Acceptable product pricing problem using L-localized solutions of max-plus interval linear equations

Product pricing is one of the most important strategies in doing any business. In this paper, we propose a specific marketing situation as an acceptable product pricing problem when the data on purchasing power and transportation cost cannot be measured exactly but can be shown as intervals of possible values. This problem is formulated as a minimization problem of a differentiable convex objective function with max-plus interval linear constraints A ⊗ x = b where x is called an L-localized solution. Its feasible region is nonconvex but could be viewed by the union of box constraints. The steepest descent algorithm is applied to optimize the objective function with respect to each of these box constraints and obtained an optimal solution from the best value.