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Estimation of the transition matrix in Markov chain model of customer lifetime value using flower pollination algorithm
Pasaribu U.S.a, Al-Ma’shumah F.a, Permana D.a,b
a Statistics Research Division, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia
b Faculty of Mathematics and Natural Sciences, Padang State University, Indonesia
[vc_row][vc_column][vc_row_inner][vc_column_inner][vc_separator css=”.vc_custom_1624529070653{padding-top: 30px !important;padding-bottom: 30px !important;}”][/vc_column_inner][/vc_row_inner][vc_row_inner layout=”boxed”][vc_column_inner width=”3/4″ css=”.vc_custom_1624695412187{border-right-width: 1px !important;border-right-color: #dddddd !important;border-right-style: solid !important;border-radius: 1px !important;}”][vc_empty_space][megatron_heading title=”Abstract” size=”size-sm” text_align=”text-left”][vc_column_text]© 2015 Udjianna S. Pasaribu, Fathimah al-Ma’shumah, and Dony Permana.Customer Lifetime Value (CLV) is a useful and important concept in marketing to help any company in budgeting marketing cost for its customers. This paper presents a fairly new class of CLV models that is Markov Chain Models (MCM). The major advantage of this model is its flexibility to be modified to several different classification schemes. One of them is the probability transition matrix containing the rate of retention and acquisition. It plays an important role to calculate the total cost to maintain the satisfaction of a customer. In contrast, a company can set the future benefit for a certain customer. The term of this is called CLV. The aim of this paper is to estimate the matrix for a customer from the target of his expected future benefit (or CLV). Mathematically, the estimation formula contains nonlinear form of the elements of the probability transition matrix and this is called as the inverse problem of CLV. The numerical method applied in this work is a metaheuristic optimization algorithm developed by Yang, 2013, that is Flower Pollination Algorithm. For the study case, health insurance data is taken along with some arbitrary constant interest rates for the next five years.[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Author keywords” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Indexed keywords” size=”size-sm” text_align=”text-left”][vc_column_text]Customer lifetime value,Flower pollination algorithm,Inverse problems,Markov chain models,Probability transition matrix[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Funding details” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”DOI” size=”size-sm” text_align=”text-left”][vc_column_text]https://doi.org/10.12988/ams.2015.52102[/vc_column_text][/vc_column_inner][vc_column_inner width=”1/4″][vc_column_text]Widget Plumx[/vc_column_text][/vc_column_inner][/vc_row_inner][/vc_column][/vc_row][vc_row][vc_column][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][/vc_column][/vc_row]