Cost-optimal replenishment of chemical baths: an application of linear programming

The concentrations of components in chemical baths used in industrial applications often have to meet certain requirements. Production or evaporation may change the relative amounts of the components so that some of the concentrations fall outside their limits, resulting in output deterioration. Determining how much should be added of each of the components is not as straightforward as it may seem at first sight. In this paper we describe a case where this problem was encountered in a quality improvement project at the factory of Philips Semiconductors Stadskanaal, the Netherlands. A linear programming model is developed that can be used to determine the cheapest set of additions under the restriction that the new concentrations in the bath meet their requirements. The simplex algorithm can then be used to solve this problem. An interesting feature of this application is that a standard basic feasible solution that is needed to start up the algorithm is available for every instance of the problem. The results of the method are compared with those of an old method that was used for computing additions. It turns out that for the cases considered, a cost reduction of about 60% is possible. Copyright (C) 2000 John Wiley & Sons, Ltd.