Operations Research Methods for Large-Scale Supply Chain Logistics Optimization

In the supply‑chain domain, operations research (OR) techniques are crucial for making optimal decisions across procurement, production, inventory, and distribution, aiming to minimize cost, maximize efficiency, and satisfy customer demand.

A typical logistics network planning model minimizes total logistics cost, including transportation and transshipment costs, and incorporates constraints such as route uniqueness, vehicle capacity, vehicle quantity, vehicle‑type selection, logical relationships between lines and routes, and minimum flow requirements for opened lines.

For a real‑world example (Company C), the model contains millions of integer variables; commercial solvers fail to find feasible solutions within 10 hours. To address this, a column‑generation approach combined with a partition‑based solving method is employed to generate high‑quality initial solutions.

Using partition solving, an initial solution is obtained in about 3 hours with a 30% gap to the relaxed optimal solution, whereas direct Gurobi solving yields no feasible solution after 10 hours, demonstrating the efficiency of the partition approach.

The column‑generation algorithm starts from the initial routes, solves a restricted master problem with relaxed integer variables, obtains dual values, evaluates non‑included candidate routes via reduced costs, adds promising routes (negative reduced cost), and iterates until no improving routes remain, after which integer variables are restored and the model is re‑solved.

A key difficulty arises when relaxing integer variables: the large‑M formulation can make the LP relaxation too loose, causing a large optimality gap between the MILP and its LP relaxation. Replacing the large‑M constraint with a tighter bound (e.g., \(z_l \ge y_r\)) mitigates this issue.

With column generation, the ultra‑large network problem is successfully solved, revealing an “hourglass” structure of three layers (5‑10 first‑stage routes × 40‑60 hub‑to‑hub routes). The optimized network shows an average of 2.49 transshipments per shipment, with few primary routes required, allowing many existing facilities to meet demand.

Overall, OR acts as the “rivets” of the supply‑chain chain, abstracting complex business processes into decision variables, objectives, and constraints, enabling clear analysis and optimal trade‑offs. The integration of advanced algorithms, cloud computing, and AI further drives the evolution toward intelligent supply chains.

This excerpt is taken from the book “Intelligent Supply Chain: Operations Research Theory and Practice”, which presents OR algorithms and industry cases to guide professionals and researchers in supply‑chain management.