Integrated Assortment–Shelf Optimization under Substitution and Space Elasticity: A Hybrid Memetic Algorithm

Objective: This study maximizes expected retail profit by jointly optimizing product assortment and shelf-space allocation, considering substitution effects and space-elastic demand. The problem’s NP-hardness, compounded by category-level bounds and store capacity, renders exact methods impractical for large-scale instances. Therefore, we develop a computationally efficient framework to generate near-optimal shelf plans aligned with real-world constraints. Methodology: We propose a hybrid Memetic Algorithm embedded with Iterated Local Search (ILS), combining evolutionary global exploration with local hill-climbing refinement. A two-phase initialization ensures every candidate planogram satisfies capacity constraints. Each chromosome encodes item-to-shelf mappings, with facings emerging endogenously. Mechanisms, including crossover, mutation, and diversity control, preserve solution validity and mitigate premature convergence. The framework was validated using real data from the Iranian retail chain Ofoq Kourosh, encompassing ۳۹ product categories and ۲۱,۰۰۰ cm of total shelf length. Results: The algorithm consistently converged toward feasible solutions. Under the original category bounds, profit reached ۳.۰۴ million; relaxing these bounds improved profit by ۶.۲% to ۳.۲۵ million. Allocation outcomes aligned with demand elasticity: impulse-driven categories reached upper limits, while low-elasticity staples stabilized near minima. Pareto analysis confirmed that roughly ۲۰% of categories generated over ۸۰% of profit. Notably, the optimized solution resulted in a ۳۷% increase in profit compared to the current store configuration. Conclusion: Results confirm the efficacy of hybrid metaheuristics for complex retail optimization. The framework consistently achieved near-optimal solutions under realistic constraints. Managerially, shelf-space allocation should prioritize high-elasticity categories while maintaining a minimal representation of staples. Future research should extend this framework to multi-store and omni-channel contexts with dynamic demand modeling.

کلیدواژه ها:

Assortment planning ، shelf-space optimization ، substitution effects ، Metaheuristics ، Local Search