An optimal design of automated storage and retrieval system with product safety consideration

Automated Storage and Retrieval System (AS/RS), as defined by the Materials Handling Institute (1982), as a combination of equipment and controls which handles, stores, retrieves materials with precision, accuracy and speed under a defined degree of automation. Existing models on the determination of optimal design of AS/RS did not incorporate product safety and did not attempt to improve flexibility of the system. Product safety refers to the minimization of the occurrence of product getting damages during its storage and retrieval. Flexibility refers to the ability of the system to adopt to certain changes in the arrival of requests.In this study, product safety and flexibility of the system were incorporated in the model. The initial model developed in this study was a multi-objective mixed integer non-linear model. The first objective function is to minimize the investment and operating cost. The second objective function is to minimize the expected number of product damages that the system can create. The model is then converted into a goal programming model that reduces the number of objective function to one. Thus, the objective function of the goal programming model is to minimize the total undesirable deviation from the target investment and operating costs and from the allowable product damages. Since the formulated model was non-linear, its convexity was proven using classical optimization technique. In order to test for the convexity of the model, the model is converted into an unconstrained external problem using Lagrangian Method. This method requires the evaluation of the determinant of a Bordered Hessian Matrix. Likewise, Karush Kuhn-Tucker (KKT) conditions are used to determine the relationship of the parameters with the decision variables that woul