Multiple-Square-Root Minimization Problem

Abstract

The Multiple-Square-Root Minimization Problem (MSR) has an objective function that consists of a sum of a linear term and at least two square root terms. The Lagrangian sub - problem for the LMRP is a typical MSR problem and there are other MSR problems in real life. A simple example is that we add other concave cost s besides the safety stock cost to the LMRP, such as the labor cost and even minimize the negation of the revenue. We tested a sort of heuristic involved, similar to the method to solve the problem of the LMRP vibrational days, and we explore the heuristic is probably the most optimal condition. The accuracy of this approach is declining at a slow rate, because the number of square roots is increasing, and when the number is not too large, it stays at a higher level.