Time Variant Interval Linear Programming for Environmental Management Systems

Abstract

Optimization technology is widely applied to maximize economic profit under ecology constrains in environmental management systems. To tackle the inherent uncertainties, inexact optimization methods have been proposed. Interval linear programming (ILP) model has drawn increasing scholarly attention. ILP model describe uncertainty by one coarse scaled stochastic process. However, uncertainty often involves multiple stochastic processes when zooming into high resolution. ILP model may not satisfied fine scale constraints. A time variant interval linear programming (TVILP) model is developed to implement temporal downscaling, and likewise, a heuristic algorithm integrating dynamic programming is proposed for Markov chained TVILP. Dynamic programming can converts time complexity exponential to polynomial. In the current paper, the performance of TVILP model is analyzed based on the following three metrics: maximal profit (M_profit), constraint violation risk (CVR), and maximal profit path risk (MPR). The performance of TVILP is further compared with the performance of Best and Worst method, the classic ILP model, Interval linear programming contractor, and Interval-parameter multi-stage stochastic linear programming. Experimental results reveal that TVILP provides refined solutions on a smaller granularity whose decision space contracts based on the most possible transition paths. Unable to obtain the maximum profit, though, TVILP does pose decreased constraint violation risk and maximal profit path risk, facilitating more feasible and reliable decision-making on environmental management.