THE PROCESS PLAN SELECTION PROBLEM Andrew Kusiak* and Gerd Finkex* *Department zyxwvutsrq of Mechanical and Industrial Engineering University of Manitoba **Department of Applied Mathematics Technical University of Nova Scotia ABSTRACT There vutsrqponmlkj on process planning problems zyxw : one by Halevi3 and Most of the planning models for FMSs are based on the assumption that for each part there the other by Chang and Wvsk*. Authors of the is only one process plan available. In this second book discussed the process planning paper, we take the more realistic standpoint that prohlem in the artificial intelligence context. for each part a number of different process plans Yalevi3 suggested a mathematical programming could be used, each of which requires specific approach to modelingandsolvingtheprocess types of tools and fixtures. zyxwvutsrqp A model for the planning problem. Kusiak4 developed three integer programming process planning models. zy TWO selection of a set of process plans with the minimum corresponding manufacturing cost and of them are based on the set covering problem and minimal number of tools and fixtures is the third on the topological ordering problem. formulated.Yeuristicalgorithmsandnumerical To define a process Dlan the following notations results are discussed. are adopted: ITR = (vRl, ... , v ) is a set of material volumes 1. INTRODUCTION to be removed with the same tool and without The loading problem has been of interest to changing the fixture. V is the set of all many researchers working in the area of Flexihle volumes to he removed for a given part. Note Manufacturing Systems (FMSs). This problem is to that V = U VI, where m is the total number of balance machine production capacity in order to tools and fixtures. Let tR be a tool for increase their utilization. Stecke6 presented a nonlinear integer programming formulation for the removing VI, and fR a fixture for presenting a part while removing VI. Then a process plan Pi problem. Two distinct linear integer programmin loading problems are considered in Ammons et al. ‘i is a set of zyxwvu 3 tuDles and Kusiak5. Each of the above mentioned To illustrate this definition consider the formulations considers a tool space constraint which is due to the physical limitation of the following example. tool magazines. All these loading problems have Example 1 been developed under the assumption that there is Given a three dimensional part in Figure 1 with only one process plan (defined as a sequence of matertal volumes VI, . . . , v9 to be removed. In m R=1 {(VI: tl, fl), .. . , (Vm; t , fm) }. operations) available for each manufactured part. As discussed inKusiak4, the following attributes are associated with each process plan: (1) a tool type (2) a fixture type or (3) a gripper type (grippers are typically used to handle rotational parts while fixtures are used for prismatic parts). In practice, for a single part, one can generate a set of different process plans. The attribute values as well as costs may vary €or each of them. Tn this paper, the idea of diversified process plans will be exploited. From the set N of process plans a subset K of process plans will be selected which will reauire (globally) the smallest set of tools, fixtures or grippers and minimum corresponding sum of costs. . .. ., Figure 1. A typical part with volume vl, . . ., to be removed. v9 ’2. THE PROCESS PLANNING PRORLEM will he formulated, let us briefly discuss the process planning problem. For the part in Figure 1 one can generate Before the process plan selection problem the following two process plans: p1 = {(vl,v’2,v3:t1,fl) , (v&,vlj.vfj:tl,f~~ , lv7,v8’t*,fl) , (Vg:t3,f*)} 1827 CH2282-2/86/0000/1827$01.00 zyxwvut 0 1986 mEE