Modern Research in Decision Making

Optimization of Product Assortment and Pricing Considering the Substitution Effect in Omni-Channel Retailing

Document Type : Original Article

Authors

Naim Ebrahimian 1
hannan Amoozad 2
Mostafa Zandieh 3

1 PhD Student, Faculty of Management, University of Tehran, Tehran, Iran

2 Professor, Faculty of Management, University of Tehran, Tehran, Iran

3 Professor, Department of Industrial Management, Faculty of Management and Accounting, Shahid Beheshti University, Tehran, Iran

Abstract
Simultaneously managing product assortment, pricing, and substitution effects in omni-channel retailing is a complex challenge due to interactions among customer demand, operational constraints, and price competition. Most previous models focus on only one of these areas, overlooking their interdependencies.
This study proposes an integrated nonlinear model that maximizes profit by considering stochastic demand, multi-stage substitution (within and across channels), inventory constraints, shelf space limitations, and fulfillment center capacities.
To solve the model, four metaheuristic algorithms—Forest Optimization, Particle Swarm Optimization, Imperialist Competitive Algorithm, and Genetic Algorithm—are employed. Their performance is evaluated using real-world data from the largest retailer in Iran and synthetic datasets. The results show that Forest Optimization significantly outperforms the other methods, achieving an average 20% increase in profit and a 15% reduction in lost sales. Additionally, it converges 25% faster, and the stability of its results is confirmed by Wilcoxon tests at a 0.05 significance level.
Scenario analysis reveals that increasing the number of channels can boost profitability by up to 30% and reduce internal competition, while expanding product variety can lower lost sales by up to 18%. These findings provide practical guidance for retailers to optimize pricing, inventory, and assortment decisions across both physical and online channels.

Keywords

Optimization
omni-channel retailing
product assortment
pricing
meta-heuristic methods
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