Cooperative coevolution of expressions for (r,Q) inventory management policies using genetic programming

There are extensive studies in the literature about the reorder point/order quantity policies for inventory management, also known as $(r, Q) $(r,Q) policies. Over time different algorithms have been proposed to calculate the optimal parameters given the demand characteristics and a fixed cost structure, as well as several heuristics and meta-heuristics that calculate approximations with varying accuracy.This work proposes a new meta-heuristic that evolves closed-form expressions for both policy parameters simultaneously - Cooperative Coevolutionary Genetic Programming. The implementation used for the experimental work is verified with published results from the optimal algorithm, and a well-known hybrid heuristic. The evolved expressions are compared to those algorithms, and to the expressions of previous Genetic Programming approaches available in the literature. The results outperform the previous closed-form expressions and demonstrate competitiveness against numerical methods, reaching an optimality gap of less than $1\% $1%, while being two orders of magnitude faster. Moreover, the evolved expressions are compact, have good generalisation capabilities, and present an interesting structure resembling previous heuristics.