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 article 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). Third, 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.

Advanced persistent threat (APT) as a new type of cyber espionage poses a severe threat to modern organizations. Artificial APT defense, in which an organization engages experienced cybersecurity experts to artificially check if there exist rootkits implanted by APT actors within the organizational internet and, if so, artificially remove the discovered rootkits, is recognized as an indispensable part of APT defense. There are two different ways of artificial APT defenses: continuous artificial defense (CAD), where the defense work is conducted at all time points, and impulsive artificial defense (IAD), where the defense work is conducted at a scheduled sequence of time points. IAD is superior to CAD in terms of the overall service cost. In the context of IAD, we refer to each sequence of service costs as an IAD policy. This paper addresses the problem of developing a cost-effective IAD policy (the IAD problem). First, by introducing an impulsive state evolutionary model for the organizational intranet, the IAD problem is reduced to an optimal impulsive control model (the IAD model). Second, by deriving the optimality system for the IAD model, an iterative algorithm for solving the IAD model (the IAD algorithm) is presented. Next, the convergence and effectiveness of the IAD algorithm are validated through numerical experiments. Finally, the effect of some factors is inspected. To our knowledge, this is the first time IAD is inspected from the perspective of optimal impulsive control theory.

With the prevalence of online social networks, the potential threat of misinformation has greatly enhanced. Therefore, it is significant to study how to effectively control the spread of misinformation. Publishing the truth to the public is the most effective approach to controlling the spread of misinformation. Knowledge popularization and expert education are two complementary ways to achieve that. It has been proven that if these two ways can be combined to speed up the release of the truth, the impact caused by the spread of misinformation will be dramatically reduced. However, how to reasonably allocate resources to these two ways so as to achieve a better result at a lower cost is still an open challenge. This paper provides a theoretical guidance for designing an effective collaborative resource allocation strategy. First, a novel individual-level misinformation spread model is proposed. It well characterizes the collaborative effect of the two truth-publishing ways on the containment of misinformation spread. On this basis, the expected cost of an arbitrary collaborative strategy is evaluated. Second, an optimal control problem is formulated to find effective strategies, with the expected cost as the performance index function and with the misinformation spread model as the constraint. Third, in order to solve the optimal control problem, an optimality system that specifies the necessary conditions of an optimal solution is derived. By solving the optimality system, a candidate optimal solution can be obtained. Finally, the effectiveness of the obtained candidate optimal solution is verified by a series of numerical experiments.

Multiplatform advertising (MPA) is recognized as an effective means of enhancing marketing revenue. In the context, we refer to the scheme of dynamically allocating the advertising expenditure among the selected media platforms as an MPA policy, and we refer to the problem of developing an MPA policy with maximum benefit as the MPA problem. This article is devoted to the solution of the MPA problem. An evolutionary model for the expected market state, in which the influence of both advertising and word-of-mouth (WOM) propagation is accounted for, is established. On this basis, the expected benefit of an MPA policy is calculated. Thereby, the MPA problem is reduced to an optimal control problem we refer to as the MPA model, where the objective functional stands for the expected benefit of an MPA strategy. The optimality system for the MPA model is derived. We refer to the MPA policy obtained by solving the optimality system as the promising MPA policy. The structure of the promising MPA policy is inspected. Through extensive comparative experiments, it is concluded that the promising MPA policy is superior to the majority of MPA policies in terms of expected benefit. Finally, how the expected benefit of the promising MPA policy is influenced by some factors is investigated.

To restrain escalating computer viruses, new virus patches must be constantly injected into networks. In this scenario, the patch-developing cost should be balanced against the negative impact of virus. This article focuses on seeking best-balanced patch-injecting strategies. First, based on a novel virus-patch interactive model, the original problem is reduced to an optimal control problem, in which (a) each admissible control stands for a feasible patch-injecting strategy and (b) the objective functional measures the balance of a feasible patch-injecting strategy. Second, the solvability of the optimal control problem is proved, and the optimality system for solving the problem is derived. Next, a few best-balanced patch-injecting strategies are presented by solving the corresponding optimality systems. Finally, the effects of some factors on the best balance of a patch-injecting strategy are examined. Our results will be helpful in defending against virus attacks in a cost-effective way.