Analisis Kestabilan dan Kontrol Optimal Model Matematika Dinamika Pelanggan Berdasarkan Kebijakan Pemasaran
Customer dynamics include the exchange of information and ongoing transactions between customers and the organization. This process has an important role in the company to run its business, so that the number of customers increase. To achieve this, many things are done by the company. One of the str...
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| Format: | Article |
| Language: | English |
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Universitas Airlangga
2020-05-01
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| Series: | Contemporary Mathematics and Applications (ConMathA) |
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| Online Access: | https://e-journal.unair.ac.id/CONMATHA/article/view/19300 |
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| author | Muhammad Iqbal Abdi Farchan Fatmawati Fatmawati Cicik Alfiniyah |
| author_facet | Muhammad Iqbal Abdi Farchan Fatmawati Fatmawati Cicik Alfiniyah |
| author_sort | Muhammad Iqbal Abdi Farchan |
| collection | DOAJ |
| description | Customer dynamics include the exchange of information and ongoing transactions between customers and the organization. This process has an important role in the company to run its business, so that the number of customers increase. To achieve this, many things are done by the company. One of the strategies is product advertising by word of mouth. The purpose of this thesis is to analyze the stability of equilibrium point and to apply the optimal control word of mouth advertising on mathematics model of the customer dynamics based on marketing policy. Mathematics model of the customer dynamics based on marketing policy without control has two equilibrium points, namely non – endemic equilibrium (E0) and endemic equilibrium (E1). Local stability of equilibrium and the existence of endemic equilibrium depends on basic reproduction number (R0). The non – endemic equilibrium tend to asymptotically stable if R0 < 1. The problem of optimal control is solved by Pontryagin's Maximum Principle. The simulation results show that the total number of referral and regular customer populations that are given control in the form of word of mouth advertising efforts at the end of the observation are 312 and 18470 with the control effort costs occurred in 1798364.63. While the total number of referral and regular customer populations that are not given control in the form of word of mouth advertising efforts at the end observation are 241 and 17260. Based on these results show that word of mouth advertising efforts have an effect to increase the number of referral and regular customer in accordance with the aim of providing optimal control. |
| format | Article |
| id | doaj-art-7d6642aa03324a508177e3d3cb466f68 |
| institution | Kabale University |
| issn | 2686-5564 |
| language | English |
| publishDate | 2020-05-01 |
| publisher | Universitas Airlangga |
| record_format | Article |
| series | Contemporary Mathematics and Applications (ConMathA) |
| spelling | doaj-art-7d6642aa03324a508177e3d3cb466f682024-12-09T03:30:25ZengUniversitas AirlanggaContemporary Mathematics and Applications (ConMathA)2686-55642020-05-0121234510.20473/conmatha.v2i1.1930015747Analisis Kestabilan dan Kontrol Optimal Model Matematika Dinamika Pelanggan Berdasarkan Kebijakan PemasaranMuhammad Iqbal Abdi FarchanFatmawati FatmawatiCicik AlfiniyahCustomer dynamics include the exchange of information and ongoing transactions between customers and the organization. This process has an important role in the company to run its business, so that the number of customers increase. To achieve this, many things are done by the company. One of the strategies is product advertising by word of mouth. The purpose of this thesis is to analyze the stability of equilibrium point and to apply the optimal control word of mouth advertising on mathematics model of the customer dynamics based on marketing policy. Mathematics model of the customer dynamics based on marketing policy without control has two equilibrium points, namely non – endemic equilibrium (E0) and endemic equilibrium (E1). Local stability of equilibrium and the existence of endemic equilibrium depends on basic reproduction number (R0). The non – endemic equilibrium tend to asymptotically stable if R0 < 1. The problem of optimal control is solved by Pontryagin's Maximum Principle. The simulation results show that the total number of referral and regular customer populations that are given control in the form of word of mouth advertising efforts at the end of the observation are 312 and 18470 with the control effort costs occurred in 1798364.63. While the total number of referral and regular customer populations that are not given control in the form of word of mouth advertising efforts at the end observation are 241 and 17260. Based on these results show that word of mouth advertising efforts have an effect to increase the number of referral and regular customer in accordance with the aim of providing optimal control.https://e-journal.unair.ac.id/CONMATHA/article/view/19300customer dynamicsmathematics modeloptimal controlstabilityword of mouth advertising. |
| spellingShingle | Muhammad Iqbal Abdi Farchan Fatmawati Fatmawati Cicik Alfiniyah Analisis Kestabilan dan Kontrol Optimal Model Matematika Dinamika Pelanggan Berdasarkan Kebijakan Pemasaran Contemporary Mathematics and Applications (ConMathA) customer dynamics mathematics model optimal control stability word of mouth advertising. |
| title | Analisis Kestabilan dan Kontrol Optimal Model Matematika Dinamika Pelanggan Berdasarkan Kebijakan Pemasaran |
| title_full | Analisis Kestabilan dan Kontrol Optimal Model Matematika Dinamika Pelanggan Berdasarkan Kebijakan Pemasaran |
| title_fullStr | Analisis Kestabilan dan Kontrol Optimal Model Matematika Dinamika Pelanggan Berdasarkan Kebijakan Pemasaran |
| title_full_unstemmed | Analisis Kestabilan dan Kontrol Optimal Model Matematika Dinamika Pelanggan Berdasarkan Kebijakan Pemasaran |
| title_short | Analisis Kestabilan dan Kontrol Optimal Model Matematika Dinamika Pelanggan Berdasarkan Kebijakan Pemasaran |
| title_sort | analisis kestabilan dan kontrol optimal model matematika dinamika pelanggan berdasarkan kebijakan pemasaran |
| topic | customer dynamics mathematics model optimal control stability word of mouth advertising. |
| url | https://e-journal.unair.ac.id/CONMATHA/article/view/19300 |
| work_keys_str_mv | AT muhammadiqbalabdifarchan analisiskestabilandankontroloptimalmodelmatematikadinamikapelangganberdasarkankebijakanpemasaran AT fatmawatifatmawati analisiskestabilandankontroloptimalmodelmatematikadinamikapelangganberdasarkankebijakanpemasaran AT cicikalfiniyah analisiskestabilandankontroloptimalmodelmatematikadinamikapelangganberdasarkankebijakanpemasaran |