Optimal Digital Product Maintenance with a Continuous Revenue Stream

2014/12/30 by James Fan, Fan, James, Christopher Griffin +1
Business, Management and Accounting · Decision Sciences · #49N90 #97M40 #Digital Platforms and Economics #FOS: Economics and business #FOS: Mathematics #General Finance (q-fin.GN) #Innovation Diffusion and Forecasting #Optimization and Control (math.OC) #Supply Chain and Inventory Management

paper · pdf · doi:10.48550/arxiv.1412.8624

openalex publication_date 2014/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use a control framework to analyze the digital vendor's profit maximization problem. The vendor captures market share by focusing costly effort on post-launch product maintenance, which influences user perception of the product and drives a revenue stream associated with product use. Our theoretical results show necessary and sufficient conditions for product maintenance to decline over a product's life-cycle, thus showing conditions when Lehman's 7th law of software evolution holds. We also numerically illustrate control paths under different market conditions.

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