Solving a multi-objective simulation model using a hybrid response surface method and lexicographical goal programming a
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Solving a multi-objective simulation model using a hybrid response surface method and lexicographical goal programming approach—a case study on integrated circuit ink-marking machines T Yang* and L Tseng National Cheng Kung University, Tainan, Taiwan In an integrated circuit (IC) packaging plant, the ink-marking machine has a significantly higher throughput than the other processing machines. When periodic demand surges result in backlog orders or in lost customers, there is a need to increase system throughput. To resolve this problem, the purchase of a new machine often results in excess capacity in addition to added operation and acquisition costs. Therefore, the productivity improvement effort has priority over the machine purchase decision. This paper seeks to optimize both throughput and cycle time performance for IC ink-marking machines. While throughput increase is the primary objective, there is an acceptable cycle time limit for a feasible solution. It is a multi-objective problem. The proposed solution methodology constructed a simulation metamodel for the ink-marking operation by using a fractional factorial experimental design and regression analysis. It is then solved by a hybrid response surface method and lexicographical goal programming approach. Solution results illustrated a successful application. Journal of the Operational Research Society (2002) 53, 211–221. DOI: 10.1057=sj=jors=2601284 Keywords: simulation; response surface method; goal programming; integrated circuit packaging; integrated circuit ink-marking
Introduction In the modelling process of many complex systems, analytical approaches are often constrained by their computational complexity. Modelling by simulation can provide detailed information. It can model nonlinear and stochastic problems and allow examination of the likely behaviour of a proposed manufacturing system under selected conditions. However, simulation is time consuming and is essentially a trial-and-error approach. It does not provide a method for optimization. The use of a metamodel has been proposed to alleviate some of these problems. A simulation metamodel uses regression analysis to suggest a functional relationship between selected decision variables and system responses. It provides an approach to statistical summarization of simulation results, allowing some extrapolation from the simulated range of system conditions and therefore potentially offering some assistance in optimization.1 Let Xj denote a factor j influencing the outputs of a realworld system ð j ¼ 1; 2; . . . ; sÞ, and let Y denote a system response vector and Y ¼ f y1 ; y2 ; . . . ; yw g. Kleijnen2 defined the metamodel as follows. The relationship between the
*Correspondence: T Yang, Institute of Manufacturing Engineering, National Cheng Kung University, 1 University Road, Tainan 701, Taiwan. E-mail: [email protected]
response variable Y and the inputs Xj of the system can be r
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