The model addresses a gap in the biomass supply chain literature. Most prior studies treat supply chain design either deterministically, which cannot capture the correlated season-wide swings of agricultural yields, or with risk-neutral objectives that hide how badly an operator can be hurt in a bad harvest year. The new formulation goes further by simultaneously minimizing expected total cost, expected net carbon dioxide equivalent emissions and the Conditional Value-at-Risk, or CVaR, of total cost, a measure of the average cost in the worst-case tail of scenarios. It is the first study, according to the authors’ positioning table, to combine the Thai residue system’s seasonal multi-feedstock character, ISO 17225 blending and calorific requirements, a seasonal collection network with an operating calendar, an avoided-burning credit and a genuinely three-objective risk-averse treatment in one model.

The decision structure is split into two stages. Before uncertainty is resolved, the model commits to strategic and tactical choices: which feedstock suppliers to contract, the design of a capacitated collection network for each harvesting season, the calendar of periods in which the network is dispatched, and the size of the vehicle fleet. After a particular scenario of supply and demand materializes, second-stage operational decisions adapt through collection, processing, storage and delivery quantities. Uncertainty is represented by Monte Carlo scenarios that preserve the temporal and spatial correlation inherent in agriculture, so an unfavorable season depresses the entire harvesting window rather than individual weeks independently.

Because this formulation is computationally brutal, the researchers paired a commercial-solver benchmark with a scalable matheuristic. The design layer embeds a capacitated routing structure, a class of problem known to be NP-hard, and evaluating the expected recourse of a two-stage program is itself #P-hard, while constructing a three-dimensional Pareto surface multiplies the burden across a grid of scalarization parameters. The matheuristic, an instantiation of success-history adaptive differential evolution called MO-SHADE, searches the combinatorial first-stage design while the second-stage recourse is evaluated exactly by linear programming, scenario by scenario, with the CVaR of the resulting policy computed afterwards. The authors prove that this ex-post risk evaluation is exact for the cost-minimizing recourse: because no constraint couples scenarios, the policy that minimizes expected cost also minimizes any monotone risk measure, CVaR included.

Seven metaheuristics were compared under identical evaluation budgets using hypervolume and IGD+ indicators with Friedman and Holm statistical testing. The self-adaptive differential-evolution variants ranked highest, though MO-SHADE and its cousin JADE were not statistically separable from one another, so no single variant is claimed as superior. On smaller instances the solver proved optimality quickly, but on a long-horizon instance with 102,845 variables it failed to converge within its budget, leaving a 2.1 percent gap even after an hour; there the matheuristic returned a design 3.42 percent cheaper at a matched budget, certified within 5.08 percent of optimal by the solver’s own dual bound. The two approaches are therefore complementary by problem size rather than competitors in the abstract.

Several modeling details turn out to carry quantifiable economic weight. Ablation experiments show that the latent-heat correction in the net-calorific-value constraint, which deducts the energy needed to vaporize retained moisture under the ISO 17225 convention, changes cost by 3.74 percent; omitting it would overstate delivered calorific value and misclassify premium grades. A terminal-inventory condition prevents a subtle accounting artifact: without it, the emission-minimizing solution would strand an average of 199 tonnes of pellets and 119 tonnes of feedstock as unsold stock whose production accrues carbon credit without any corresponding delivery. The operating calendar, which deactivates the collection network in unproductive periods, saves between 0.01 and 1.08 percent of cost depending on how concentrated the harvest is within each season, and is worth modeling only when idle periods fall inside a harvesting season rather than occupying a whole season.

The policy analysis yields what may be the study’s most consequential finding: the avoided-burning carbon credit, not the network design, decides whether the pellet pathway is carbon-negative. As the credit is scaled from zero to twice its nominal value, the net emissions of the cost-optimal solution fall monotonically from plus 105,681 to minus 400,266 kilograms of CO2-equivalent. In the primary case, where bagasse receives no credit because it is combusted in mill boilers rather than open-burned in fields, carbon negativity is reached at 0.60 of the nominal credit, compared with 0.42 when the full credit is granted. Strikingly, the cost-minimal design is invariant to the credit, and even a monetized carbon price of up to 4,000 baht per tonne of CO2-equivalent fails to change the design, because the cost-optimal solution already captures about 98 percent of the attainable avoided emissions.

A second policy lever, residue availability, behaves differently. As availability rises from 0.6 to 1.4 of the nominal level, modeling the residue released to the plant by a stricter open-burning ban, cost falls from 7.66 to 6.74 million baht while net emissions become more negative, moving from minus 89,298 to minus 182,181 kilograms of CO2-equivalent. Under the model’s fixed-price assumption, a stricter burning ban is simultaneously cheaper and cleaner for the plant operator. The authors caution that this is a statement about the operator’s response to feedstock availability at unchanged prices, not a market-equilibrium prediction, since a real ban would also move residue prices and suppliers’ outside options.

The risk axis of the three-objective trade-off proved nearly degenerate on the studied instances. A design that lexicographically minimizes CVaR reduces tail cost by about 0.37 percent at a 0.38 percent premium in expected cost, and the value of the stochastic solution is small, between 0.24 and 0.31 percent in risk-neutral form and at most 2.12 percent in pure CVaR form, because the recourse layer absorbs scenario variation at nearly the same cost under either first-stage design. The authors argue that the three-objective formulation is justified by the emission axis, which does not co-move closely with cost or risk, and by the generality of the framework rather than by large expected-cost or tail-cost gains.

The study is framed as a demonstrative Thai-calibrated case rather than an operational case study: fuel properties, moisture contents and residue ratios rest on published Thai field measurements, but the monetary and logistics parameters are not calibrated to any particular mill’s accounts, and the largest instance has eight suppliers and a single plant. The collection layer is an aggregated relaxation whose solutions require a route-decomposition step, and route-duration limits are not represented. Within those limits, the work delivers a transferable optimization tool whose clear message for policy is that calibrating the avoided-burning credit, the parameter of greatest consequence, deserves priority field measurement if residue diversion is to be promoted as a climate strategy.

Subject of Research: Risk-averse three-objective two-stage stochastic optimization of a seasonal sugarcane and rice residue pellet supply chain in Thailand

Article Title: Risk-averse three-objective two-stage stochastic design of a seasonal biomass pellet supply chain

Article References: Moonsri, K., & Worasan, K. (2026). Risk-averse three-objective two-stage stochastic design of a seasonal biomass pellet supply chain. Results in Engineering, 32, Article 113676. https://doi.org/10.1016/j.rineng.2026.113676

Image Credits: AI Generated

DOI: 10.1016/j.rineng.2026.113676

Keywords: biomass pellets, supply chain optimization, two-stage stochastic programming, CVaR, avoided open burning, differential evolution, Thailand, sugarcane bagasse, rice straw, ISO 17225, carbon emissions, matheuristic

The research, led by William Kirschenman, who completed the work as a Ph.D. student at NC State and is now an assistant professor at the Naval Postgraduate School, appears in two peer-reviewed journals: Naval Research Logistics and Omega. For Kirschenman, the problem is not an abstract puzzle. As a former company commander, he experienced firsthand how the order and placement of equipment can determine whether a mission succeeds. Wargaming amphibious landings, he says, revealed just how difficult it becomes to keep a unit organized in the sequence that best supports the mission when the environment is chaotic or contested. That practical frustration became the mathematical motivation for a new generation of packing models.

At the technical core of the first study is a two-dimensional orthogonal packing problem, a variant of the classic bin packing problem in which rectangular items must be placed without overlap inside a confined rectangular container. Traditional formulations of this problem typically minimize the number of bins used or the amount of unused space. The NC State team instead embedded a prioritization matrix into the bin packing framework, allowing items to be clustered with one another or pulled toward specific access points based on assigned priority weights. In other words, the model does not merely ask whether an item fits; it asks whether the item sits where it should relative to the doors, hatches or exits through which it will be retrieved, and whether it sits near the other items it belongs with.

This blending of ideas is what the authors describe as combining bin packing principles with facility layout concepts. Facility layout design, a longstanding field within industrial engineering, concerns itself with the spatial arrangement of departments and workstations to optimize flows and adjacencies. By importing that spatial-priority logic into packing, the researchers created a single mixed-integer linear programming model, or MILP, capable of balancing space efficiency against proximity to access points and adjacency among functionally related items. The result is a formulation that extends the utility of packing optimization to applications demanding far more nuanced layout preferences than simple volume maximization.

There was, however, an immediate computational obstacle. Every additional constraint, every priority level, every adjacency requirement multiplies the number of possible configurations the optimizer must consider. The researchers found that the potential combinations quickly outstripped available computing power when the full model was handed to a commercial solver as one monolithic problem. Their answer was a sliding-window matheuristic, a hybrid technique that breaks the large optimization problem into a sequence of smaller, overlapping subproblems. The algorithm solves each window of the packing space in turn, carrying forward the consequences of earlier decisions, and thereby obtains a good overall solution in a fraction of the time a direct solve would require.

The computational experiments were striking. When the sliding-window matheuristic was tested against a direct MILP solve using a commercially available optimization solver, the matheuristic consistently outperformed the monolithic approach in both runtime and solution quality. It also proved superior among the adapted heuristic and metaheuristic alternatives the team considered. For practitioners, that means high-quality, priority-aware packing plans can be produced on ordinary computing hardware rather than waiting hours or days for an exact solver to grind through an intractable search space, or settling for a crude rule-of-thumb arrangement.

The second study pushed the framework into an even more demanding arena: loading large maritime vessels. On a ship, geometry is only half the battle. Too much weight placed too high or too far to one side can cause the vessel to list, tilting dangerously, so load stability becomes a hard constraint that the packing plan must satisfy. As co-author Brandon McConnell, a research associate professor in NC State’s Edward P. Fitts Department of Industrial and Systems Engineering, explains, adding the stability constraint means working around a fixed center of gravity, and the correctness of the balance cannot be confirmed until the entire area has been packed, which usually forces adjustments. The team studied three solution approaches for this globally constrained problem: a monolithic MILP model, a sliding-window matheuristic, and a sliding-window matheuristic augmented with in-stride load balancing penalties applied during the solve.

Testing revealed a clear winner. The most efficient path was to run the existing sliding-window model first and then adjust selected lower-priority items at the end as needed to achieve stability, a post-processing strategy that selectively relaxes and re-optimizes item positions with minimal disruption to the prioritized layout. This simpler pipeline of matheuristic followed by repair emerged as the recommended practical configuration, offering the strongest overall combination of balance success, solution quality and runtime. The in-stride variant, which enforces balance during the initial solve, remains a narrower alternative for cases where achieving balance in the first stage is paramount. Notably, the matheuristic pipelines generated high-quality, load-balanced solutions for single-vessel scenarios within a few minutes on average, fast enough to let planners rapidly evaluate multiple loading configurations during time-critical deployment planning.

The implications stretch well beyond the military context that inspired the work, although combat loading, the art of arranging equipment on maritime transport so that mission-critical gear can be offloaded first while units stay cohesive and the vessel stays stable, remains the flagship application. The same mathematics applies to warehouse storage, where fast-moving goods should sit nearest the packing stations, and to multi-drop delivery services, where parcels for the last stops on a route must be loaded deepest and parcels for the first stops must be within easy reach. In every case, the model’s ability to encode multiple levels of prioritization, enforce groupings of related items, and respect physical constraints like balance turns a notoriously fiddly human judgment call into a reproducible computation.

The research team also included H. Sebastian Heese, Owens Distinguished Professor of Supply Chain Management; Michael Kay, associate professor of industrial and systems engineering; and Russell King, the Dopaco Distinguished Professor of Industrial and Systems Engineering, all of NC State. Kirschenman, a two-time selectee for the General Omar Bradley Research Fellowship in Mathematics, which helped support the research, sees the work as a bridge between abstract optimization and the messy realities of logistics. As McConnell puts it, the model could help ensure that mission-critical gear is offloaded first, save a warehouse worker’s time and energy, and lead to faster goods retrieval with fewer mistakes for any delivery business. In a world where supply chains are under unprecedented strain, teaching computers to pack with both intelligence and speed may prove one of the quiet but consequential advances of applied operations research.

Subject of Research: Prioritized two-dimensional orthogonal packing optimization with load balancing for military and commercial logistics

Article Title: Cracking the packing code – new models incorporate item priority, location and weight distribution

Article References: Cracking the packing code – new models incorporate item priority, location and weight distribution. (n.d.). Original publication

Image Credits: AI Generated

DOI: Not provided

Keywords: packing problem, optimization, mixed-integer linear programming, matheuristic, military logistics, load planning, warehouse storage, supply chain, vessel stability, operations research, bin packing, Naval Research Logistics