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<p>This paper deals with an inverse median location problem on block graphs with <i>uncertain</i> modification costs in which the vertices are considered as existing customer points. This problem consists of changing the vertex weights of the underlying block graph at the minimum cost so that a prespecified facility location becomes optimal under the perturbed vertex weights. First, the corresponding <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> </InlineEquation>-optimal model is established and discussed for the original uncertain problem which yields optimal solutions under some confidence levels <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\alpha \in [0,1]\)</EquationSource> </InlineEquation>. To find an <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> </InlineEquation>-optimal solution, we develop a novel unified algorithm with polynomial time complexity where all the uncertain cost coefficients have regular distributions. Moreover, we show that the inverse uncertainty distribution of the optimal modification cost, which gives the <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> </InlineEquation>-minimum cost for each confidence level <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> </InlineEquation>, can be represented in polynomial time.</p>

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A unified algorithm for inverse median facility location optimization on block graphs in uncertain environment

  • 期刊论文

  • 发表日期：

    2025年12月17日

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  • Roghayeh Etemad,
  • Behrooz Alizadeh,
  • Somayeh Ahmadi

摘要

This paper deals with an inverse median location problem on block graphs with uncertain modification costs in which the vertices are considered as existing customer points. This problem consists of changing the vertex weights of the underlying block graph at the minimum cost so that a prespecified facility location becomes optimal under the perturbed vertex weights. First, the corresponding \(\alpha \) -optimal model is established and discussed for the original uncertain problem which yields optimal solutions under some confidence levels \(\alpha \in [0,1]\) . To find an \(\alpha \) -optimal solution, we develop a novel unified algorithm with polynomial time complexity where all the uncertain cost coefficients have regular distributions. Moreover, we show that the inverse uncertainty distribution of the optimal modification cost, which gives the \(\alpha \) -minimum cost for each confidence level \(\alpha \) , can be represented in polynomial time.