A multi-zone discrete search model for a hidden target with discounted probabilistic effort allocation

This study aims to develop a discrete search model for detecting a hidden target located on one of several real lines intersecting at the origin. The target position is represented by a vector of independent random variables with a symmetric truncated multivariate probability distribution. Each search region is divided into several high-probability subintervals after excluding low-probability ones and redistributing their probabilities. The model considers the search effort to be constrained by a normally distributed random variable, while incorporating a discount parameter to account for uncertainty. A discrete optimization problem is formulated and solved to maximize the detection probability with minimum search effort. In addition, the stability of the minimal search effort is analyzed. The results, illustrated through an application example, demonstrate the effectiveness of the model in improving search efficiency and reducing cost, thereby providing a practical contribution to search-and-rescue models.