Planning merchandise investments using fuzzy optimization

This article presents a model of retail buyers investing in merchandise for resale to consumers. Given a selection or portfolio of merchandise to buy for a store, the retailer must determine the optimal percentage investment in each item. Depending upon the buyer's investment objectives and tolerance of risk, the profit of the portfolio is maximized while the risk is simultaneously minimized. We first model this investment decision using mean-variance optimization and then reformulate the nonlinear programming model to include a fuzzy objective function and fuzzy constraints. Our results indicate that the fuzzy approach increases the flexibility and profitability of the model, assisting the retailer to build portfolios of merchandise that satisfy consumer demand under conditions of uncertainty.