GuidePackaging & Paper

Trim loss optimization: cutting reels and sheets with less waste

Trim loss is the part of every parent reel, deckle or sheet that ends up as edge strip, narrow leftover or unpaid over-run instead of a customer order. Reducing it is a well-studied mathematical problem, but results on the floor depend on knife limits, width rules, tolerances, due dates and the setups each pattern change costs. This guide explains how trim optimizers work, which constraints decide the outcome and how to measure trim honestly.

Reviewed 7 min read

On this page
  1. Where trim waste comes from in mills and converting plants
  2. One-dimensional versus two-dimensional cutting in practice
  3. How trim optimizers search for cutting patterns
  4. The column generation loop behind most trim modules
  5. Floor constraints a trim optimizer must encode
  6. Choosing the objective: trim, pattern changes or due dates
  7. Linking trimming with sequencing and grade-change scheduling
  8. Data, honest trim metrics and where machine learning fits
  9. Planning a week of corrugator orders with an optimizer
  10. Questions and answers
  11. Sources

Where trim waste comes from in mills and converting plants

On a paper machine, the usable deckle has to be divided into customer reel widths at the winder. Whatever cannot be filled becomes side trim or a narrow reel that goes to stock or back to the pulper. The same arithmetic repeats on the rewinders and slitters of converters that buy jumbo reels.

Corrugators add a second decision: which roll width to run for each group of orders. A wide roll fits more lanes across the slitter-scorer but wastes more when the combination is poor, while switching roll widths costs splices and time. Sheet-fed folding carton and label plants face a two-dimensional version, laying out blanks on a press sheet. In every case, over-runs beyond what the customer pays for and narrow leftovers belong in the waste picture alongside the visible edge strip.

One-dimensional versus two-dimensional cutting in practice

AspectReel and deckle trimming (1D)Sheet and blank layouts (2D)
Where it happensPaper machine winders, rewinders, slitters and corrugator slitter-scorersSheeters, press sheets for folding cartons and labels, die layouts
What is decidedWhich order widths share each set, and how many sets to runHow blanks are arranged on a sheet, and which sheet size to use
Typical constraintsKnife count, minimum and maximum widths, edge trim, reel diametersGrain direction, gripper and bleed margins, guillotine cuts, die limits
Usual solution methodColumn generation with a knapsack subproblem, then integer roundingLayout heuristics and integer programming for guillotine or free-form cuts

How trim optimizers search for cutting patterns

A cutting pattern is one way of filling a parent width with order widths, plus the leftover. Even a modest order book allows an enormous number of patterns, so listing them all is impractical. Gilmore and Gomory's linear programming approach, published in Operations Research in 1961 and extended in 1963, sidesteps this by generating patterns only when they would improve the plan12.

The method alternates between a master problem, which decides how often to run each known pattern to meet demand at least cost, and a pricing problem, which uses the master's dual prices to find the most valuable new pattern by solving a knapsack. When no new pattern helps, the fractional plan is rounded or repaired into whole sets. Commercial trim modules often add heuristics for speed or for rules that do not fit the linear model, and small instances can be solved exactly with integer programming.

The column generation loop behind most trim modules

01Master problem02Dual prices perwidth03Knapsack pricing04Add improvingpattern
  1. Master problem

    Chooses how often to run each known pattern so every order is covered at least cost.

  2. Dual prices per width

    Show how much one more unit of each order width is worth to the current plan.

  3. Knapsack pricing

    Finds the single most valuable pattern that respects knife and width rules.

  4. Add improving pattern

    A pattern that beats its cost joins the master problem; if none does, the loop stops.

Conceptual loop based on the Gilmore and Gomory method. After it stops, the fractional solution is rounded into whole sets.

Floor constraints a trim optimizer must encode

0 of 10 checked

Choosing the objective: trim, pattern changes or due dates

  • If

    Knife positioning is automated and changes are quick

    Then

    Minimize trim with a light penalty on the number of distinct patterns.

    Extra patterns cost little, so the optimizer can chase waste.

  • If

    Knives are set by hand and each change stops the winder

    Then

    Penalize pattern changes explicitly and accept slightly more trim.

    Setup time and setup waste outweigh small trim gains.

  • If

    Late orders carry penalties or risk losing the customer

    Then

    Make due dates hard constraints and optimize trim within them.

    A plan that is lean but late is not a good plan.

  • If

    Narrow leftover reels pile up in the warehouse

    Then

    Add a cost for creating stock reels and cap how much tolerance is used.

    Stock that never sells is trim recorded later.

Linking trimming with sequencing and grade-change scheduling

  1. Pool orders by grade and window

    Group open orders by grade, caliper or board construction and by dispatch window, so each optimization run has a coherent order set.

    Output
    Order pools
    Owner
    Production planner

  2. Choose deckles and roll widths

    Pick the parent or roll width for each pool, using forecasts of the order mix where the choice is made before all orders are known.

    Output
    Width plan
    Owner
    Planner with optimizer

  3. Optimize the trim plan

    Run the optimizer with the chosen objective and constraints, then review exceptions such as orders left unplanned.

    Output
    Cutting patterns and set counts
    Owner
    Planner

  4. Sequence the sets

    Order sets to reduce knife moves and keep reel diameters consistent, then check the campaign against grade-change practice on the paper machine.

    Output
    Run sequence
    Owner
    Scheduler

  5. Publish and re-plan on change

    Send the plan to MES, freeze the sets about to run, and re-optimize the rest when orders change or defects reduce usable width.

    Output
    Released schedule
    Owner
    Planner

Data, honest trim metrics and where machine learning fits

An optimizer is only as good as its inputs from ERP and MES: order widths and quantities with tolerances, grade codes that mean the same in both systems, current roll inventory, machine limits and setup times. Common traps are tolerances stored as free text, duplicate grade codes after mergers, and defect information that never leaves the inspection system.

Measure trim the same way before and after any change. Report side trim, narrow leftovers sent to stock or broke, over-runs beyond what customers pay for, and setup waste as separate lines, and compare periods with a similar order mix. A single percentage that quietly drops one of these makes any optimizer look good.

Machine learning earns its place around the optimizer rather than inside it: forecasting the order mix when widths must be chosen early, predicting run and setup times, and estimating usable width from inspection maps. Choosing the patterns is a well-posed problem where exact methods beat learned guesses. ColdAI's packaging work covers scheduling and changeover optimization on converting lines3, and our operations practice applies the same thinking beyond the plant.

Planning a week of corrugator orders with an optimizer

Questions and answers

Is trim optimization the same as nesting?

They are related but not the same. Trim optimization usually means cutting reels by width or cutting rectangles from sheets, where patterns are combinations of widths or blanks. Nesting usually means fitting irregular shapes, such as carton blanks with flaps, onto a sheet or die. The algorithms, constraints and software differ, although a folding carton plant may need both.

Is the trim module in our ERP good enough?

It can be, if your constraints are simple and the module represents them correctly. Problems appear when knife limits, tolerances, defect zones or setup costs cannot be expressed, so planners override plans by hand. Test it by replaying a past period of orders through the module and through a dedicated optimizer, measuring trim and setups the same way in both.

How often should a trim plan be re-optimized?

Whenever the order book changes enough to matter, when defects reduce usable width, or at each scheduling cycle. Freeze the sets about to run so the floor is not chasing a moving plan, and re-optimize only the unreleased part. Constant re-planning can create more setup waste than it saves in trim.

Does lower trim help with sustainability reporting?

Less trim means less fiber, energy and chemistry per ton of saleable product, which feeds material-efficiency and emissions figures. The reporting benefit depends on measuring trim consistently and on how your footprint method treats broke and internally recycled waste. Agree that method with your sustainability team before claiming an improvement.

Sources

  1. A Linear Programming Approach to the Cutting-Stock Problem (Gilmore and Gomory) — Operations Research, INFORMS · checked 10 October 2026
  2. A Linear Programming Approach to the Cutting Stock Problem, Part II (Gilmore and Gomory) — Operations Research, INFORMS · checked 10 October 2026
  3. Packaging & Paper: production optimization and delivery approach — ColdAI

More in Packaging & Paper

Back to Packaging & Paper

Next step

Replay last month's orders through a trim optimizer

Send an export of recent orders, roll or deckle widths and your machine limits. We will compare your actual trim with an optimized plan for the same orders, using a trim definition agreed with you first.

Benchmark my trim plan