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The Cost of Myopia with Respect to a Switching Time in an Advertising Model

Author

Listed:
  • Alessandra Buratto

    (University of Padova)

  • Luca Grosset

    (University of Padova)

  • Maddalena Muttoni

    (University of Padova)

  • Bruno Viscolani

    (University of Padova)

Abstract

The ability to react to abrupt changes constitutes a fundamental skill for decision makers, especially in dynamic contexts where problem structures can change over time. However, there are situations in which planners are myopic, i.e., unaware of the impending changeover. The latter context inevitably results in a loss of profit. This paper aims to assess the cost of adopting a myopic approach toward system changes. We consider a marketing problem modeled à la Nerlove and Arrow, where the demand for a product is influenced by the goodwill of the firm that produces, advertises, and sells it. Moreover, we assume that production costs may change abruptly with a hazard rate that depends on the demand for the product. To address this situation, we formulate and solve an optimal control problem with stochastic switching time. We compare the optimal profit of a planner who is aware of the possibility of a switch to the one of a planner who is myopic with respect to such an event.

Suggested Citation

  • Alessandra Buratto & Luca Grosset & Maddalena Muttoni & Bruno Viscolani, 2025. "The Cost of Myopia with Respect to a Switching Time in an Advertising Model," International Series in Operations Research & Management Science,, Springer.
    • Handle: RePEc:spr:isochp:978-3-031-88638-6_7
    DOI: 10.1007/978-3-031-88638-6_7
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