Gray fuzzy dynamic-programming – application to municipal solid-waste management planning problems

This paper integrates the concepts of grey systems and fuzzy sets into optimization analysis by dynamic programming as a means of accounting for system uncertainty. The developed grey fuzzy dynamic programming (GFDP) model improves upon previous DP methods by allowing uncertain input information to be directly communicated into the optimization process and solutions through the use of different alpha-cut levels of fuzzy numbers for the input fuzzy information, and the use of a grey fuzzy linear programming (GFLP) method for an embedded LP problem. The modelling approach is applied to a hypothetical problem for the planning of waste flow allocation and treatment/disposal facility expansion within a municipal solid waste management system. The solutions of the GFDP model corresponding to different alpha-cut levels provide optimal decisions regarding different development alternatives in a multi-period, multi-facility and multi-scale context, as well as the upper and lower limits of waste flow allocation. The results indicate that reasonable and useful solutions can be achieved through the developed GFDP approach.