Improvement of the Sales Comparison Approach using Analytical Hierarchy Process and linear optimization: methodological setting

The theory and methodology of real estate appraisal are arranged in a well-known hierarchical structure whose levels are approaches, methods, and models. This study deals with the first of the three approaches - market, income, and cost. The market approach is rooted in the principle of price equilibrium; hence, a subject’s value can be identified based on the price of similar assets, provided technical and economic data for at least a few recent transactions are available.Under the above framework, the sales comparison adjustment grid and a variety of related models and techniques are among the most commonly used by practitioners and appraisers to assess the market value of real estate assets, even though they are affected by some severe flaws and deficiencies. The most prominent weaknesses the literature pointed out lie in the selection criteria for the comparables, the sample size, and the weighting of the comparables’ attributes. The weighting process, especially, is undermined by subjectivity, uncertainty, and a certain lack of reliability.Several attempts have been made to overcome the drawbacks affecting the weighting process in the sales comparison adjustment grid, resulting in promising mathematical and statistical approaches, which are nonetheless inconvenient and way too complex for most appraisers. Here, we propose to solve the subjectivity issue in the weighting of the comparables’ attributes using a process that practitioners can easily replicate on a worksheet, without requiring expert knowledge of mathematics and statistics.The solution we put forward combines the Analytic Hierarchy Process (AHP) and linear optimization. A relationship is established between the properties in the sales comparison adjustment grid and the hierarchical value tree on which AHP builds. From the bottom to the top of the tree: comparables are the alternatives, while attributes are the criteria. Since the sale price should reflect and summarize how much the consumers value the property features, the rankings of the comparable according to their sale price and according to their weighted attributes should converge. The criteria (i.e., attributes) weights are thus iteratively searched by matching the ranking of the alternatives (i.e., comparables) according to their sale price and the ranking of the same according to their attributes. In other words, optimal weights are identified as the attributes’ marginal prices that minimize the overall distance between those rankings.