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http://repository.ipb.ac.id/handle/123456789/62157
Title: | Optimum Control in Advertising Problem Kontrol Optimum pada Masalah Periklanan |
Authors: | Bakhtiar, Toni Kusnanto, Ali Prihartini, Utami |
Keywords: | Bogor Agricultural University (IPB) |
Issue Date: | 2010 |
Abstract: | Advertising is a form of communication and promotion of goods or services. It aims to convey the information in form of a message through the media and persuade that generate responses from audiences. A company must pay some additional cost to make advertising. Thus, it generates new problems, because in general a company will attempt to maximize the profit. It is necessary to find a right advertising policy from the company to allocate their advertising budget with some constraints. This paper discusses the sales-advertising response model that emphasizes the relationship between advertising costs and sales levels. The advertising models used in this paper are V-W model and Contagion model. Advertising problem is formulated in a form of optimal control problem which involves the S-shaped response function as a form of application for the solutions of profit maximization problem. The optimum control problem is solved using Pontryagin’s maximum principle. Then, fixed points of the models are analyzed. From V-W and Contagion models it can be concluded that if the cost of advertising is constant then it will be obtained a constant level of sales, so that obtained constant profits rate is over time. Involvement of S-shaped response function produced three fixed points, i.e. stable node, saddle and unstable spiral. The simulation results show that at the beginning, the company has not advertised, there is no incentive for the company to produce. Then, after the company begins to advertise, the level of benefits is still very small even resulted in a negative value at Contagion model. The reason is because it costs too much while the sales rate can not cover the costs of making advertising. At third fixed point, the rate of return insulated and enlarged from time to time as long as a company is still productive. |
URI: | http://repository.ipb.ac.id/handle/123456789/62157 |
Appears in Collections: | UT - Mathematics |
Files in This Item:
File | Description | Size | Format | |
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G10upr.pdf Restricted Access | Fulltext | 1.97 MB | Adobe PDF | View/Open |
Abstract.pdf Restricted Access | Abstract | 370.46 kB | Adobe PDF | View/Open |
BAB I Pendahuluan.pdf Restricted Access | BAB I | 411.4 kB | Adobe PDF | View/Open |
BAB II Landasan Teori.pdf Restricted Access | BAB II | 636.66 kB | Adobe PDF | View/Open |
BAB III Model Periklanan.pdf Restricted Access | BAB III | 417.85 kB | Adobe PDF | View/Open |
BAB IV Pembahasan.pdf Restricted Access | BAB IV | 524.39 kB | Adobe PDF | View/Open |
BAB V Kesimpulan.pdf Restricted Access | BAB V | 399.7 kB | Adobe PDF | View/Open |
Cover.pdf Restricted Access | Cover | 381.42 kB | Adobe PDF | View/Open |
Daftar Pustaka.pdf Restricted Access | Daftar Pustaka | 399.7 kB | Adobe PDF | View/Open |
Lampiran.pdf Restricted Access | Lampiran | 1.57 MB | Adobe PDF | View/Open |
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