A mixed-integer linear programming model for bulk grain blending and shipping

Abstract This paper addresses a blending and shipping problem faced by a company that manages a wheat supply chain. The problem involves the delivery of bulk products from loading ports to destination ports, which may be served by different vessel types. Since the products demanded by customers are mainly exported in bulk to overseas customers, the shipment planning is of great economic importance. The problem is formulated as a mixed-integer linear programming model. The objective function seeks to minimize the total cost including the blending, loading, transportation and inventory costs. Constraints on the system include blending and demand requirements, availability of original and blended products; as well as blending, loading, draft and vessel capacity restrictions. When solved, the model produces: (1) the quantity of each original product to be used to make blended products, (2) the quantity of each product to be loaded at each port and to be transported from each port to each customer, and (3) the number of vessels of each type to be hired in each time period. Numerical results are presented to demonstrate the feasibility of the real world bulk grain blending and shipping model.