Dual-Interval Linear Programming Model and Its Application to Solid Waste Management Planning

A dual-interval parameter linear programming (DILP) model was developed and applied to the planning of municipal solid waste (MSW) management systems under uncertainty. The DILP can address system uncertainties with complex presentations. Parameters in the DILP can be expressed as interval numbers; however, due to the complexity of the real world, highly uncertain information may exist in the boundaries of interval parameters. When sufficient information for these boundaries is available to access intervals, the novel concept of dual interval (being an interval-boundary interval) can be developed for handling such uncertainties and be introduced into the existing interval-parameter linear programming (ILP) framework; this leads to the DILP method where the uncertain parameters are represented as single or dual intervals. The DILP approach improves upon the ILP method by allowing dual uncertainties (presented as dual intervals) to be incorporated into the optimization processes. Decision alternatives can be generated through analysis of the single- and dual-interval solutions according to projected applicable conditions. Applicability of the developed model was demonstrated through a case of long-term MSW management planning. Reasonable solutions can be obtained, which are useful for generating desired decision alternatives and providing more information to decision makers.