Faculty of Engineering and Applied Science, University of Regina, Regina, Saskatchewan, Canada.
Waste Manag. 2012 Jun;32(6):1244-57. doi: 10.1016/j.wasman.2012.01.019. Epub 2012 Feb 26.
To tackle nonlinear economies-of-scale (EOS) effects in interval-parameter constraints for a representative waste management problem, an inexact piecewise-linearization-based fuzzy flexible programming (IPFP) model is developed. In IPFP, interval parameters for waste amounts and transportation/operation costs can be quantified; aspiration levels for net system costs, as well as tolerance intervals for both capacities of waste treatment facilities and waste generation rates can be reflected; and the nonlinear EOS effects transformed from objective function to constraints can be approximated. An interactive algorithm is proposed for solving the IPFP model, which in nature is an interval-parameter mixed-integer quadratically constrained programming model. To demonstrate the IPFP's advantages, two alternative models are developed to compare their performances. One is a conventional linear-regression-based inexact fuzzy programming model (IPFP2) and the other is an IPFP model with all right-hand-sides of fussy constraints being the corresponding interval numbers (IPFP3). The comparison results between IPFP and IPFP2 indicate that the optimized waste amounts would have the similar patterns in both models. However, when dealing with EOS effects in constraints, the IPFP2 may underestimate the net system costs while the IPFP can estimate the costs more accurately. The comparison results between IPFP and IPFP3 indicate that their solutions would be significantly different. The decreased system uncertainties in IPFP's solutions demonstrate its effectiveness for providing more satisfactory interval solutions than IPFP3. Following its first application to waste management, the IPFP can be potentially applied to other environmental problems under multiple complexities.
为了解决具有区间参数约束的代表性废物管理问题中的非线性规模经济(EOS)效应，开发了一种基于不精确分段线性化的模糊柔性规划(IPFP)模型。在 IPFP 中，可以量化废物量和运输/运营成本的区间参数;可以反映净系统成本的期望水平，以及废物处理设施和废物产生率的容量的容忍区间;并且可以将目标函数中的非线性 EOS 效应转换为约束条件进行逼近。提出了一种求解 IPFP 模型的交互式算法，该模型本质上是一个区间参数混合整数二次约束规划模型。为了展示 IPFP 的优势，开发了两个替代模型来比较它们的性能。一个是基于传统线性回归的不精确模糊规划模型(IPFP2)，另一个是所有模糊约束的右侧均为相应区间数的 IPFP 模型(IPFP3)。IPFP 与 IPFP2 之间的比较结果表明，两个模型中的优化废物量都具有相似的模式。然而，在处理约束中的 EOS 效应时，IPFP2 可能会低估净系统成本，而 IPFP 可以更准确地估计成本。IPFP 与 IPFP3 之间的比较结果表明，它们的解决方案会有很大的不同。IPFP 解决方案中的系统不确定性降低表明，与 IPFP3 相比，它可以提供更令人满意的区间解决方案。IPFP 首次应用于废物管理后，可潜在地应用于多种复杂性下的其他环境问题。
