Dynamic optimal pricing considering advertising and improvement quality strategies over product life-cycle horizon

Determining effective policies to boost demand in each phase of the product life cycle (PLC) holds paramount importance for every supply chain member, profoundly influencing decision-making at each stage. This paper delves into the dynamic nature of the PLC, considering the distinct characteristics of each phase. Through an exploration of a differential game model, the manufacturer strategically adopts appropriate policies in each PLC phase, encompassing a blend of advertising and product quality enhancement. During the introduction-growth phase, the manufacturer concentrates on advertising to introduce the product and increase demand. Transitioning into the maturity phase, alongside sustained advertising efforts, the manufacturer allocates resources to enhance product quality. The key contributions of this study encompass the proposal of an optimal control model tailored to PLC phases, the formulation of differential equations governing quality level and goodwill, and the determination of optimal trajectories for wholesale and retail prices, advertisements, and quality levels through Stackelberg equilibrium. Furthermore, the study conducts a comprehensive analysis of the impact of these policies on the demand function, goodwill, and profit of supply chain members. A case study involving an Iranian mobile phone accessories manufacturer is scrutinized, offering managerial insights. Noteworthy findings highlight that higher initial product quality diminishes the necessity for advertising throughout the product life cycle, resulting in cost reduction. Additionally, the optimal pricing strategy for new products entering the market involves commencing with a low price and gradually increasing it in response to consumer demand.