Inexact joint-probabilistic chance-constrained programming with left-hand-side randomness: An application to solid waste management

In practical waste management systems, amounts of waste transported and treated are not always equal on a daily basis. To distinguish between these two kinds of amounts and reflect their random relationships effectively, an inexact joint-probabilistic left-hand-side chance-constrained programming (IJLCP) method was developed and applied to a municipal solid waste management problem under dual uncertainties. Dual uncertainties are defined as two kinds of uncertainties existing in the same programming model. Improving upon conventional right-hand-side chance-constrained programming, the IJLCP can not only reflect uncertainties presented in terms of interval parameters (unit transportation/treatment costs, capacities of waste treatment facilities, waste generation rates, waste transportation/treatment amounts and so on) and left-hand-side random variables (the relationship between waste transportation and treatment amounts), but also examine the reliability of satisfying (or risk of violating) the entire system constraints. A non-equivalent but sufficient linearization form of IJLCP for solving this type of problem was proposed and proved in a straightforward manner. The performance of IJLCP was analyzed under scenarios at joint and individual probabilities and compared with the corresponding internal-parameter programming model. The results indicated that the net system costs would both decrease with increasing joint probability levels and decrease slightly at different individual probabilities with the same joint probabilities. The two types of dual uncertainties were discussed as well.