Provided are a computer program product, system, and method for generating constraints based on reported crop arrivals to marketplaces and remote sensed data to estimate farm yields of farm fields. A total arrival quantity constraint for a marketplace is generated comprising a function of a reported arrival of crops at a marketplace and an estimated arrival to the marketplace comprising a sum of farm yields for the farm fields, wherein the farm yields comprise variables to optimize. Sensed data of the farm fields is used to determine relationships of the farm yields for the farm fields. Comparative farm yield constraints are generated comprising relationships of the farm yields for different pairs of farms. A constraint optimization problem is solved based on the total arrival quantity constraint and comparative farm yield constraints to calculate the farm yields of the farm fields.