Application of Uncertain Variables to Production Planning in a Class of Manufacturing Systems

A production planning problem is addressed in the paper. It consists in the determination of a production plan of products to maximize a total utility connected with their manufacture, taking into account a limited amount of types of resources which are necessary for the production. An uncertain version of the problem is considered when an amount of the resources are not precisely known. The formalism of uncertain variables is proposed in the paper to solve this problem. The solution algorithms for two versions of the uncertain production planning problem are presented. It turned out possible to replace the uncertain problems by their deterministic counterparts. A simple numerical example illustrates the solution algorithms.