مدیریت مالی هوشمند

مدیریت مالی هوشمند

تخصیص بودجه تبلیغاتی جذب و نگهداشت مشتری با رویکرد کنترل پویا: مطالعه موردی صنعت لبنیات ایران

نوع مقاله : مقاله پژوهشی

نویسنده
گروه اقتصاد کشاورزی، دانشگاه سید جمال الدین اسدابادی، اسدآباد، همدان
چکیده
هدف: در این پژوهش، هدف، تعیین سیاست بهینه تخصیص بودجه تبلیغاتی بین فعالیت‌های جذب مشتریان جدید و نگهداشت مشتریان فعلی در صنعت لبنیات ایران، با تمرکز بر پنج برند اصلی در دو بازار شیر و پنیر و ارزیابی تفاوت‌های راهبردی بین برندهای بزرگ، متوسط و کوچک در شرایط رقابتی و محدودیت منابع است.
روش: مطالعه حاضر، از چارچوب نظریه کنترل بهینه پویا کلاسیک (نظریه پونتریاگین) و مدل تعمیم‌یافته ویدال-ولف برای مدل‌سازی رابطه بین تبلیغات و سهم بازار استفاده می‌کند. معادله حالت سهم بازار شامل دو نوع تلاش تبلیغاتیِ، جذب و نگهداشت است. مسئله بهینه‌سازی به‌صورت بیشینه‌سازی سود تنزیل‌شده کل با قید معادلات دیفرانسیل حالت، شرایط اولیه و مرزی تدوین گردید. با استفاده از اصل حداکثر پونتریاگین، هامیلتونی، تشکیل و شرایط مرتبه اول بهینگی استخراج شد. داده‌های مورد استفاده شامل فروش ماهانه، هزینه‌های تبلیغاتی، قیمت‌ و حاشیه سود برای دوره سه‌ساله 1401 تا 1403 می‌باشد.
یافته‌ها: نتایج نشان می‌دهد، نسبت بهینه تخصیص بودجه برای برندهای رهبر، حدود 70 درصد برای جذب و 30 درصد برای نگهداشت است، در حالی که برندهای پیرو، به نسبت نزدیک به 50 به 50 نیاز داشتند. شاخص بازگشت سرمایه تبلیغاتی بین 65/1 تا 12/3 متغیر است. نسبت ارزش طول عمر مشتری به هزینه جذب از 6/33 برای برند 5 تا 7/134 برای برند 1 پنیر می‌باشد. دوره بازگشت سرمایه برای برند 1 پنیر، 9 ماه و برای برند 5 شیر، 36 ماه برآورد شد. ارزش سایه‌ای یک درصد سهم بازار برای برند 1 پنیر، در ابتدای دوره 5/20 میلیارد ریال و 2/14 میلیارد ریال در شیر بود.
نتیجه‌گیری: این مطالعه با تعمیم مدل کنترل بهینه ویدال-ولف به فضای رقابت چندبرندی، کالیبراسیون پارامترهای شوک رقابتی بر مبنای چارچوب دورفمن-اشتاینر و برآوردهای GARCH (به‌جای فرض‌های بدون پشتوانه تجربی رایج در ادبیات)، و برازش با داده‌های واقعی صنعت لبنیات ایران، قاعده‌ای عملی برای تخصیص بودجه تبلیغاتی ارائه می‌دهد. با توجه به نتایج، تخصیص بهینه بودجه تبلیغاتی به‌شدت به قدرت برند، موقعیت رقابتی و دسته محصول وابسته است. برندهای رهبر باید بر حفظ نسبت ۷۰-۳۰ و تقویت وفاداری تمرکز کنند، برندهای میان‌رده نیاز به افزایش بودجه نگهداشت به ۳۵ تا ۴۰ درصد دارند و برندهای پیرو باید نسبت را به ۵۰-۵۰ نزدیک کرده و ۷۰ تا ۸۰ درصد بودجه را به تبلیغات دیجیتال اختصاص دهند.
کلیدواژه‌ها
موضوعات

عنوان مقاله English

Advertising Budget Allocation for Customer Acquisition and Retention Using a Dynamic Control Approach: A Case Study of Iran’s Dairy Industry

نویسنده English

Habib Shahbazi
Department of Agricultural Economics, Seyyed Jamaleddin Asadabadi University, Asadabad, Hamedan
چکیده English

Objective: This study aims to determine the optimal advertising budget allocation policy between customer acquisition and retention activities in Iran’s dairy industry, focusing on five major brands across milk and cheese markets, and to evaluate strategic differences among large, medium, and small brands under competitive conditions and resource constraints.
Method: The study employs the classical dynamic optimal control theory framework (Pontryagin’s principle) and the generalized Vidale–Wolfe model to capture the relationship between advertising and market share. The market share state equation incorporates two types of advertising effort: acquisition and retention. The optimization problem is formulated as maximizing total discounted profit subject to state differential equations, initial conditions, and boundary conditions. Using Pontryagin’s maximum principle, the Hamiltonian is constructed and first-order optimality conditions are derived. Data include monthly sales, advertising expenditures, prices, and profit margins for the three-year period 2022–2024.
Findings: Results indicate that the optimal budget allocation ratio for market-leading brands is approximately 70% for acquisition and 30% for retention, whereas follower brands required a ratio close to 50–50. The advertising return on investment index ranges from 1.65 to 3.12. The customer lifetime value-to-acquisition cost ratio ranges from 33.6 for Brand 5 to 134.7 for Brand 1 in cheese. The payback period is estimated at 9 months for cheese Brand 1 and 36 months for milk Brand 5. The shadow value of one percentage point of market share for cheese Brand 1 was 20.5 billion rials at the beginning of the period and 14.2 billion rials for milk.
Conclusion: By extending the Vidale–Wolfe optimal control model to a multi-brand competitive setting, calibrating competitive shock parameters based on the Dorfman–Steiner framework and GARCH estimates (rather than the empirically unsupported assumptions common in the literature), and fitting the model to real data from Iran’s dairy industry, this study provides a practical decision rule for advertising budget allocation. The findings indicate that optimal advertising budget allocation is strongly dependent on brand strength, competitive position, and product category. Market leaders should maintain a 70–30 ratio and focus on loyalty reinforcement; mid-tier brands need to increase their retention budget share to 35–40%; and follower brands should move toward a 50–50 ratio and allocate 70–80% of their budget to digital advertising.

کلیدواژه‌ها English

Advertising budget optimization
customer acquisition
customer retention
dairy industry
Vidale-Wolfe model
optimal control
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