Interactive multiobjective optimization approach to the input–output design of opening new branches

We demonstrate a real-world application of the interactive multiple objective optimization (MOO) approach to the simultaneous setting of input and output amounts for the opening of new branches. As illustrated by the case example, all the branches of a fast-food company employ multiple inputs to generate multiple outputs. The company launches several new branches each year and, therefore, needs to plan the quantities of inputs and outputs to be used and produced before their operations. Such input–output settings are a vital practical problem that arises whenever a new branch is opened in a host of different industries. In this paper, we show in detail the entire process of the application from modeling the case problem to generating its solution. In the modeling stage, a data envelopment analysis model and a statistical method are subsequently utilized to form a nonlinear MOO problem for the input–output settings. To solve this problem, we then develop and apply an interactive MOO method, which combines the two earlier interactive methods (Geoffrion et al., 1972; Zionts and Wallenius, 1976), while compensating for their drawbacks and capturing their positive aspects.