A robust optimization model under uncertain environment: An application in production planning

Abstract

An intuitive way to handle optimization problems with data affected by the uncertainty set is to undergo a robust optimization problem where the solution must be satisfied for any possible realization of the data in the uncertainty set. In this work, we addressed an uncertain linear programming problem in which some constraints involves the product of two uncertain parameters that are robust in nature. Hereafter, we discuss the max–min regret approach and subsequently with the help of Lagrangian duality, establish an equivalent approximation of the robust counterpart of such types of uncertain programming problems. Further, for the application purpose, we propose a multi-objective, multi-product production planning model of a captive repair shop for overhauling and repairing products or machines which indicates the relevance of the theoretical performance.