A novel unconstrained methodology for economic analysis of the level of repair with a case study of a multi-indenture and multi-echelon repair network

Abstract

The multi-indenture and multi-echelon economic analysis of repair levels is commonly modelled as a constrained 0–1 programming problem. However, with the increase in the scale of the decision variables, the proportion of feasible solutions in the solution space sharply decreases, posing a challenge for traditional solution methods. In this paper, the transformation of the initial problem into an unconstrained integer programming problem is demonstrated. Specifically, the total number of feasible decisions can be solved analytically through a decision flow method, and a bijective relationship between decision sequence numbers and feasible decisions is established using a mixed-radix system, converting the optimization variables to feasible decision sequence numbers; in this way, the initial problem becomes unconstrained. The advantages of this approach include the following: (1) All the solutions in the transformed solution space are feasible, which significantly improves the efficiency of the solution and reduces the dimensionality of the decision variables; and (2) the proposed model is highly flexible in terms of considering additional variables, such as decision time, transportation modes, and repair locations. Furthermore, the sequence numbers of each feasible solution are transformed into binary sequences, and the binary particle swarm optimizer (BPSO) algorithm can be employed to solve the model. The proposed methodology is applied to the case of a three-indenture and three-echelon repair network considering multiple fault modes, and the results are compared with those of previous studies. The results validate the rationality and substantial advantages of the proposed methodology for economic analysis in terms of computational speed and convergence performance.