j. Soc. Cosmet. Chem., 32, 287-301 (September/October 1981) Optimization techniques in product formulation JOSEPH B. SCHWARTZ, Merck Sharp & Dohme Research Laboratories, lVest Point, PA 19486. a) Received May 6, 1981. Presented at the SCC Annual Scientific Seminar, lVashington, D.C., May 22, 1981. Synopsis Methods of optimization are well documented in the literature of several fields and are easily adapted to formulation and processing studies in the pharmaceutical and the cosmetic industries. The techniques most widely used for optimization are of two basic types: one where experimentation continues as the study proceeds and a second where experimentation is completed before optimization takes place. The first type may be represented by procedures such as EVOLUTIONARY OPERATIONS (EVOP) and the SIMPLEX METHOD the second type includes the more classical MATHEMATICAL and SEARCH METHODS. For these techniques of the second type, appropriate statistical design of experiments is an important consideration. Based on the resulting data from the required number of experiments, one is able to generate a mathematical model to which the appropriate optimization technique is applied. No matter which method is selected it is important that the formulator be able to distinguish the independent (formulation or controlable) variables from the dependent variables (product properties). Properly designed experimentation and subsequent analysis can lead not only to the optimum or most desirable product and process, but, if carried far enough, can shed light on the mechanism by which the independent variables affect the product properties. There are appropriate statistical techniques by which such analyses can be carried out. It has been shown that such models can be used to accurately predict not only the physical properties of the drug product (such as dissolution, tablet disintegration time, and tablet breaking strength), but also biological properties (such as peak plasma time and absorption rate constant). The application to cosmetic products is indicated. INTRODUCTION The procedure for optimizing the formulation and process for a drug product, or a cosmetic product, is generally the process of making it as perfect as possible within a given set of restrictions or constraints. Physical, chemical, and biological properties must all be given due consideration in the selection of components and processing steps for that dosage form or product. The final product must be one which meets not only the requirements placed on it from a bioavailability standpoint, but also the practical mass production criteria of process and product reproducibility. With a rational approach to the selection of the several excipients and the manufacturing steps a)Present address: Philadelphia College of Pharmacy and Science, 43rd St., Woodland Ave. and Kingessing Mall, Philadelphia, PA 19104. 287

288 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS for the system of interest, we qualitatively select a formulation. It is at this point that optimization can become a useful tool--to quantitate a formulation that has been qualitatively determined. Optimization is not a screening technique. The word "optimize" means to make as perfect, effective or functional as possible. There must be, and there is, a better method than trial and error to determine the best formulation and process. In development projects, we generally experiment, by a series of logical steps, carefully controlling the variables, and changing one at a time, until a satisfactory system is produced. And it is satisfactory but how close is it to the best or the optimum? And how do we know? The techniques of optimization will tell us mathematically (1). OPTIMIZATION PROBLEMS There are two general types of optimization problems--the constrained and the unconstrained. Constraints are those restrictions placed upon the system due to physical limitations or perhaps simple practicality (e.g., economic considerations). In unconstrained optimization problems, there are no restrictions. For a given formula- tion one might say: make the hardest tablet possible, or make lotion with the lowest degree of caking. The constrained problem, on the other hand, would be stated: make the hardest tablet possible, but it must disintegrate in less than fifteen minutes, or the lotion must have minimum caking but it must be pourable. It is obvious that the unconstrained optimization problem is almost nonexistent. There are always restrictions which the formulatot wishes to place or must place on his system and many of these restrictions are competing. We must keep in mind that not only are the restrictions competing, but also that an ingredient or processing step which may have beneficial effects on one property is very often detrimental to another and we must balance these effects. It is sometimes necessary to trade off properties i.e., to sacrifice one characteristic for another. Thus, the primary objective may not be to optimize absolutely, but to compromise effectively and thereby produce the best formulation under a given set of restrictions. An additional complication in the pharmaceutical and cosmetic fields is that formulations are not usually simple systems. They often contain many ingredients and variables which may interact with one another to produce unexpected, if not unexplainable, results. The development of a solid, semisolid, or liquid formulation and the associated process usually involve a number of variables. Mathematically, they can be divided into two groups--independent and dependent. The INDEPENDENT VARIABLES are the formulation and process variables directly under the control of the formulator. These might include the level of a given ingredient or the mixing time for a given process step. The DEPENDENT VARIABLES are the responses or the characteristics of the resulting product. These are a direct result of any change made in the formulation or process. To study formulations in a rational manner, we must be able to distinguish between the two. The techniques most widely used for optimization may be divided into two general categories: one, where experimentation continues as the optimization study proceeds and a second, where the experimentation is completed before the optimization takes