Journal of Industrial Engineering Research in Production Systems

Journal of Industrial Engineering Research in Production Systems

Joint Decisions of Pricing and Shipment Consolidation per Customer for The Last-Mile Delivery with Uncertain Demand

Document Type : Research Paper

Authors
Melina Safari Nasab 1
Mohsen Sheikh Sajadieh 2
Matineh Ziari 3
1 Department of Systems and Industrial Engineering, Amirkabir University of Technology, Tehran, Iran. M.Sc. Graduate, Faculty of Industrial Engineering and Management Systems, Amirkabir University of Technology, Tehran, Iran
2 Department of Systems and Industrial Engineering, Faculty of Industrial Engineering and Management Systems, Amirkabir University of Technology, Tehran, Iran
3 Department of Industrial Engineering, Faculty of Industrial Engineering, University of Tehran, Tehran, Iran
10.22084/ier.2026.31251.2209
Abstract
With the increasing growth of online stores and e-commerce businesses, a significant portion of customer needs are now met through these channels. This research focuses on product pricing and solving the problem of separate order deliveries in the final stage of product delivery. Separate order deliveries occur when multiple orders from a single customer are shipped in separate trips within a specific time period. This study targets a two-level supply chain consisting of a delivery center and a number of end customers. Each customer can place multiple orders over a given time period. Additionally, the research considers product variety, and the time at which each customer places an order for a product is uncertain and varies under different scenarios. To address this uncertainty, a robust nonlinear integer programming model based on the scenario-based Mulvey robust optimization approach is proposed. To solve the mathematical model in large-scale instances, a heuristic algorithm is employed. Finally, the problem is numerically solved in various dimensions, demonstrating the strong performance of the heuristic algorithm with an accuracy of 95% to 99% and a maximum solution time of 9 seconds for the largest instance—compared to the exact solution method using GAMS software, which requires over 7,200 seconds to converge. Furthermore, the order consolidation policy proves superior to the first-come-first-served approach across various parameters. The results of sensitivity analysis on key problem parameters provide valuable managerial insights for practical implementation.
Keywords
Time-Based Shipment Consolidation Policy, Last-Mile Delivery, Pricing, Customer&‌‌‌rsquo
s Willingness to Pay, Demand Uncertainty, Robust Optimization
Subjects
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Journal of Industrial Engineering Research in Production Systems
Volume 13, Issue 27
September 2026
Pages 21-39