Numerical solutions comparison for interval linear programming problems based on coverage and validity rates

摘要

In this paper, two-step method (TSM), alternative solution method (SOM-2) and best-worst case (BWC) method are introduced to solve a type of interval linear programming (ILP) problem. To compare the performance of the methods, Monte Carlo simulation is also used to solve the same ILP problem, whose solutions are assumed to be real solutions. In the comparison, two scenarios corresponding with two assumptions of distribution functions are considered: (ⅰ) all the input parameters obey normal distribution; (ⅱ) all the input parameters obey uniform distribution. Based on the simulation results, coverage rate (CR) and validity rate (VR) are proposed as new indicators to measure the quality of the numerical solutions obtained from the methods. Results from a numerical case study indicate that the TSM and SOM-2 solutions can cover the majority of valid values (CR ＞ 50%, VR ＞ 50%), compared to the conventional BWC method. In addition, from the point of CR, TSM is more applicable since the solutions of TSM can identify more feasible solutions. However, from the point of VR, SOM-2 is preferred since it can exclude more baseless solutions (this means more feasible solutions are contained in the SOM-2 solutions). In general, TSM would be preferred when only the range of the system objective needs to be determined, while SOM-2 would be much useful in identifying the effective values of the objective.