Landfill space consumption dynamics in the Lower Rio Grande Valley by grey integer programming-based games

The Lower Rio Grande Valley (LRGV) region in South Texas emerges as a warehouse and transportation center between Central America and the US with positive growth impacts due to the North American Free Trade Agreement (NAFTA). In 10 years time, a 39.8% population increase has resulted in a 25% boost in solid waste per capita disposal rate in the region. A landfill space shortage drives a need for landfill operators to understand their optimal management strategies in this highly-competitive market. Initially, a strategic plan for optimal solid waste pattern distribution minimizes net costs for cities. This is accomplished through a grey integer programming algorithm that encapsulates all uncertainty present in the solid waste system. Secondly, a series of grey integer submodels construct payoff matrices for a zero-sum two-person game. The ensuing game theoretic analysis is critical for evaluating optimal pricing strategies for tipping fees available to the most significant regional landfills (e.g. Browning-Ferris Industries (BFI) and City of Edinburg) as they compete over disposal contracts. The BFI landfill intrinsically benefits from its competitive pricing policy and central location to solid waste generators. The City of Edinburg landfill, on the other hand, wishes to secure its lucrative solid waste management revenue. It desires a gaming strategy backed by optimality that integrates ambiguity in solid waste generation, design capacity boundaries, and unitary shipping costs. Results show that a two-tiered analysis via grey integer programming-based games may pave the way for ‘grey Nash equilibria’ pricing tactics that will help the Edinburg landfill maintain its waste contracts.