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Although the safe consumption of goods such as food products, medicine, and vaccines is related to their freshness, consumers frequently understand less than suppliers about the freshness of goods when they purchase them. Because of this lack of information, apart from sales prices, consumers refer only to the manufacturing and expiration dates when deciding whether to purchase and how many of these goods to buy. If dealers could determine the sales price at each point in time and customers’ intention to buy goods of varying freshness, then dealers could set an optimal inventory cycle and allocate a weekly sales price for each point in time, thereby maximizing the profit per unit time. Therefore, in this study, an economic order quality model was established to enable discussion of the optimal control of sales prices. The technique for identifying the optimal solution for the model was determined, the characteristics of the optimal solution were demonstrated, and the implications of the solution’s sensitivity analysis were explained.

Previous studies have demonstrated the relevance of food freshness and consumer utility. Although consumers judge food freshness through the senses [

The research frameworks for studying the inventory optimization problems of fresh (or perishable) goods tend to be highly complex because the freshness of goods affects consumer utility and thus their demands. The earliest literature review on the inventory model for deteriorating items was a review of inventory models for perishable goods conducted by Nahmias [

The traditional economic order quantity (EOQ) model was designed to solve the problem encountered by buy-in and sell-out dealers, who determine the inventory standard of goods at the beginning of each period in response to the given demand rate of goods, thereby minimizing the cost per unit time. To expand the applications of the conventional EOQ model, various types of extended inventory models have been developed by inventory management scholars in recent years in their studies on fresh (or perishable) goods inventories. According to loosened assumptions, these extended models (some of which can be categorized as hybrid models comprising more than one type) can be divided into the following types.

Numerous inventory models for fresh (or perishable) goods have been proposed in the past 20 years, with pricing problems being one of the most extensively researched topics in the past 10 years. Most research on pricing problems has concentrated on discount optimization; only a few scholars have specifically studied dynamic price optimization, and most of which studies have been conducted in the past 5-6 years [

Thus

From (

Through (

Assume

Because the objective function of (

To solve (

Let

Applying the existing theory of calculus of variations to this type of problem [

The condition of the Euler equation:

The condition of

Because the set of feasible solutions for (

Integrating (

Figure

The optimal inventory cycle

Next, (

Problem (

This function illustrates that the rate of change of the initial inventory standard

If the sensitivity analysis result of

As shown in Figure

However,

Partially differentiating

The incorporation of (

Effect of the increase in

By partially differentiating

Partially differentiating

This study divided the inventory promotion model of fresh goods into four categories and examined published academic journals papers that have investigated these categories, finding that few scholars have studied the dynamic pricing of fresh goods. The EOQ model established in this study enables dealers to determine sales prices at each point in time after the relationship between consumer reactions to the freshness of the goods and purchasing intentions is determined.

The optimal inventory cycle

We also analyzed the sensitivity of the optimal solution to changes in each variable. The results revealed the following. (a) The optimal inventory cycle

The main contribution of this research model to management is the incorporation of consumers’ demand response to the manufacture and expiration dates (or degree of freshness) of fresh goods. Retailers tend to have both old and new goods on their shelves when replenishing fresh goods—that is, they stock same goods with differing expiration dates. They may even have differing expiration dates despite having the same manufacture dates because of environmental factors such as transportation and storage. Therefore, retailers can set the prices at different time points of the goods’ shelf life instead of adopting a straightforward price discount as in the past, which may cause them to lose part of their expected profits. Using the parameters to determine the rate of change for the optimal solution can assist fresh goods retailers in conducting immediate price control.

From (

In (

By partially differentiating

Effect of the increase in

Effect of changes in

In (

The author declares that they have no conflicts of interest.