An integrated (1, T) inventory policy and vehicle routing problem under uncertainty: an accelerated Benders decomposition algorithm

ABSTRACT

Inventory control and logistics are both important to the success of a supply chain. These problems become highly complicated when the demand of end-users is uncertain. The demand uncertainty could have a considerable destructive effect on a supply chain, e.g. bullwhip effect. Therefore, this paper proposes a two-stage approach to study an inventory-routing problem for a three-echelon single-item supply chain, consisting of suppliers, manufacturers, distributors, and wholesalers. The approach utilizes the $(1,T)$ ordering policy in the first stage to determine the optimal replenishment ordering quantity of wholesalers under uncertainty. This stage aims to minimize the inventory holding and lost-sales costs. To the best of our knowledge, this is the first application of the $(1,T)$ policy to an inventory-routing problem. Afterward, a mathematical formulation is proposed in the second stage to study a new vehicle routing problem. This model minimizes the transportation cost. Based on the literature, the vehicle routing problem is NP-hard; therefore, a new accelerated Benders decomposition algorithm is developed to solve large-scale instances of the problem. The algorithm incorporates a modified $ϵ$-optimality accelerator. The computational results show the superior performance of the modified accelerator compared to the conventional one. To evaluate the performance of the accelerated Bender decomposition algorithm, we compare it with the mathematical programming and a Genetic algorithm using twenty benchmark examples. We also introduce and assess a real-case study in the automotive parts industry. Finally, we analyze some key features of the case study to provide managerial implications.

KEYWORDS:

• (1, T) Inventory Policy
• Bullwhip Effect
• Vehicle Routing Problem
• Uncertainty
• Benders Decomposition Algorithm
• Genetic Algorithm
• Automotive Parts Industry

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. Department of Trade and Industry, UK, 1990.

2. https://www.google.com/maps/d/edit?mid=1KP2WvpI8AQTJuk4VdW05yPsD28RCU-zv