Robust material handling system design with standard deviation, variance and downside risk as risk measures

The design and planning of major storage systems belong to the class of systems design problems under uncertainty. The overall structure of the system is determined during the design stage while the values of the future conditions and the future planning decisions are not known with certainty. Typically the future uncertainty is modeled through a number of scenarios and each scenario has an individual time-discounted total system cost. The overall performance of the material handling system (MHS) is characterized by the distribution of these scenario costs. The central tendency of the cost distribution is always computed as the expected value of the distribution. Several alternatives for the dispersion of the distribution can be used. In this study the standard deviation, variance, and the downside risk of the cost distribution are investigated as the risk measures of the system. We propose an algorithm to efficiently identify all configurations of the MHS that are Pareto-optimal with respect to the tradeoff between the expected value of the costs and the risk; such Pareto-optimal configurations are also called efficient. Although the MHS model has non-linear constraints, our proposed algorithm can solve such non-linear models taking into account both the expected costs and the risk. The final selection of the storage system for implementation can then be made based on the Pareto graph and other considerations such as the risk preferences of the system owner. The algorithms developed are illustrated through a case study which helps in developing business insights for the warehouse and MHS design planners and decision makers.