Constrained Spatial Layout and Simultaneous Production Evaluation for a Production System

Abstract

This paper proposes a mathematical model called Multi-objective Production System Design (MOPSD) model and a two-staged solving procedure. The MOPSD model not only considers the two-dimensional layout of a production system under the constrained factory space to achieve the minimal total material transportation flow but also determines the optimal assigned number of workstations and the optimal system cycle time concerning a simultaneous production situation. The first major objective of MOPSD model is regarded as a Quadratic Assignment Problem (QAP), but it considers the size of operation element, the multiple production lines, and the constrained two-dimensional factory space where traditional QAP studies are seldom mentioned. The second objective of the MOPSD model is to determine the optimal system cycle time as well as the optimal assigned number of workstations under the simultaneous production situation for preventing the underestimation of the system production rate. The first-stage solving procedure of the MOPSD model applies the space discrete technique to make the infinite deployable locations become finite, and then one can achieve the major objective through the system layout. In addition, the Four Position Coding Technique (FPCT) is developed to code the nodes in the deployed production system obtaining from the first stage, and therefore those FPCT codes can function as the input parameters in the second-stage solving procedure. These two solving procedures are constructed by the syntax of Lingo 9.0 extended version, and a numerical example is followed to describe the detailed solving procedure. In summary, the repeated characteristic of the MOPSD model and its solving procedure make this study a valuable decision support tool because they are constructed by the packaged software Lingo 9.0. That is, a factory can easily duplicate to solve other cases by changing its input parameters only.