Dynamic optimization of interdependent model between marketing and production departments

Abstract

In this study, new model having rational properties with respect to salesadvertising relationship is proposed. With an empirical study, this model is analyzed in detail by comparison with the existing sales-advertising model. Extension to discrete-time versions of two continuous-time models(new model and the existing model) is also shown. In addition, in order to check the equilibrium and stability under optimal closed-loop systems of two models, the system analysis is performed. Then, taking into consideration interdependency of production and marketing departments, interdependent model based on new model of sales-advertising and HMMS model of production-inventory is developed. It is compared with separate models of advertising and production planning. Extension to discrete-time version is also shown. Though numerical examples, it is shown that simultaneous planning of advertising and production can result in significant savings.