A shopping-path length estimation using Markov-chain-based shopper dynamics model

Shunichi Ohmori*, Masao Ueda, Kazuho Yoshimoto

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We propose a framework of estimating shopping-path length, in which the floor is represented by the graph G(V,E) with a vertex set V and an arc set E and the shopping-path length is measured by the number of zones (vertices) shoppers visit. We used the Markov-chain to model the dynamics of distribution of shoppers on the vertecies in the graph. We derive the (discrete) probability distribution of shopping path length using the transition matrix in the Markov-chain, and derive the expected path length. We proposed the index called the improvement importance index to quantify how local changes in the transition probability affect the entire shopping path length. We have tested our framework to the test data from an industrial application and the estimated path-length is compared to the actual one. We have a result that the error of estimation is 0.2%.

Original languageEnglish
Pages (from-to)68-73
Number of pages6
JournalOperations and Supply Chain Management
Issue number2
Publication statusPublished - 2019


  • Logistic
  • Supply chain management
  • Vehicle routing

ASJC Scopus subject areas

  • Management Information Systems
  • Statistics, Probability and Uncertainty
  • Management Science and Operations Research
  • Information Systems and Management


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