Optimal blending of out-of-specifications substances

A chemical company produces powdery substances by a process that is difficult to control tightly. As a result, a significant proportion of production lots fail to meet the specifications of one or more of the key measurable characteristics. These lots are stored in bins that can be later blended in fixed amounts so as to produce a larger batch that is within specifications on all measurements. The blending of these bins is formulated here as an integer programming problem. This paper describes the sequential solution procedure used to find an optimal solution. The sequential procedure includes a penalty function at each step that is designed to force ‘bad’ lots, the most out-of-specifications, to blend first. The introduction of a variable step size eliminated the need for a branch-and-bound procedure.