An inexact fuzzy-queue programming model for environmental systems planning

In this study, an inexact fuzzy-queue programming (IFQP) model is developed for municipal solid waste (MSW) management under uncertainty, where fuzzy queue (FQ) model is introduced into the interval-fuzzy linear programming (IFLP) framework. The proposed IFQP model can not only handle uncertainties that are presented in terms of fuzzy sets and discrete intervals, but also reflect the influence of FQ in decision-making problems. Moreover, it can help quantify the satisfaction degrees of the system cost and constraints under uncertainty. It improves upon the existing optimization model with advantages in data availability, uncertainty reflection and result analysis. In its solution process, the model is transformed into two deterministic submodels based on an interactive algorithm. Interval solutions which are stable in the decision space can be obtained by solving the two submodels sequentially. The developed model is applied to a case of long-term planning of MSW management systems to demonstrate its applicability. It can effectively reflect dynamic, interactive, and uncertain characteristics of municipal waste management systems. The decision variable solutions provide optimal schemes for waste flow allocation corresponding to lower and upper bounds of system cost. The results indicate that reasonable solutions have been generated. They are helpful for supporting: (i) decision making or justification of waste-allocation patterns of MSW management system, and (ii) in-depth analysis of tradeoffs among system cost, satisfaction degree, and environmental constraint under uncertainty.