Process sequence optimization based on a new cost±tolerance model S. H. YEO, B. K. A. NGOI and H. CHEN School of Mechanical and Production Engineering, Nanyang Technological University, Nanyang Avenue, Singapore 2263 Received March and accepted July 1997 Identi®cation of the optimal production sequence and allocation of machining tolerance are important activities in process planning for reducing production cost. This paper presents an approach that is capable of determining the optimal production sequence and its optimal process tolerance to achieve the minimum production costs. A new mathematical model, representing the cost±tolerance relationships and showing signi®cant accuracy improvement over existing models, is introduced to allocate process tolerance. Stock allowance constraints on the selected switching tolerance are also considered to yield practical solutions. A prototype system for hole-making components is used to verify and evaluate the eectiveness of the new approach. Ó 1998 Chapman & Hall Keywords: Extended spline model, process sequence, cost±tolerance relationship, stock allowance 1. Introduction Computer-aided process planning (CAPP) is a function whereby detailed operation instructions are prepared in order to transform a design part to a ®nal product. Process planning outlines the machining operations, machine tools, ®xtures and tools which form the framework for job scheduling, NC programming, shop ¯oor control and other manufacturing tasks. A sub-domain of process planning is process sequencing and tolerance allocation. The process sequence task is to decide the type of manufacturing pro- cesses in order to meet the speci®cations of the part. For example, a series of processes, namely drilling, semi-®nish boring and grinding can be used to generate a hole surface feature. Allocation of manufacturing tolerances for each process are combined appropriately to arrive at the desired tolerance. Eective tolerance allocation plays an important role in reducing manufacturing cost. It is therefore im- portant to identify the optimal sequence and to allocate the manufacturing tolerance for the series of processes. Quantitative studies in process sequence and tolerance allocation have been performed using relatively simple models of the cost±tolerance relationship; e.g. Speckhart (1972), Spotts (1973) and Sutherland and Roth (1975). Based on the general characteristics of a production cost± tolerance data curve, various models are proposed, namely the exponential model, reciprocal squared model and reciprocal powers model. Though these simple models are determined easily, however, large modeling errors are in- troduced. Simpli®ed models do not fully represent the cost± tolerance relationship. Their usage does not lead to opti- mum process sequences. In summary, the technique used in allocating manufacturing tolerance is largely dependent on human experience and on handbooks or a company's proprietary information. Quantitative comparison of various production se- quences and their diering combinations signi®cantly in- ¯uence the generation of an optimal process plan. The cost analysis of process sequence generation is still limited. The objective of this research, is to develop an accurate model for the cost±tolerance relationship and to generate an optimal process sequence. It is the extended spline model which is based on the least-squares criterion. Using illustrative examples in this work, it is found that its ap- plication is suitable and adopted in the optimization methodology for process sequencing. 2. Production cost±tolerancing Quantitative manufacturing knowledge is an abstraction of empirical production data. One important abstraction is the relation between design accuracy and production cost. It has been recognized that a tighter tolerance leads to Journal of Intelligent Manufacturing (1998) 9, 29±37 0956-5515 Ó 1998 Chapman & Hall