Cost-effective company response policy for product co-creation in company-sponsored online community

TL;DR

This work introduces the CRP problem for product co-creation in company sponsored online communities and casts it as an open-loop deterministic optimal-control problem with an epidemic-like state evolution for community activity. The authors derive the optimality system via the Pontryagin Maximum Principle and solve it with a forward-backward sweep based CRP algorithm, demonstrating rapid convergence and superior cost-benefit performance across extensive numerical experiments. They also compare against a dynamic-programming alternative (CRP2) and discuss practical implementation steps, parameter estimation, and factor sensitivity. The study shows that cost-effective CRPs can be realized by optimally shaping the company response rate over the co-creation horizon, with practical guidance on data collection and policy deployment, thereby offering a principled framework for value co-creation in online communities.

Abstract

Product co-creation based on company-sponsored online community has come to be a paradigm of developing new products collaboratively with customers. In such a product co-creation campaign, the sponsoring company needs to interact intensively with active community members about the design scheme of the product. We call the collection of the rates of the company's response to active community members at all time in the co-creation campaign as a company response policy (CRP). This paper addresses the problem of finding a cost-effective CRP (the CRP problem). First, we introduce a novel community state evolutionary model and, thereby, establish an optimal control model for the CRP problem (the CRP model). Second, based on the optimality system for the CRP model, we present an iterative algorithm for solving the CRP model (the CRP algorithm). Thirdly, through extensive numerical experiments, we conclude that the CRP algorithm converges and the resulting CRP exhibits excellent cost benefit. Consequently, we recommend the resulting CRP to companies that embrace product co-creation. Next, we discuss how to implement the resulting CRP. Finally, we investigate the effect of some factors on the cost benefit of the resulting CRP. To our knowledge, this work is the first attempt to study value co-creation through optimal control theoretic approach.

Figures (6)

• Figure 1: Diagram of the community state evolutionary model.
• Figure 2: The experimental results in Experiment 1: (a) the resulting sequence of CRPs, denoted $\{x^{(k)}\}_{k=1}^4$, (b) $J(x)$ versus $x$, $x \in \{x_1^*, x_1, \cdots, x_{100}\}$.
• Figure 3: The experimental results in Experiment 2: (a) the resulting sequence of CRPs, denoted $\{x^{(k)}\}_{k=1}^{5}$, (b) $J(x)$ versus $x$, $x \in \{x_2^*, x_1, \cdots, x_{100}\}$.
• Figure 4: The experimental results in Experiment 3: (a) the resulting sequence of CRPs, denoted $\{x^{(k)}\}_{k=1}^{5}$, (b) $J(x)$ versus $x$, $x \in \{x_3^*, x_1, \cdots, x_{100}\}$.
• Figure 5: The CRP $x_2^*$ obtained in Experiment 4.

Theorems & Definitions (7)

• Remark 1
• Theorem 1
• Theorem 2
• Theorem 3
• Remark 2
• Remark 3
• Remark 4