Optimal purchase and selling strategy for wholesaler of produce: sorted or unsorted selling?

Produce (e.g. fruit and vegetable) varies in quality when it is picked from plants. Then a produce wholesaler has two sales strategies: (1) unsorted selling (US), i.e. selling the produce to the market at one price and (2) sorted selling (SS), i.e. pre-sorting the produce into different grades by quality and selling them at different prices. When the SS strategy is adopted, the demands of the different grades are uncertain and substitutable. In this paper, we study the joint optimal purchase and sales strategy for selling mixed quality produce to customers with heterogeneous quality preferences. We first derive the optimal purchase policies under the two strategies and then identify the conditions under which the SS or US strategy is optimal. We show that the optimal sales strategy is determined by the marginal purchase and sorting cost and the fixed investment cost, the overall quality level of the produce, and the substitution rate for the high-quality and low-quality produce. This finding differs from the conventional wisdom that the SS strategy is optimal in the produce retail business. Finally, we conduct numerical studies based on real-world data to generate managerial insights from the analytical findings.