Robust Optimization in Simulation: Taguchi and Krige Combined

Abstract

O ptimization of simulated systems is the goal of many methods, but most methods assume known environments. We, however, develop a "robust" methodology that accounts for uncertain environments. Our methodology uses Taguchi's view of the uncertain world but replaces his statistical techniques by design and analysis of simulation experiments based on Kriging (Gaussian process model); moreover, we use bootstrapping to quantify the variability in the estimated Kriging metamodels. In addition, we combine Kriging with nonlinear programming, and we estimate the Pareto frontier. We illustrate the resulting methodology through economic order quantity (EOQ) inventory models. Our results suggest that robust optimization requires order quantities that differ from the classic EOQ. We also compare our results with results we previously obtained using response surface methodology instead of Kriging.

A Simulation-Optimization strategy to deal simultaneously with tens of decision variables and multiple performance measures in manufacturing

“…The work of (Mollaghasemi and Evans 1994), falls into the category of iterative multiple criteria optimization, although their approach favors the definition of a preference structure among PMs a priori, which departs from the non-parametric point of view advocated in this work. The works of (Zakerifar, Biles, and Evans 2011;Couckuyt, Deschrijver, and Dhaene 2012;Dellino, Kleijnen, and Meloni 2012) approach multiple criteria simulation optimization models using Kriging models with various degrees of success, adding evidence to the soundness of using metamodeling strategies to support the determination of competitive solutions in the presence of conflicting PMs. Indeed, there seems to be interest in the assessment of multiple criteria using simulation in different production applications such as planning and scheduling (Duvivier et al 2007), inventory management (Mortazavi and Arshadi khamseh 2014), as well as scientific endeavors such as the analysis of intermolecular interaction (St6bener et al 2014).…”

A Robust Simulation for EOQ Model with Exponential Distributed Demand

“…Gao et al [12] pointed out that the two-layer Kriging model can reduce uncertainty analysis, and then improved the computational efficiency. Through cross-validation, Dellino et al [6] proved that two-layer Kriging model has smaller relative prediction errors than one-layer Kriging model. Thus, we use two-layer Kriging model to conduct simulation optimization. )…”

“…Many researchers use some statistical methods to describe the distribution of demand rate such as normal distribution and exponential distribution [5][6]. But the assumption that the demand rate follows normal distribution is not very reasonable for new items and deteriorating items.…”

“…In EOQ model, the order quantity is set as the decision factor which is determined by the manager and the demand rate is set as the environmental or noise factor which cannot be controllable. Dellino et al [6] developed a robust methodology that combines Taguchi's robust view and Kriging model and illustrated in EOQ model with the normal distributed demand rate.…”

“…In the Kriging model only the input/output data can be observed which makes the Kriging model has wide applicability. Also, the metamodels of Kriging model have high-performance in computationally expensive simulation models [9][10]. In addictive, simulation experiments can reduce the cost of conducting real experiments and explore many more factors, factor levels and even factor combinations, which is helpful to find the optimal value.…”