مدل برنامه ریزی خطی مخلوط عدد صحیح برای ترکیب دانه فله و حمل و نقل

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.

This paper was motivated by a problem faced by a company that manages wheat distribution planning. In the specific problem, which is the focus of this paper, products are loaded on bulk vessels of various capacities for delivery to overseas customers. A vessel involves a major capital investment, and its daily operating cost often amounts to several thousands of dollars. Proper shipment planning may, therefore, result in significant improvements in economic performance, which means survival in an increasingly competitive market. The distribution network consists of a number of loading ports and destination ports (customers) that may be served by different vessel types. The vessels under consideration are hired for a single voyage at a time. In each voyage the assigned vessel may be loaded in at most two ports, and discharged in a single destination port, where the customer is located. Different original products may be blended at ports prior to loading. The problem is to assign an appropriate type and number of vessels to each customer order, while determining the quantities to be blended, and loaded at each port, and transported from each port to each customer. The planning process for blending and shipping should take into account the original and blended product availability at ports, vessel capacity and blending requirements, loading, blending and draft capacity restrictions at ports, and demand satisfaction. This problem is solved to minimize the total cost, which includes the blending, loading, transportation and inventory costs. A planning horizon of up to 3 months has been considered. A mixed-integer linear programming (MILP) model is formulated to represent the bulk grain blending and shipping problem. The model can be used both as a tool for tactical planning, and a strategic tool to analyze the effects of cost components on the model in various situations. This paper points out the unique and practical contribution of the proposed optimization model for solving a real life bulk grain blending and shipping problem. Our mathematical model includes several components from traditional optimization models. The shipping aspect of the distribution system can be considered as a specialized version of a transshipment model. The blending aspect of the problem falls into the category of a capacity allocation problem. Finally, we also have a time-expanded model, as we deal with a multi-period problem. The paper is organized in the following manner. The next section provides a review of the related research. Section 3 describes the distribution-planning problem in detail. The problem is formulated as an optimization model in Section 4. In Section 5, a small example problem is presented to illustrate the applicability of the model. Computational results using the data from a real-life case study are reported in Section 6. Finally, the last section gives some concluding remarks.

A comprehensive model for the real bulk grain blending and shipping problem has been developed. The model allows the simultaneous determination of the number of vessels of each type to be hired by route and period, determination of the amount of products blended, and loaded at each port, and transported from each port by route, vessel type, and period. The formulation of the real blending and shipping problem has been emphasized. This paper makes two primary contributions. First, and perhaps the most important, it proposes a model that integrates blending, loading and transportation decisions simultaneously into one model in order to obtain an optimal solution. Second, a novel variable structure is developed to represent the amount of products loaded at each port on each vessel on each route and during each time period. A natural extension of the distribution-planning model is to include land transportation from storage sites to loading ports. The optimization of the marine transportation simultaneously with land transportation is an ongoing project within this research. Another extension of the model relates to the consideration of a limited number of vessels. Adding this to the problem will certainly increase its complexity and efficient decomposition techniques are needed to solve it. In conclusion, we believe that the proposed model and resulting MIP approach can be used as an important tool in the strategic and tactical decision making in the considered industry. This model provides a reasonable starting point for many industries where bulk commodity logistics problem is considered.