Measure Constraint Model and Its Properties of Closed-Loop Logistics Network

Based on the chance theory, the transportation costs of unit from the factories to the stores are regarded as random variables with probability distribution, and the transportation costs of unit from the customers to the stores and the demands of customers are regarded as uncertain variables with uncertainty distribution. A new closed-loop logistics network model with objective of minimizing the expected total cost (uncertain random variable) of closed-loop logistics is established based on the measure-constraint of the balance between production and sale, transportation costs and demands of customers in the paper. It is called the measure-constraint model of uncertain random closed-loop logistics network. The properties of the model in special uncertainty distribution are given. It is gained to the specific form that it is equivalent to primary model.