基于需求擴(kuò)散和隨機(jī)技術(shù)進(jìn)步的連續(xù)產(chǎn)品引入過程(編輯修改稿)
2025-03-28 14:14 本頁面
【文章內(nèi)容簡介】 time, infinitehorizon scenario, consider a single base product that progresses through a series of product generations over time. ? The benefits of improved technology are realized only through introduction of a new product generation that incorporates the latest technology available in RD. ? An improvement in the incumbent product technology leads to a higher sales potential for the new product generation. However, each new generation requires a fixed introduction cost. The firm seeks an introduction policy that maximizes profits. Model ? In each period, the firm has the option to either introduce the latest technology or continue selling at the current incumbent technology level (wait). ? We model the level of technology in RD using a single index, and assume that this level improves stochastically during each period. ? Our objective is to characterize the firm’ s optimal introduction policy given this stochastic RD process. Model—Notation and Assumptions ? We begin with the following definitions under a dynamicprogramming framework: Model—Notation and Assumptions Model—Notation and Assumptions ? We consider a durable base product for which product technology is additive and introduction of a new product generation results in plete obsolescence of the previous generation。 ., once a new generation is introduced, sales of the previous generation immediately drop to and remain at zero. This property is referred to later as the “ plete replacement” condition. ? It is assumed that (1) available product technology improves in each period according to a stochastic process, and (2) sales for any given generation follow a demand diffusion process. Model—Notation and Assumptions ? Both the technology level and the price of a new product are expected to influence the product’ s market potential and associated demand diffusion dynamics . To understand the effects of progressing technology independent of other pounding factors, we assume a very specific but realistic pricing strategy that maintains constant unit profit margins. Model—Notation and Assumptions ? As mentioned above, sales potential is assumed to be an increasing function of product technology level. ? Moreover, we do not model capacity constraints and assume that all demand can be met so that sales equals demand. Model Formulation the following assumption is made on the sales rate curves: Model Formulation ? (i) ensures that, all else equal, product sales rate is nondecreasing in product technology. ? Part (ii) acmodates realistic durablegood market scenarios in which the potential market size is finite and current period sales do not exceed total remaining market potential. ? Condition (iii) limits the rate at which sales decrease and in a discretetime framework guarantees that the sales rate from one period to the next does not decrease at a faster pace than sales accumulated within the period. Model Formulation Model Formulation ? The optimum introduction policy is puted from the optimality equation: Model—Relationship to Demand Diffusion ? For the scenario considered in this paper, there is a natural link between this sales model and that of a typical (continuoustime) diffusion model. Consider the Bass diffusion model for a single innovative product: Model—Relationship to Demand Diffusion Mahajan and Muller (1996) present an extension of the Bass model for the case of multiple product generations. Model—Relationship to Demand Diffusion Model—Relationship to Demand Diffusion where a and b are coefficients of innovation and imitation, respectively. Because cumulative sales is tracked as a state variable, the decision model (1)–(3) clearly captures the interaction between product generations when sales curves are of the demand diffusion form (6). Moreover, an examination of (6) shows that the demand diffusion form satisfies Assumption 1 subject to a mild restriction on problem parameters. Optimal Policy Optimal Policy Optimal Policy ? The first result states that as the two systems progress over time, the cumulative sales level of the firm with lower initial cumulative sales will never surpass the firm with
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