In real-world municipal solid waste (MSW) management systems, identification of proper policies under uncertainty for accomplishing desired waste-disposal targets is critical. An inexact minimax regret integer programming (IMMRIP) method for the long-term planning of MSW management is developed. It incorporates the technique of minimax regret analysis (MMR) into an interval-parameter mixed-integer linear programming (IMILP) framework. The IMMRIP method can handle dual uncertainties presented as both random variables and interval values; it only needs a list of scenarios without any assumption on their probability distributions. It can facilitate dynamic analysis for decisions of system-capacity expansion and/or development within a multi-facility and multi-period context. Moreover, it can also be used for analyzing multiple scenarios associated with different system costs and risk levels. An interval-element cost matrix can be transformed into an interval-element regret matrix based on an interactive algorithm. Solutions based on an inexact minimax regret criterion can identify desired alternatives for MSW management and planning under a variety of uncertainties. In a companion paper, the developed method will be applied to a real case study in the City of Regina, Canada.