Bridgestone Solves Multi-Plant Tire Production Planning with Mixed Integer Programming (MIP) via Hexaly 🔗

Foundation: Production planning across multiple manufacturing plants is the problem of deciding how much of each product to make at which facility, in which period, using which machines, over a rolling planning horizon. When decisions are discrete, such as whether to run a production campaign or which batch to assign to a specific line, the problem becomes a Mixed Integer Program (MIP). Tire manufacturing adds two complicating constraints: switching a line between tire types takes different amounts of time depending on which type precedes which, so the order of production runs matters, not just the mix; and each run must last long enough to justify the setup cost, ruling out short bursts of any single type. Together these make the feasibility structure particularly hard for standard linear relaxations.

Bridgestone, one of the world's largest tire manufacturers, engaged Hexaly to plan multi-plant tire production across a four-to-five month rolling horizon. The planning model simultaneously balances manufacturing efficiency, service levels, machine capacity, and inventory targets. Hexaly's solver combines Mixed Integer Linear Programming (MILP) with decomposition methods and was benchmarked against a Gurobi Mixed Integer Linear Programming (MILP) baseline under the same computational time budget. The case study confirms Hexaly as the production solver for the rolling-horizon plan, deployed in an ongoing operational context rather than as a one-off pilot.

Bilevel Late Acceptance Hill Climbing for the Electric Capacitated Vehicle Routing Problem 🔗

This paper addresses a structural gap in metaheuristic search — algorithms that explore large solution spaces by iterative improvement rather than exhaustive enumeration — for electric fleet routing: conventional Vehicle Routing ProblemThe problem of finding the best set of routes for a fleet of vehicles given customer locations, demands, and constraints. First explained 7 Apr 2026. approaches treat routing as the sole decision variable and cannot cheaply evaluate whether a candidate route is battery-feasible when charging station stops must be scheduled along it. Qin, Bazargani, Burke, Coello Coello et al. propose b-LAHC, a bilevel Late Acceptance Hill Climbing (LAHC) framework that structurally separates routing decisions (outer search) from charging scheduling decisions (inner solver), allowing the outer metaheuristic to explore routes freely while the inner level verifies and optimises charging independently for each proposed route. The paper sets 9 out of 10 new best-known solutions on the Institute of Electrical and Electronics Engineers (IEEE) WCCI-2020 benchmark set, with an average 1.07% improvement over prior published records.

Hedging Market Risk and Uncertainty via a Robust Portfolio Approach 🔗

Foundation: You own British Airways shares; when oil prices spike, jet fuel costs rise and the shares fall. To cushion that loss, you also hold oil futures — a contract that gains when oil rises — so the two positions partially cancel each other out: that pairing is a hedge. Standard hedging calculates how much of those oil futures to hold relative to your airline shares, using historical price relationships, but when those estimates are unreliable, the ratio can overshoot or undershoot — leaving you either over-hedged and paying unnecessary transaction costs, or under-hedged and exposed when the market moves against you. Robust optimisationA class of optimisation that finds solutions which remain near-optimal under the worst-case realisation of uncertain parameters. First explained 8 Apr 2026. addresses this by finding a hedge ratio that works acceptably across a range of plausible estimates, rather than betting on one estimate being exactly right.

The key idea is to treat each historical price relationship — the kind that tells you how much British Airways shares tend to move when oil prices shift — as uncertain within a tolerance band, rather than trusting one fixed estimate. When those bands are symmetric (equally uncertain in either direction), the safest ratio of oil futures to airline shares turns out to have a direct formula: no optimisation solver needed, just a calculation run at each rebalancing step. Backtested on stock, bond, and commodity exchange-traded funds (ETFs) from 2016 to 2024, the robust hedge ratios delivered better downside protection and less unnecessary trading than standard dynamic hedges — a gap that widened once transaction costs were counted.

Bilevel Optimisation

"In many competitive and hierarchical situations, optimising in isolation ignores the fact that others are also optimising." — John von Neumann, on the foundations of game theory and strategic optimisation

Bilevel optimisation (BO) describes any problem where one decision-maker, the leader, optimises their own objective while knowing that a second decision-maker, the follower, will respond by solving their own optimisation problem. The leader cannot control the follower's choice directly, only the environment in which the follower optimises. The leader's feasible set is therefore constrained not by simple inequalities but by the optimality condition of the follower's problem: the leader must predict the follower's best response to every candidate decision.

One-line version: Bilevel optimisation is not a big MIP with two groups of variables: it has two separate decision-makers with potentially conflicting goals, and the leader's feasible set is defined by the follower's optimality condition, not by a closed-form constraint.

Related terms: Stochastic Programming · Two-Stage Robust Optimisation · Benders Decomposition

→ Full concept page