In economics, a demand curve is almost always downward-sloping, reflecting the willingness of consumers to purchase more of the commodity at lower price levels. In addition, the demand for seasonal products (such as fashion apparels, beverages etc.) or perishable goods (such as meat and seafood, dairy products, fruit and vegetables, pharmaceutical products, and chemicals) decreases over time. Hence, demand is a function of price and stock-age. With large business transactions, a seller usually demands a down payment (i.e., an advance payment) to ensure that the buyer is making a serious offer. Conversely, a buyer frequently requests to hold a fraction of total purchase cost until the business transaction is completed and satisfactory (i.e., a credit payment). As a result, a combination of advance, cash, and credit (ACC) payments is commonly used in business transactions. This paper develops a supplier–retailer–customer chain in which the retailer receives an upstream ACC payment from the supplier while in return offers a down-stream cash-credit (some in cash and the remainder in credit) payment to customers, the demand is influenced by the combined effect of selling price and stock age, and the deterioration rate is time-varying. The retailer must determine optimal unit price and replenishment time to maximize the present value of total profit, which is strictly concave in selling price and strictly pseudo-concave in replenishment time. Finally, a sensitivity analysis is performed, and several managerial insights are obtained. For instance, an increase in the fraction of advance payment forces the retailer to raise selling price.

Advertisements play an important role in communicating with target customers. A higher advertisement frequency increases costs but may increase the chances of acquiring new customers. Moreover, faced with a wide-ranging array of products that might fit specific needs, customers usually buy according to expectations about value and satisfaction. When customers are satisfied with a purchasing experience, they are more likely to buy again and share their experiences with others. Hence, companies are concerned about increasing customer value and service satisfaction to develop and manage customer relationships. This maintains a company’s competitive edge and can improve its market share. In this article, we incorporate the frequency of advertisements and the cost of customer relationship management (CRM) into the demand function under a product life cycle (PLC). Customers can return products in the appreciation period offered by a retailer. A profit-maximizing model is developed to analyze the joint marketing and ordering policy of each stage of a product’s life cycle with a product return guarantee. We construct an algorithm to identify the optimal decisions. Finally, numerical examples are presented to illustrate the proposed model, and managerial insights are obtained from a sensitivity analysis, followed by conclusions and future research.

In the supplier–retailer–consumer system, the retailer’s replenishment and pricing strategies impact the entire transaction process, forming a comprehensive trading market. Suppliers offer advance-cash-credit payments to retailers, while retailers provide customers with cash-credit payment options. In the current health-conscious consumer market, purchasing decisions are influenced not only by commodity prices but also by the freshness of products, particularly perishable goods. Growing awareness of climate change and the advent of carbon emission policies have raised concerns about the environmental costs of business transactions. This study focuses on perishable products whose demand is influenced by both price and freshness. It explores the adoption of various payment methods by suppliers and retailers, as well as the impact of carbon emission cap-and-trade policies or carbon tax policies on management and pricing strategies. Suitable inventory models are established to determine the optimal replenishment and pricing strategies for maximizing the current value of total profit. We illustrate that the current value of total profit demonstrates joint concavity concerning both the selling price and the replenishment time. Finally, we verify the proposed models using numerical examples and present the findings of sensitivity analyses. The findings of this study yield several valuable insights for inventory management of perishable goods.

This study investigated non-instantaneous deteriorating items because not all products deteriorate immediately. In the high-tech product life cycle, the product demand increases linearly substantially in the growth stage and maintains a near-constant level in the maturity stage. This is a ramp-type demand rate. To satisfy the demand as shortages occur, partial backlogging is necessary. The advance-cash-credit payment scheme, comprising advance, cash, and credit payments, has gained popularity in business transactions to improve cash flow flexibility among supply chain participants. This study explored a partial backlogging inventory model with ramp-type demand for non-instantaneous deteriorating items under generalized payment. The proposed model also incorporated discounted cash flow analysis to account for the time value of the profit function. This study attempted to determine the optimal replenishment strategy to maximize the present value of the total profit. Finally, we conducted a sensitivity analysis to examine the efficacy of the proposed model and gain managerial insights. The optimal total profit rises with an increase in the permissible delay period and sale price but decreases with an increase in ordering and purchase costs. Then, the decision-maker can refer to the managerial insights to choose the appropriate parameter value for the operation.

Price is a pivotal determinant of market demand, as higher prices typically reduce sales while lower prices stimulate them. Thus, incorporating price-dependent demand into inventory models is both realistic and necessary. In practice, limited storage capacity often forces retailers to rent additional space, motivating the adoption of two-warehouse systems. Trade credit also plays a critical role in supply chain management: suppliers may offer cash discounts or deferred payments to encourage larger orders, while retailers extend credit to customers to boost sales. To reduce default risk, however, retailers usually provide only partial credit. Considering the time value of money, costs and profits are assessed using discounted cash-flow analysis to account for payment delays and inflation. This study develops an integrated supplier–retailer–customer chain model that (1) incorporates price-dependent demand, (2) includes a rented warehouse for limited storage, (3) considers partial trade credit, (4) links two-level trade credit terms to order quantity, and (5) evaluates financial performance on a present-value basis. The model aims to maximize total profit by determining optimal price, replenishment cycle, and order quantity. Numerical and sensitivity analyses confirm that extending supplier credit can lower prices and improve overall profitability, offering useful insights for strategic inventory management.