The L-shaped Method for Large-scale Mixed-integer Waste Management Decision Making Problems

Abstract

It is without a doubt that deciding upon strategic issues requires us to somehow anticipate and consider possible variations of the future. Unfortunately, when it comes to the actual modelling, the sheer size of the problems that accurately describe the uncertainty is often extremely hard to work with. This paper aims to describe a possible way of dealing with the issue of large-scale mixed integer models (in term of the number of possible future scenarios it can handle) for the studied waste management decision making problem. The algorithm is based on the idea of decomposing the overall problem alongside the different scenarios and solving these smaller problems instead. The use of the algorithm is demonstrated on a strategic waste management problem of choosing the optimal sites to build new incineration plants, while minimizing the expected cost of waste transport and processing. The uncertainty was modelled by 5,000 scenarios and the problem was solved to high accuracy using relatively modest means (in terms of computational power and needed software).