**1. Introduction**

Sustainable business decisions require taking into account a wide range of factors and methodologies [1–4]. Therefore, a number of models have been proposed for efficient inventory management. In 1913, Harris introduced an economic order quantity concept to solve this problem in the form of a static formula (and started static inventory management models vein).

However, typical static economic order quantity (EOQ) models [5,6] do not satisfy practitioners because of their incapacity to consider changing consumer demand, requiring constant orders in equal periods of time [7]. Unpredictable and constantly changing demands, affecting the size and frequency of orders, lead to situations in which classical inventory management models become unfit for solving practical inventory management problems and motivate a search for new or modified alternatives. In the last decade, we observed increased scientific interest in solving this problem. Firstly, Sana [8] proposed an EOQ model for perishable goods reacting to retail price changes, although practical implementation is restricted by neglecting the minimizing effect of a negative power function of price, which generates high sensibility in consumer's demand. Later, Dobson et al. [9] proposed that perishable goods, with the demand rate as a linearly decreasing function of the age of the products, act similarly to nonperishable goods with the unit holding cost equal to the ratio of contribution margin to lifetime. In their model, they obtain traditional nonperishable Economic Order Quantity (EOQ)-like lower and upper bounds on the cycle length and the profit and show that they lead to near-optimal results for typical examples, like grocery items. Zeng et al. [10] formulate an extension to Wilson's model varying quantity of order and different ordering periods. Their model generates a substantial

economic effect when a significant change in consumer demand is noticed and (or) a long period of planning the logistics process must be ensured.

Conventional models for inventory management with uncertain demand, such as variations of Harris formulation [11–13], Markov equation-based ones [14,15], and Wilson's formulation [16–19] are designed to minimize the expected costs of replenishment and stock-outs. They assume that complete satisfaction of uncertain and hardly predictable demand is too expensive or even deemed impossible. All these models are designed under the constant order quantity principle, where the size of the following order is based on the objective to minimize the whole cost of a company's inventory management.

The problem of economic order quantity (EOQ) is quite well-known and has been widely discussed in the scientific literature [20–24]. Determination of the EOQ has a particular importance in trade and retail activities. The optimal ordering plan allows for the companies to achieve smooth operation and competitive advantage [25–27].

In the context of steady economic growth, the EOQ models assuming steady demand for perishable consumer goods are suitable for determining the lot size [28–30]. There has been research on the EOQ with respect to the credit market [31] and stock dynamic sizing optimization under the Logistic 4.0 environment for material management of a very high-speed train [32].

However, the fluctuations in the demand and lead time have not been taken into account. Indeed, such fluctuations become more important during disruptions of the supply chains (e.g., due to pandemic events). The emergence of trade barriers requires retailers to reconsider the optimal lot size. This issue is further aggravated by fluctuations in the market prices of particular products. Indeed, the crisis affects the consumer behavior and demand for particular goods [33–35]. The changes in demand are reflected by the prices of the products retailed [36,37]. Therefore, one needs to adjust decisions to order and store goods. Even without facing serious crisis, changes in pricing occur over time in terms of both retail market and storage costs. Thus, a mathematical model capable of determining the optimal economic order quantity under varying reordering time and price parameters is obvious. Although there has been a wide range of models proposed for determining the lot sizes (Table 1), none of them are able to handle the varying stock quantity based on varying price and reordering time.


**Table 1.** Overview of the existing economic order quantity (EOQ) models.


**Table 1.** *Cont*.

This paper presents a model for determining the optimal lot size with fluctuating price building on the classical Wilson's formulation following extensions by Slesarenko and Nestorenko [49] and by Zeng et al. [10]. The proposed model optimizes the discounted costs of all orders rather than the costs per order. Due to this fundamental difference, our model is more relevant to economic decision making and ensures symmetry in the decision process. Presenting practical application of models with different parameters, we also show how this model performs in real-life situations.
