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Shop Floor Optimisation by the Numbers
Splitting, loading, balancing, choosing, cutting, nesting, sequencing and grouping work in a factory, with bounds that show how good a plan is
Solve the hard choices of a job shop: machine loading, line balancing, project selection, bar cutting, sheet nesting, sequencing, cells and simulated annealing.
Start readingAbout this book
Every day a shop makes choices that look simple and are not: which press brake gets which job, which tasks go to which station on the assembly line, which improvement projects fit the year’s budget, how to cut a stack of tube lengths from stock, how to lay blanks on a sheet, which job the laser runs next and which machines share a bay. Each has a small number of inputs and an enormous number of possible answers. Twelve jobs on two machines can be split 4,096 ways; eight jobs can be run in 40,320 orders; twenty jobs in more orders than a computer could check in a lifetime.
This book shows how to make these choices well with arithmetic a planner can check. It counts the possibilities, uses simple rules that are known to work, calculates bounds that show how far a plan could still be from the best, and, when the problem is too large to check, uses local search and simulated annealing. The ideas come from operations research and from the statistical physics of disordered systems, which treats a plan as a configuration and its cost as an energy to be minimised.
It is for production engineers, planners, supervisors, estimators and owners of fabrication, machining and assembly shops. It assumes school algebra and comfort with a spreadsheet. Each chapter works the running case with real numbers, includes one plausible mistake and how it was caught, links the KEVOS® tool that does the chapter’s calculation where one exists, and ends with an exercise and its worked answer.
The running case
Every chapter follows one fictional shop. This is an illustration. A sheet-metal and assembly shop in Geelong, Victoria, makes a powder-coated steel electrical enclosure called EC-600, a 600 × 600 × 250 mm wall cabinet, alongside job work for local customers.
- Cutting and forming: a fibre laser with a 3,000 × 1,500 mm bed, two identical press brakes and a cold saw for square hollow section bought in 6.5 m lengths, with a 3 mm kerf and 10 mm trimmed from each end.
- Joining: three weld bays for frames, stands and job work.
- Assembly: a three-station final assembly line for EC-600, with 420 minutes of net working time a shift and demand for 60 cabinets a day.
- Improvement budget: A$60,000 excluding GST for the year’s capital projects.
Times, prices, demands and savings in the book are invented for the case and do not describe KEVOS® work, any real business or any real product.
How to use the book
Read Chapter 1 first: it introduces the counting, the bounds and the vocabulary every later chapter uses. Chapters 2 to 4 split work between machines and stations, Chapters 5 to 7 choose and cut within limits, Chapter 8 orders work on one machine, Chapter 9 groups machines, and Chapter 10 gives a general method for problems too large for the others. Each chapter can be read alone after Chapter 1.
Every calculation in the book was checked by running it, including the exhaustive searches that prove which plans are best. The KEVOS® tools linked from the chapters perform the same calculations with the reader’s own data.
Source limits and professional responsibility
The methods here are standard heuristics and bounds. They give good plans quickly, and the bounds say how good; they do not replace judgement about what the plan leaves out, such as operator skills, tooling, material availability, quality risk or a customer’s priorities. Real schedules change hourly, and a plan is only as good as the times and quantities put into it. This book is educational. Planning decisions that affect safety, contracts or people’s working hours remain the responsibility of the people who make them.
Who this book is for
Production engineers, planners, supervisors, estimators and owners of fabrication, machining and assembly shops who decide how work is split between machines, which jobs or projects to take, how to cut stock and in what order to run work.
What you will learn
- Recognise when a shop-floor choice is combinatorial, count its possibilities and decide whether to search them all, use a rule or use a heuristic.
- Split and load work across machines and balance an assembly line to takt time, with lower bounds that prove how close a plan is to the best.
- Choose jobs or improvement projects within a budget, cut bars and nest sheet blanks with least waste, and check every plan against its bound.
- Sequence jobs on one machine for flow time, lateness or late jobs, and group machines into cells that minimise material moves.
- Use local search and simulated annealing on problems too large to solve exactly, and judge when a result is good enough.
Inside this book
Chapters
- 01Why shop-floor choices explodeCount the possible plans in common shop-floor choices, describe a plan by its cost and constraints, and use lower bounds, exact rules and heuristics to decide how hard to search.
- 02Splitting work between two machinesSplit jobs between two identical machines so both finish together: the halving bound, longest-first and differencing rules, exhaustive checks and how many perfect splits to expect.
- 03Loading several machinesLoad jobs onto three or more identical machines: the two lower bounds, the longest-first rule and its guarantee, its worst case, jobs that arrive during the day, and a capacity check over the week.
- 04Balancing an assembly lineBalance an assembly line to takt: takt time, the least number of stations, precedence, the positional weight rule, exhaustive checks, and the KEVOS® takt, bottleneck and cycle time tools.
- 05Choosing jobs and projects within a budgetChoose the projects or jobs that give the most benefit within a budget or capacity: the knapsack problem, ratio and largest-first rules, the fractional bound and exact table methods.
- 06Cutting bars with least wasteCut a list of tube or bar lengths from stock with the fewest bars: the material lower bound, the first-fit decreasing rule in the KEVOS® stock cut planner, cutting patterns, offcuts and stock length.
- 07Nesting blanks on sheetsLay rectangular blanks on stock sheets for least waste: grid and two-block layouts in the KEVOS® sheet nesting tool, the area bound, sheet size choice, mixed nesting and what utilisation hides.
- 08Sequencing jobs on one machineOrder jobs on one machine for least flow time, least lateness or fewest late jobs with the shortest-first, due-date and Moore rules, and order changeovers to cut set-up time.
- 09Grouping machines into cellsGroup workstations into bays or cells so that as little material as possible moves between them: flow matrices, graph partitioning, exhaustive checks, swap-based improvement and its local optima.
- 10Local search and simulated annealingSolve problems too large for exhaustive search: moves and local optima, the simulated annealing rule, choosing a temperature schedule, penalties for constraints and when to stop.
Apply This in Practice
Use these KEVOS® tools to try the method from this reading with your own numbers.
Applies this method
Bottleneck and Line Balance
Finds the constraint among up to three steps against takt, with its load, the line's daily capacity and balance efficiency, used to check the chapter's station balances.
Used in Balancing an assembly line
Applies this method
Capacity Check
Estimates practical output for a period from available hours, parallel stations, cycle time and efficiency, and compares it with demand: the weekly check behind the chapter's loading.
Used in Loading several machines
Applies this method
Cycle Time vs Takt
Compares a line's actual cycle time with the cycle demand requires, reporting headroom and output at the actual cycle, as the chapter checks its balanced line.
Used in Balancing an assembly line
Applies this method
Setup Reduction Value
Values a set-up reduction project from current and target set-up times, changeovers a year, hourly cost and investment: hours released, annual value and payback.
Applies this method
Sheet Nesting Yield Check (Parts per Sheet, Material Utilisation, Sheets and Cost per Part)
Finds the best grid or two-block layout of rectangular blanks on a sheet, with utilisation, sheets for an order and material cost per blank, as the chapter compares sheet sizes.
Used in Nesting blanks on sheets
Applies this method
Takt Time
Calculates takt time and the required hourly rate from net available production time and required output, the pace the chapter balances the assembly line to.
Used in Balancing an assembly line
Applies this method
Three-Size Stock Cut Planner
Plans cutting up to three piece lengths from stock bars by first-fit decreasing with kerf and end trim, and proves the bar count minimal when it meets the material bound.
Used in Cutting bars with least waste
References and source notes
The manuscript and worked examples are original KEVOS® writing. References inform particular concepts; their authors do not endorse this book. Web references were consulted on 31 October 2026.
- H. Nishimori, Oxford University Press (International Series of Monographs on Physics 111). Statistical Physics of Spin Glasses and Information Processing: An Introduction (2001). In copyright. Used only as a map of the ideas behind Chapters 1, 2, 5, 9 and 10: number partitioning, graph partitioning, the knapsack problem and simulated annealing treated as problems of finding the lowest-energy state of a many-variable system. No text, structure, figures, tables or problems are reproduced, and all cases and calculations are KEVOS® originals.
- M. R. Garey and D. S. Johnson, W. H. Freeman, San Francisco. Computers and Intractability: A Guide to the Theory of NP-Completeness (1979). Named in Chapter 1 as the standard account of why problems such as partitioning, bin packing and sequencing have no known method that is fast for every instance.
- R. L. Graham, SIAM Journal on Applied Mathematics 17(2), 416–429. Bounds on multiprocessing timing anomalies (1969). Source of the worst-case guarantee for the longest-processing-time rule quoted in Chapter 3.
- N. Karmarkar and R. M. Karp, Report UCB/CSD 82/113, University of California, Berkeley. The differencing method of set partitioning (1982). Named in Chapter 2 as the origin of the differencing heuristic for splitting work between two machines.
- W. E. Smith, Naval Research Logistics Quarterly 3(1–2), 59–66. Various optimizers for single-stage production (1956). Named in Chapter 8 as the origin of the shortest-processing-time rule for least average flow time.
- J. R. Jackson, Research Report 43, Management Science Research Project, University of California, Los Angeles. Scheduling a production line to minimize maximum tardiness (1955). Named in Chapter 8 as the origin of the earliest-due-date rule for least maximum lateness.
- J. M. Moore, Management Science 15(1), 102–109. An n job, one machine sequencing algorithm for minimizing the number of late jobs (1968). Named in Chapter 8 as the source of the method for least number of late jobs, worked there on the running case.
- G. B. Dantzig, Operations Research 5(2), 266–288. Discrete-variable extremum problems (1957). Named in Chapter 5 for the ratio rule and the fractional bound used to judge a knapsack selection.
- P. C. Gilmore and R. E. Gomory, Operations Research 9(6), 849–859. A linear programming approach to the cutting-stock problem (1961). Named in Chapter 6 as the origin of cutting-pattern methods, the approach used there to find the plan the first-fit rule missed.
- B. W. Kernighan and S. Lin, Bell System Technical Journal 49(2), 291–307. An efficient heuristic procedure for partitioning graphs (1970). Named in Chapter 9 as the origin of swap-based improvement for splitting a network into two groups.
- N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller and E. Teller, Journal of Chemical Physics 21(6), 1087–1092. Equation of state calculations by fast computing machines (1953). Named in Chapter 10 as the origin of the acceptance rule used in simulated annealing.
- S. Kirkpatrick, C. D. Gelatt and M. P. Vecchi, Science 220(4598), 671–680. Optimization by simulated annealing (1983). Named in Chapter 10 as the paper that introduced simulated annealing for optimisation problems.