for the purchasing amount; the slots are “prior payment with a discount”, “posterior payment with a penalty”, and “to be paid at the time of replenishment”. Most recently, a two-echelon supply chain model with two warehouses was analyzed by Padiyar et al. [55] with cloudy fuzzy inflation.

Since trade credit allows customers to buy products without an instant payment, many organizations utilize this to increase their economic strength and attract new customers. Many researchers have focused more on trade credit in the past two decades and have included various trade credit policies in their pricing models. The notion of trade credit policy was first brought on by Goyal [56]. Following that, multiple researchers have applied this policy in their pricing models. For instance, Taleizadeh [57] discussed an inventory system with a single-layer trade credit policy by allowing for multiple prepayments for the credit amount. A two-level trade credit financing supply chain model was analyzed by Wu et al. [58]. Sarkar et al. [59] introduced a deteriorating inventory system using a two-level trade credit policy where the supplier offers a full trade credit to the buyer or retailer. In contrast, the buyer provides a partial trade credit to the customer. A green inventory system considering a single-level trade credit policy from vendor to buyer was developed by Tiwari et al. [60]. Numerous researchers [61,62,63] have recently developed models using single-level trade credit facilities from supplier to retailer. The concept of a single-level trade credit facility from retailer to customer is used in [64,65,66], and two-level trade credit policies have been used in their inventory model [67,68].