Modelling and analysis of a symbiotic waste management system

A municipal solid waste management system is symbiotic when there exists physical exchange of material or by-products between different treatment units. We propose a mathematical model for studying the interactive behaviour of different waste treatment operators in a symbiotic environment. Each operator is a self-interested entity, who sets his gate fee charge to maximise his own payoff. We study the properties and gate fee strategies of the operators, and also perform sensitivity analysis on various model parameters to discuss the local operator behaviour and the effects of various intervention strategies. We also propose a numerical algorithm to solve the model, yielding the optimal equilibrium gate fee charges, payoff and market share levels of different operators. Finally, computational studies based on a two-unit scenario in a case study of organic waste recycling is performed to demonstrate the interactive and dynamic behaviours of different operators. Our results strongly suggest that, to improve new treatment technology utilisation, subsidising the operating cost of the new treatment unit is more effective in the long-run than exerting control on the gate fee upper bounds of the operators by the system regulator. Furthermore, providing residual post-treatment discounts for treatment units can benefit the service users, rather than the waste treatment operators.