Scenario-Based Distributionally Robust Optimization for the Stochastic Inventory Routing Problem

40 Pages Posted: 17 Jan 2022

See all articles by Runjie Li

Runjie Li

Nanjing University

Zheng Cui

Zhejiang University - School of Management

Yong-Hong Kuo

The University of Hong Kong - Department of Industrial and Manufacturing Systems Engineering

Lianmin Zhang

The Chinese University of Hong Kong, Shenzhen - Shenzhen Research Institute of Big Data

Abstract

We consider a class of the inventory routing problem in a discrete and finite time horizon, where the demands at retail stores are uncertain and vary across different scenarios. The supplier is required to determine the times to visit retailers, the replenishment quantities to each retailer, and the routing of a vehicle so as to minimize the sum of stockout, holding, and transportation costs. We propose a scenario-based distributionally robust optimization framework to tackle this problem. We transform the distributionally robust optimization model into a mixed-integer problem, which can be solved efficiently by our proposed algorithm. We adopt a warm-start procedure that utilizes the solution to the nominal model in our methodological framework. Then we apply a Tabu search algorithm, integrated with column generation, to solve a set-partitioning-like integer linear programming model so that a better route set can be identified. By doing so, a large-scale scenario-based distributionally robust optimization model can be solved. We conduct a case study of a fuel company and construct realistic instances to demonstrate the performance of our proposed method. Computational results suggest that the model taking into account various scenarios is more effective when random demands can be classified; the model with a linear decision rule outperforms a non-adaptive model; and the model with the route set identified by an improved algorithm can deliver a better solution than the original route set.

Keywords: Inventory routing, distributionally robust optimization, scenario-based, decision rule, column generation

Suggested Citation

Li, Runjie and Cui, Zheng and Kuo, Yong-Hong and Zhang, Lianmin, Scenario-Based Distributionally Robust Optimization for the Stochastic Inventory Routing Problem. Available at SSRN: https://ssrn.com/abstract=4010328 or http://dx.doi.org/10.2139/ssrn.4010328

Runjie Li

Nanjing University ( email )

Nanjing
China

Zheng Cui

Zhejiang University - School of Management ( email )

Hangzhou, Zhejiang Province 310058
China

Yong-Hong Kuo (Contact Author)

The University of Hong Kong - Department of Industrial and Manufacturing Systems Engineering ( email )

8/F Haking Wong Building
Pokfulam Road
Hong Kong
China

Lianmin Zhang

The Chinese University of Hong Kong, Shenzhen - Shenzhen Research Institute of Big Data ( email )

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