# A Novel Mixed-Integer Linear Programming Formulation for Continuous-Time Inventory Routing

arXiv: https://arxiv.org/abs/2310.11240 · HTML: https://mlsanity.com/paper/2310.11240/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Oct 2023.

## Built on by (most cited first, 1 of 1)

- [Towards An Unsupervised Learning Scheme for Efficiently Solving Parameterized Mixed-Integer Programs](https://mlsanity.com/paper/2412.17623/) (2024)

## Abstract (arXiv)

Inventory management, vehicle routing, and delivery scheduling decisions are simultaneously considered in the context of the inventory routing problem. This paper focuses on the continuous-time version of this problem where, unlike its more traditional discrete-time counterpart, the distributor is required to guarantee that inventory levels are maintained within the desired intervals at any moment of the planning horizon. In this work, we develop a compact mixed-integer linear programming formulation to model the continuous-time inventory routing problem. We further discuss means to expedite its solution process, including the adaptation of well-known rounded capacity inequalities to tighten the formulation in the context of a branch-and-cut algorithm. Through extensive computational studies on a suite of 90 benchmark instances from the literature, we show that our branch-and-cut algorithm outperforms the state-of-the-art approach. We also consider a new set of 63 instances adapted from a real-life dataset and show our algorithm's practical value in solving instances with up to 20 customers to guaranteed optimality.