A genetic algorithm approach for multi-product multi-period continuous review inventory models

• A genetic algorithm is developed for multi-product/period (Q, r) inventory model.
• A novel integer linear programming model (ILP) is proposed for the problem.
• Shelf life, budget, storage capacity, and promotions constraints are considered.
• Approach verified by pharmaceutical case study to yield high-quality solutions.
• Proposed genetic algorithm is more effective than ILP model on large problems.

This paper formulates an approach for multi-product multi-period (Q, r) inventory models that calculates the optimal order quantity and optimal reorder point under the constraints of shelf life, budget, storage capacity, and “extra number of products” promotions according to the ordered quantity. Detailed literature reviews conducted in both fields have uncovered no other study proposing such a multi-product (Q, r) policy that also has a multi-period aspect and which takes all the aforementioned constraints into consideration. A real case study of a pharmaceutical distributor in Turkey dealing with large quantities of perishable products, for whom the demand structure varies from product to product and shows deterministic and variable characteristics, is presented and an easily-applicable (Q, r) model for distributors operating in this manner proposed. First, the problem is modeled as an integer linear programming (ILP) model. Next, a genetic algorithm (GA) solution approach with an embedded local search is proposed to solve larger scale problems. The results indicate that the proposed approach yields high-quality solutions within reasonable computation times.