A Mathematical Model to Evaluate Time, Cost and Customer Satisfaction in Omni-Channel Distribution

Document Type : Research Paper


1 Department of Industrial Engineering, North Tehran Branch, Islamic Azad University, Tehran, Iran

2 Department of Industrial Engineering, Khatam University, Tehran, Iran


Today, upon the higher internet usage and the Covid-19 pandemic, the use of omni-channel distribution has experienced significant growth. The shopping experience in omni-channel distributions is influenced by the physical environment of the buyer, delivery time, and the cost of production to distribution of the goods which have a significant impact on customer loyalty and customer satisfaction. The lack of comprehensive studies in this field, and the number of constant variables in most of the available studies in the literature, especially uncertainty-laden demand, illustrate the significance of this study. After a related literature review and experts’ interviews, based on omni-channel Approach, all important factors influencing time, cost, and customer satisfaction have been included within a multi-objective mathematical model. Thus, defining constraints and decision variables, the objective functions have been solved within two new meta-heuristic algorithms, namely MOGWO and NSGA-II. Besides, these algorithms have been validated using NPS, DM, MID, and SNS indices. Upon comparing the outputs of these two algorithms and inserting 30 numerical instances, it has been shown that the MOGWO method has a stronger Pareto frontier and organized scattering for Pareto solutions. However, averagely, the NSGA-II algorithm produces fewer and more values compared with the first and second objectives, respectively.


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