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

Abstract

There are extensive studies in the literature about the reorder point/order quantity policies for inventory management, also known as $(r,Q)$ 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 $1\mathrm{\%}$, 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.

Keywords:

• evolutionary computation
• genetic programming
• inventory replenishment
• meta-heuristics

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Rui L. Lopes  http://orcid.org/0000-0002-1579-1330

Notes

1 Automatically Defined Functions (ADF) are useful code fragments extracted into separate functions, which can be called multiple times either while executing the result producing branch or another ADF. This means ADFs underlie selection pressure in the same way as the main programme tree.

2 Grammatical Evolution is a form of Genetic Programming with a linear representation of the genome, where the construction of the programme graph is guided by a grammar with precise rules.

3 The full method tends to produce full/bushy trees, by choosing functions until the depth limit is reached.

4 The grow method does not require functions to be chosen at any point; if the maximum depth has not yet been reached, either a function or a terminal may be selected, causing more diverse tree structures with some branches longer than the others.

5 https://github.com/rmlopes/inventory-research

6 Both the mutation and the crossover rates were tested over the values $\{0.05,0.2,0.5,0.8,0.95\}$.

7 The maximum tree-depth and the maximum number of nodes are closely related parameters. For the former only one value was used. For the latter the maximum number of nodes in CCGP was tested from $\{60,50,40,30\}$ yielding the best results for the largest value; for eCCGP two values were tested (60 and 25), with this approach being able to achieve similar results with both we opted for the smallest aiming for more compact solutions.

8 Similarly to the results presented in Section 5.2, the gaps are highly skewed towards lower values, hence non-parametric tests were used after confirmation with normality tests.

Additional information

Funding

The work presented in this article is part of the Project ‘TEC4Growth – Pervasive Intelligence, Enhancers and Proofs of Concept with Industrial Impact/NORTE-01-0145-FEDER-000020’, financed by the North Portugal Regional Operational Programme (NORTE 2020), under the PORTUGAL 2020 Partnership Agreement, and through the European Regional Development Fund (ERDF). The work is also financed by the Project ‘NORTE-07-0124-FEDER-000057’, supported by the North Portugal Regional Operational Programme (ON.2 O Novo Norte), under the National Strategic Reference Framework (NSRF). The second author is also grateful to the Portuguese Foundation for Science and Technology (FCT) for awarding him the PhD grant SFRH/BPD/110777/2015.