Expected performance evaluation and optimization of a multi-distribution multi-state logistics network based on network reliability

In this paper, a logistics network is modeled as a cost-related multi-distribution multi-state flow network (CMMFN) where each arc is featured with more than one capacity distribution and each capacity distribution corresponds to a specific cost. Expected performance (EP) that represents the probability-weighted average delivery capacity can serve as a comprehensive measurement of the operational quality of a logistics network. A more direct relationship between EP and network reliability is constructed, and then an improved d-minimal cut (d-MC) additive algorithm is presented to compute EP. Moreover, an EP optimization model is developed subject to a given cost. To facilitate the solution of the EP optimization model, a concept of critical cost vector is defined and a method, called CCV method, is put forth to find all critical cost vectors. Finally, an efficient algorithm integrating the improved d-MC algorithm with the CCV method is proposed for the EP model. An illustration of the proposed model and methods is given through an example; moreover, their applications are demonstrated via a case study.