Inexact Mixed-integer Linear Programming Research Articles

Inexact mixed-integer programming with interval-valued membership function for sustainable power-generation capacity planning

In this study, inexact mixed-integer linear programming with interval-valued membership function (IMILP-IMF) is developed for power-generation capacity planning. IMILP-IMF can deal with uncertainties described as fuzzy sets with interval-valued membership function, and allows uncertainties to be directly communicated into the optimization process and the resulting solution. IMILP-IMF is applied to a case study of supporting long-term planning for an electric power system (EPS). It can facilitate dynamic analysis for decisions of capacity expansion planning within a multi-facility, multi-option and multi-period context. Solutions of energy resources allocation, capacity expansion, air pollution control, and electricity generation with a minimized system cost are obtained. Results reveal that, from a long-term planning point of view, more capacities of renewable energy generation need to be installed to replace the outdated facilities to transfer the EPS to a clean, sustainable and reliable one. Results of power-generation capacity planning in association with economic consideration and environmental requirement can also help decision makers to formulate the relevant policies, optimize energy supply structure, as well as facilitate the sustainable development of electric power systems. The findings will help generate decision alternatives under multiple scenarios, and thus offer insight into the tradeoffs between economic and environmental objectives.

A Generalized Fuzzy Integer Programming Approach for Environmental Management under Uncertainty

In this study, a generalized fuzzy integer programming (GFIP) method is developed for planning waste allocation and facility expansion under uncertainty. The developed method can (i) deal with uncertainties expressed as fuzzy sets with known membership functions regardless of the shapes (linear or nonlinear) of these membership functions, (ii) allow uncertainties to be directly communicated into the optimization process and the resulting solutions, and (iii) reflect dynamics in terms of waste-flow allocation and facility-capacity expansion. A stepwise interactive algorithm (SIA) is proposed to solve the GFIP problem and generate solutions expressed as fuzzy sets. The procedures of the SIA method include (i) discretizing the membership function grade of fuzzy parameters into a set ofα-cutlevels; (ii) converting the GFIP problem into an inexact mixed-integer linear programming (IMILP) problem under eachα-cut level; (iii) solving the IMILP problem through an interactive algorithm; and (iv) approximating the membership function for decision variables through statistical regression methods. The developed GFIP method is applied to a municipal solid waste (MSW) management problem to facilitate decision making on waste flow allocation and waste-treatment facilities expansion. The results, which are expressed as discrete or continuous fuzzy sets, can help identify desired alternatives for managing MSW under uncertainty.

Managing water resources system in a mixed inexact environment using superiority and inferiority measures

A superiority–inferiority-based fuzzy-stochastic integer programming (SI-FSIP) method is developed for water resources management under uncertainty. In the SI-FSIP method, techniques of fuzzy mathematical programming with the superiority and inferiority measures and joint chance-constrained programming are integrated into an inexact mixed integer linear programming framework. The SI-FSIP improves upon conventional inexact fuzzy programming by directly reflecting the relationships among fuzzy coefficients in both the objective function and constraints with a high computational efficiency, and by comprehensively examining the risk of violating joint probabilistic constraints. The developed method is applied to a case study of water resources planning and flood control within a multi-stream and multi-reservoir context, where several studied cases (including policy scenarios) associated with different joint and individual probabilities are investigated. Reasonable solutions including binary and continuous decision variables are generated for identifying optimal strategies for water allocation, flood diversion and capacity expansion; the tradeoffs between total benefit and system-disruption risk are also analyzed. As the first attempt for planning such a water-resources system through the SI-FSIP method, it has potential to be applied to many other environmental management problems.

Identifying optimal regional solid waste management strategies through an inexact integer programming model containing infinite objectives and constraints

The previous inexact mixed-integer linear programming (IMILP) method can only tackle problems with coefficients of the objective function and constraints being crisp intervals, while the existing inexact mixed-integer semi-infinite programming (IMISIP) method can only deal with single-objective programming problems as it merely allows the number of constraints to be infinite. This study proposes, an inexact mixed-integer bi-infinite programming (IMIBIP) method by incorporating the concept of functional intervals into the programming framework. Different from the existing methods, the IMIBIP can tackle the inexact programming problems that contain both infinite objectives and constraints. The developed method is applied to capacity planning of waste management systems under a variety of uncertainties. Four scenarios are considered for comparing the solutions of IMIBIP with those of IMILP. The results indicate that reasonable solutions can be generated by the IMIBIP method. Compared with IMILP, the system cost from IMIBIP would be relatively high since the fluctuating market factors are considered; however, the IMILP solutions are associated with a raised system reliability level and a reduced constraint violation risk level.

An integrated multi-criteria decision analysis and inexact mixed integer linear programming approach for solid waste management

This paper reports on an integration of multi-criteria decision analysis (MCDA) and inexact mixed integer linear programming (IMILP) methods to support selection of an optimal landfill site and a waste-flow-allocation pattern such that the total system cost can be minimized. Selection of a landfill site involves both qualitative and quantitative criteria and heuristics. In order to select the best landfill location, it is often necessary to compromise among possibly conflicting tangible and intangible factors. Different multi-objective programming models have been proposed to solve the problem. A weakness with the different multi-objective programming models used to solve the problem is that they are basically mathematical and ignore qualitative and often subjective considerations such as the risk of groundwater pollution as well as other environmental and socio-economic factors which are important in landfill selection. The selection problem also involves a change in allocation pattern of waste-flows required by construction of a new landfill. A waste flow refers to the routine of transferring waste from one location in a city to another. In selection of landfill locations, decision makers need to consider both the potential sites that should be used as well as the allocation pattern of the waste-flow at different periods of time. This paper reports on our findings in applying an integrated IMILP/MCDA approach for solving the solid waste management problem in a prairie city. The five MCDA methods of simple weighted addition, weighted product, co-operative game theory, TOPSIS, and complementary ELECTRE are adopted to evaluate the landfill site alternatives considered in the solid waste management problem, and results from the evaluation process are presented.