WO2017000021A1

WO2017000021A1 - A method and a computer program for determining a combination of patterns for cutting bulk material

Info

Publication number: WO2017000021A1
Application number: PCT/AU2016/050509
Authority: WO
Inventors: Mike ALLISON
Original assignee: 8-Sigma Consulting Pty Ltd
Priority date: 2015-06-29
Filing date: 2016-06-16
Publication date: 2017-01-05

Abstract

A method of determining a combination of patterns for cutting bulk material into items of a range of desired sizes according to customer demand is disclosed. The method comprises obtaining bulk material specifications and determining all possible cutting patterns based on the range of desired sizes, the customer demand, the bulk material specifications and based on capabilities of equipment for cutting the bulk materials. The method further comprises, prior to the commencement of cutting, selecting a combination of cutting patterns from all possible cutting patterns determined according to step (b) that reduces waste of the bulk material and that satisfies customer demand.

Description

A METHOD AND A COMPUTER PROGRAM FOR DETERMINING A COMBINATION OF PATTERNS FOR CUTTING BULK MATERIAL

TECHNICAL FIELD

A method and a computer program are disclosed for determining a combination of patterns for cutting bulk material into desired sizes according to customer demand. In particular, the method and the computer program are adapted to assess waste produced by cutting bulk material according to combinations of cutting patterns and to reduce l o waste, where possible .

In the context of cutting large (i.e. jumbo) coils of steel strip, the term "waste" excludes edge-trim on each side of the strip. It will be appreciated, however, that the method and the program can be applied to cut a range of bulk materials, including, but 15 not limited to, paper, film, fabric, rubber and other materials in large coil form.

BACKGROUND ART

Large coils of steel strip ("jumbo" coils) are produced by steel mills and slit into 2 o narrower width coils, i.e. smaller coils, at steel slitting mills. The slitting process

involves setting up a number of hardened steel cutting rollers, known as knives on a mandrel. The "jumbo" coil is pulled over the mandrel to achieve continuous shearing into the smaller coils.

The principal difficulty in choosing the arrangement of knives is to ensure the correct numbers of smaller coils and their respective widths are produced, while minimising the amount of steel left on the "Jumbo" coil. Any steel not formed into a smaller coil for a customer order becomes scrap, i.e. waste, and results in loss of revenue. Similar scrap problems exist in the slitting of paper, film, fabric, rubber and other materials in large coil form.

This relationship between the jumbo coil widths, the configuration of knives to produce smaller coils and waste is illustrated in Figure 1. Edge trim of steel strip coils is an irreducible minimum waste caused by technological limitations of coil production and stability of the slitting mechanism.

The arrangement of knives on the mandrel is known as the "nesting pattern". Determination of the "nesting pattern" for reducing waste is extremely complex. Many millions of possible combinations are possible. Some slitting mills determine "nesting patterns" manually and some automated methods exist within Enterprise Resource Planning (ERP) software. In each case, nesting patterns are compiled by fitting small widths of smaller coils into the remaining cuttable width of a jumbo coil after the wider widths of smaller coils are set. Combinations of these nesting patters are then selected so that the customer order of certain numbers of smaller coils of various widths is satisfied. The applicant has found that the existing manual and automated methods for determining nesting patterns does not reduce scrap to an extent that it may possibly be reduced.

Additionally, the number of smaller coils produced by the nesting pattern combination that exceed the customer order will contribute to stock inventory. Steel slitters seek to minimise stock inventory because it represents steel that they have purchased from steel mills but not yet been able to sell to customers. In the event that the steel slitter is working on jumbo coils purchased by the customer, i.e. commission slitting, any waste (including additional smaller coils not required to fulfil an order) is a cost borne by the customer. While some of the cost of waste can be recouped by recycling the steel, the overall value of the waste steel is about 10% of the original price for the same amount of steel.

The above references to the manual and automated methods for determining nesting patterns do not constitute an admission that they form a part of the common general knowledge of a person of ordinary skill in the art. The above references are also not intended to limit the application of the apparatus and method as disclosed herein. SUMMARY OF THE DISCLOSURE

According to the invention there is provided a method of determining a combination of patterns for cutting bulk material into items of a range of desired sizes according to customer demand, the method comprising: obtaining bulk material specifications; determining all possible cutting patterns based on the bulk material specifications and based on capabilities of equipment for cutting the bulk materials; and prior to the commencement of cutting, selecting a combination of cutting patterns from all possible cutting patterns determined according to step (b) that reduces waste of the bulk material and that satisfies customer demand.

The step of determining all possible cutting patterns causes the method to assess a greater range of combinations of cutting patterns. It follows that, with the assessment of this greater range, the method will be able to determine the waste produced by a greater range of combinations and, therefore, has a greater chance of selecting a combination that reduces waste more than other combinations selected by other methods. The applicant's test work to date is in the field of slitting jumbo steel coils into a variety of strip widths to satisfy customer orders. This test work, which is discussed in more detail below, shows that improvements in waste reduction can be achieved compared with conventional methods for selecting cutting combinations.

The applicant anticipates that it is possible to reduce the amount of bulk material that needs to be cut in order to fulfil customer orders. This view stems again from the applicant's test work in slitting jumbo steel coils which demonstrates that, for significant orders that require, for example, 25 jumbo steel coils according to convention methodology, the above described method may select a cutting pattern combination that requires only 18 jumbo steel coils. Accordingly, in some circumstances there may be an overall reduction in the amount of bulk material required to meet an order in addition to a reduction in the amount of waste produced.

It follows from the above discussion that the term "bulk material" is not limited to a single body material, such as a single jumbo steel coil. The term is used throughout this specification to refer to the option of cutting a single body into multiple items to fulfil the customer demand and to refer to the option of cutting multiple bodies each into multiple items to fulfil the customer demand. In relation to the latter, the combination of cutting patterns, therefore, includes the possibility of using different patterns for different bodies to satisfy the customer demand. The step of determining all possible patterns, therefore, includes determining all of the possible cutting patterns for satisfying the customer demand when multiple bodies of bulk material are required.

The applicant anticipates that the method is not limited to cutting jumbo steel coils and that it can be applied to cut a range of bulk materials, including, but not limited to, paper, film, fabric, rubber and other materials in large coil form.

The step of determining all possible cutting patterns may comprise identifying an initial pattern that includes the smallest desired size and then identifying subsequent patterns by varying the number of one or more of the larger desired sizes in the cutting pattern.

The initial pattern may comprise the maximum number of the smallest desired size that fits the dimensions of the bulk material and the customer demand for that desired size.

The step of determining all possible cutting patterns may include incrementally varying the number of the larger desired sizes and, for each incremental change, cycling through the number of items with the smallest desired size.

The step of determining all possible cutting patterns may further comprise disregarding cutting patterns that are larger than the physical dimensions of the bulk material.

The step of determining all possible cutting patterns may further comprise disregarding patterns that result in the number of any one of the desired sizes exceeding the customer demand by a predetermined amount.

The customer demand may comprise consolidated demand from multiple separate customers.

The customer demand may include an allowance for a predetermined number of items of each desired size to contribute to stock inventory.

The bulk material specifications may include the composition, thickness and cuttable width.

In the circumstance that the bulk material comprises coiled steel, the capabilities of the cutting equipment may include the maximum number of simultaneous cuts, including edge trimming cuts, having regard to the bulk material specifications and the cutting width of the cutting equipment

The step of selecting a combination of cutting patterns may comprise the steps of (i) selecting a combination of cutting patterns that satisfies customer demand and determining the waste produced by that combination of cutting patterns and (ii) determining a revised combination of cutting patterns by replacing one or more cutting patterns in the combination of cutting patterns selected in step (i) with one or more alternative cutting patterns selected so that the revised combination produces less waste than is produced by the combination of cutting patterns selected in step (i).

The step of selecting a combination of cutting patterns may further comprise repeating step (ii) to determine a revised combination that produces less waste than other revised combinations determined by step (ii). The step of selecting a combination of cutting patterns may be carried out by subjecting the cutting patterns identified in step (b) to linear programming that is optimised to reduce waste.

The invention also provides a computer program adapted to control a computing device to implement the method described above.

The invention also provides a computer readable medium comprising a computer program as described above.

BRIEF DESCRIPTION OF THE DRAWINGS

Notwithstanding any other forms which may fall within the scope of the apparatus and method as set forth in the Summary, specific embodiments will now be described, by way of example only, with reference to the accompanying drawings in which:

Figure 1 is an oblique view of a slitting line.

Figure 2 is a schematic representation of the width of a jumbo roll and a juxtaposed arrangement of knives in a nesting pattern.

DESCRIPTION OF EMBODIMENT

The following description of an embodiment of the invention is in the context of slitting jumbo coils of steel strip. It will be appreciated, however, that the description is not intended to limit the scope of the invention which has application to other bulk materials in large rolls or coils. Fabric, film, paper and rubber are examples of such materials.

A slitting line 10, as shown in Figure 1, includes a jumbo coil of steel strip 12 mounted on a pay off mandrel 14 that is driven by an electric motor 16. A slitter 18 comprises a pair of juxtaposed, contra-rotating mandrels 22 which define a nip through which the strip 12 passes. Each mandrel 22 is fitted with a series of circular knives spaced across the width of each mandrel 22 at positions to shear the steel strip 12 into smaller strands 24 of desired widths. Each strand 24 passes through a tension stand 25 alongside other strands 24 and is wound onto on a drum 26 which is driven by an electric motor 28.

Customer demand for steel strip will typically be for a variety of strand 24 widths. Accordingly, the slitter 18 will need to be set up for eachjumbo coil according to the strand 24 widths required by the customer demand and the number of strands 24 of that width required by the customer demand. However, the set up for the slitter 18 depends upon a number of factors:

• The maximum number of cuts that the slitter 18 can make simultaneously;

• The thickness of the steel strip; and

• The composition of the steel strip.

These factors determine the resistance placed on the slitter 18 and which must be overcome by the electric motor 20 which drives the slitter 18. Accordingly, nesting patterns for the circular knives are dependent upon the bulk material properties (e.g. thickness and composition) and on the capabilities of the slitter.

Prior to slitting jumbo coils to fulfil a customer demand, a combination of nesting patterns must be determined. Specifically, the nesting patterns should be selected to meet the customer demand for the amount of requested steel strip in the requested strand 24 widths. An example of a customer order is outlined in Table 1.

Steel Strand width No. of strands quantity (kg) (mm) to fulfil order

62,425 227 44

10,250 205 8

4,425 170 4

15,000 150 16 7,000 140 8

2,530 135 3

10, 150 58 28

9,550 51 30

Table 1 - Customer order of steel strip cut to certain strand widths

Given that the jumbo coils have a set maximum width (once edge-trim is removed) the selection of nesting patterns is important because it will affect the amount of waste steel strip that remains after fulfilling the customer order. An example of a combination of nesting patterns that fulfills that customer order is shown in Table 2. This combination of nesting patterns is prepared according to conventional methodology. For ease of reference, this combination of nesting patterns will be referred to hereinafter as "the conventional solution".

The conventional methodology typically selects nesting patterns on the basis of grouping the same larger strand widths in a nesting pattern and then fitting narrow strand widths on the end of a group to reduce waste as much as possible. This is evident in the nesting patterns shown in Table 2. For example, nesting pattern number 1 includes 7 strands, four of which are each 227 millimetres in width, one strand of width 135 millimetres, one strand of width 58 millimetres and one strand of width 51 millimetres. Nesting pattern number 6 includes 8 strands, each being 150 millimetres in width. The same applies to nesting patterns numbers 2 and 3 which include three strands of 205 millimetres and five strands of 177 millimetres respectively and both groups are supplemented by a number of smaller strand widths. With the exception of nesting pattern number 6, which exactly fills the cuttable jumbo roll width, all other nesting patterns use smaller strand sizes to fill the jumbo roll width as far as possible. This reduces waste but may result in excess production, beyond customer demand.

The combination of nesting patterns shown in Table 2 satisfies the customer order by processing 25 jumbo coils through a slitter arranged with the combination of nesting patterns. Specifically, nesting pattern number 1 is used to slit 10 jumbo coils. Two jumbo coils are slit according to each of nesting patterns 5 and 6 and three jumbo coils a slit according to each of nesting patterns 2 and 4. Five jumbo coils are slit according to nesting pattern 3. As a result, the slitting line needs to be adjusted six times to change over the nesting patterns for slitting the 25 jumbo coils. In other words, the operator needs to shut-down operation of the slitting line six times to adjust the nesting patterns in order to meet the customer demand. Each time the slitting line is shut-down, there is a loss in production time.

The number of strands of each strand width produced by the conventional solution is indicated in Table 2, together with the customer ordered quantities. The ordered quantities match the produced quantities for strand widths of 227 and 51 millimetres. However, the conventional solution produces extra strands for strand widths of 205, 177, 150, 140, 135 and 58 millimetres. For example, the customer order required four strands of 177 millimetres wide steel strip, but the conventional solution produces thirty-seven strands of steel strip at 177 millimetres wide. The additional thirty-three strands will go into stock inventory. In total, 64 strands will go into stock inventory as a result of the conventional solution. Selecting the right combination of nesting patterns to reduce excess strands going into stock will benefit slitting operations.

Excess inventory is undesirable because the steel used to produce those strand widths is already being paid for by the entity running the slitting operation and it will remain in stock inventory until another customer requires a strand of steel in the same width, thickness and composition. Accordingly, there is a desire to reduce the amount of slit steel strips that go into stock inventory. While the stock inventory may ultimately be sold to a further customer, the waste produced by the combination of nesting patterns cannot be sold to a customer.

Table 2 - Conventional solution to fulfilling customer demand in Table 1

The value of this waste can be recouped to an extent by selling the waste steel strip to recyclers. However, waste steel strip is valued at approximately 10% of the original purchase price of the equivalent amount of steel in a jumbo role. Accordingly, there is a 90% value decrease in the waste produced by the combination of nesting patterns. For this reason, selecting the right combination of nesting patterns to reduce waste will benefit slitting operations. According to the conventional solution shown in Table 2, the overall waste amounts to 2.7% of the total steel in the 25 jumbo coils (excluding edge trim) required to fulfill the customer order according to the nesting pattern combination of the conventional solution.

The applicant prepared a solution to the same customer order, but based on an alternative method for determining the combination of nesting patterns. The applicant's solution is shown in Table 3.

The outcome of the applicant's solution is that the customer order is fulfilled in that the required number of strands of selected width are produced. Additionally, only eighteen additional strands are produced and will go into stock. This contrasts with the conventional solution which produces an additional 61 strands which go into stock inventory.

Furthermore, the applicant's solution produces the customer order of strands with five different nesting patterns. This is significant because it means that the operator shuts-down the slitting line one less time than compared with the convention solution. As a result, the slitting line will take less time to complete the customer demand and it will move to the next slitting job faster. The slitting line is, therefore, more productive.

Table 3 - Applicant solution to fulfilling customer demand in Table 1

Furthermore, the applicant's solution utilises 18 jumbo coils, i.e. 7 coils less than the conventional solution. This has a very significant impact on the overall cost for fulfilling the customer demand because a jumbo coil may cost US$7,500 for a 7,500kg coil of steel. In other words, the cost of bulk material input for the Applicant's solution 5 is US$52,500 less than the bulk material cost according to the conventional solution.

This is a direct cost saving to the customer in commissioned slitting or to the slitting mill in fulfilling the order.

The applicant's solution is arrived at through two steps. The first step is to l o determine all the possible nesting patterns that will produce strands that will contribute to fulfilling the customer order. The second step is to determine which combinations of the determined nesting patterns will fulfil the customer order and reduce waste.

The process of determining all the possible nesting patterns is systematic in that every possible nesting pattern is determined. The process is carried out by operation of a computer that follows a computer program that selects the nesting patterns and stores them. The computer program rejects nesting patterns that exceed the width of the jumbo coil and that produce an unreasonable result. An example of an unreasonable result includes nesting patterns that produce a number of strands for a given strand width that exceeds the customer demand for the number of strands of that strand width. In one form, nesting patterns may be rejected if they produce more than one strand in excess of the customer demand for that strand width. This limitation on unreasonable results enables the stock inventory addition to be controlled to an extent at the nesting pattern determination stage. Stock inventory addition is also controlled in the process of selecting combinations of nesting patterns to fulfil the customer demand.

An example of determining all possible nesting patterns is shown in Table 4. In this example, the customer order includes only three different strand widths and demand for 4 strands of 45 millimetres, 5 strands of 38 millimetres and 5 strands of 36 30 millimetres.

Enumeration of all possible strand widths for a customer order including strands of 45, 38 and 36mm

5 With regard to Table 4, enumeration of nesting patterns according to the first step is carried out by the program first generating a nesting pattern that includes as many of the smallest strands as are in the customer order, subject to the combined strand widths not exceeding the width of the jumbo coil. If the combined width is less than the jumbo coil width, additional strands of the next larger sizes may be added. That l o nesting pattern is stored and becomes one of the nesting patterns that may be selected to form one nesting pattern in the combination of nesting patterns that it ultimately selected in the applicant's solution. Storing this nesting pattern is, however, subject to the nesting pattern not exceeding the width of the jumbo coil.

15 The next nesting pattern is identified by incrementing the number of strands of the next largest strand width and choosing as many of the smallest size that still fits within the jumbo coil width and that do not exceed the customer order for that strand size, as may be required to fully utilise the jumbo coil width. The second nesting pattern will be stored along with the first nesting pattern and may ultimately be selected to form one nesting pattern in the combination of nesting patterns that forms the applicant's solution.

The program continues by incrementally varying the number of strands of each larger strand width in the customer order (e.g. 38mm and 45mm in Table 4) and, for each incremental change in one of the larger strand widths, cycles through each of the smaller strand widths. Each variation on the number of different strands of different widths is stored as a possible nesting pattern for the combination provided that the possible nesting pattern complies with the limitations on selecting nesting patterns.

Varying the number of strands includes selecting zero strands of a given strand width in the customer demand. In this way, all the viable nesting patterns that could be used to meet the customer order are identified. It can be seen by comparing the nesting patterns in the applicant's solution with the nesting patterns in the conventional solution that the applicant's solution has nesting patterns that include a considerably greater variety of strand widths in each nesting pattern. This variety causes each pattern to have less waste than convention nesting patterns that group the same strand widths.

Each of those nesting patterns will have a combined width of included strands that is equal to or less than the width of the coil. This means that each nesting pattern has an associated amount of waste (excluding edge trim). The second step in determining a solution involves determining which combinations of the identified nesting patterns will at least fulfil the customer order and will reduce waste.

This second step involves subjecting the identified and stored nesting patterns to linear programming that is configured to reduce waste. There are a number of methods for carrying out the linear programming. Given the number of nesting patterns, this second step is also carried out by computer. The linear programming involves selecting a first combination of nesting patterns from the stored nesting patterns based on the combination meeting the customer demand. The waste produced by that combination is determined and one alternative nesting pattern from the range of stored nesting patterns is substituted into the combination for one of the originally selected nesting patterns. The waste for the new combination is determined to be more or less than the waste of the original combination. If less, the substituted nesting pattern is retained and another nesting patter in the combination is substituted by an alternative that is selected to 5 produce less waste. The process of substituting nesting patterns continues until the waste produced by the combination is reduced to a point where further reductions are very small.

This method of selecting a combination of nesting patterns is one example of how linear programming can be used to arrive at a solution for slitting steel strip to meet the customer demand. It will be appreciated, however, that other forms of linear programming can be used to achieve the same effect of selecting a combination of nesting patters that at least meets the customer demand and that reduces waste. Those forms of linear programming are considered to fall within the scope of the second step, i.e. determining which combinations of the identified nesting patterns will at least fulfil the customer order and reduce waste.

It is possible that two or more combinations of nesting patterns may achieve the same objective, i.e. the same or a very similar level of waste. Which combination is o ultimately selected will depend on the extent to which the customer demand is to be met. In other words, the selection of a combination will depend on the number of additional strands that will be allowed to contribute to stock inventory.

In practice, orders from a number of individual customers may be consolidated 5 where the orders require amounts of steel strip of the same composition and thickness.

In this case, the consolidated orders make up the customer demand described above.

The applicant's solution shown in Table 3 produces some strands in excess of the customer demand. Those strands will go into stock inventory. However, when the o next customer order arrives for steel of the same thickness and composition and for strands widths held in the stock inventory, the number of strands held in the stock inventory is subtracted from the customer order to arrive at the customer demand. The process of determining a solution is then based on the customer demand which accounts for the customer order and the stock inventory.

The first step of identifying all possible nesting patterns is typically

implemented using software but alternatively may be implemented using hardware or a combination of software and hardware. The first step may be implemented using any suitable computer program written in any suitable programming language. The computer program is typically stored on a computer readable medium such a hard disk drive (HDD) or random access memory (RAM).

Additionally, the second step of selecting a combination of nesting patterns to at least meet customer demand and to reduce waste is typically implemented by using software. It may be implemented using any suitable computer program written in any suitable programming language. The computer program is typically stored on a computer readable medium such a hard disk drive (HDD) or random access memory (RAM).

Selecting a combination of nesting patterns to reduce waste is affected by the extent to which the accuracy of meeting the customer demand is required. By way of example, input to the selection of nesting patterns may require optimisation to meet the customer demand exactly, i.e. no additional strands going into stock inventory. In this case, waste will be higher, but the ultimate selection of nesting patterns can reduce the amount of waste and still meet customer demand exactly.

The above described embodiment of the invention is an example of 1- dimensional cutting where the pattern of cuts spans 1 dimension, in this example, the width of the jumbo coil. It should be appreciated that the method may be embodied in many other forms. In other forms, the invention may be used to reduce waste during 1- dimensional cutting of bulk materials, such as paper, film, fabric, rubber and other materials in large coil form.

In the claims which follow, and in the preceding description, except where the context requires otherwise due to express language or necessary implication, the word "comprise" and variations such as "comprises" or "comprising" are used in an inclusive sense, i.e. to specify the presence of the stated features but not to preclude the presence or addition of further features in various embodiments of the apparatus and method as disclosed herein.

It is to be understood that, references to "conventional" or "conventional solution" reference do not constitute an admission that the reference forms a part of the common general knowledge in the art, in Australia or any other country.

Claims

1. A method of determining a combination of patterns for cutting bulk material into items of a range of desired sizes according to customer demand, the method comprising: obtaining bulk material specifications;

(b) determining all possible cutting patterns based on the range of desired sizes, the customer demand, the bulk material specifications and based on capabilities of equipment for cutting the bulk materials; and

(c) prior to the commencement of cutting, selecting a combination of cutting patterns from all possible cutting patterns determined according to step (b) that reduces waste of the bulk material and that satisfies customer demand.

2. The method defined in claim 1, wherein the step of determining all possible cutting patterns comprises identifying an initial pattern that includes the smallest desired size and then identifying subsequent patterns by varying the number of one or more of the desired sizes in the cutting pattern.

3. The method defined in claim 2, wherein identifying the subsequent patterns includes incrementally varying the number of the larger desired sizes and, for each incremental change, cycling through the number of items with the smallest desired size.

4. The method defined in claim 3, wherein the initial pattern comprises the maximum number of items with the desired size that fits within the dimensions of the bulk material and does not exceed customer demand for the number of items of that smallest desired size.

5. The method defined in any one of the preceding claims, wherein the step of determining all possible cutting patterns further comprises disregarding cutting patterns that are larger than the physical dimensions of the bulk material.

6. The method defined in any one of the preceding claims, wherein the step of determining all possible cutting patterns further comprises disregarding patterns that result in the number of any one of the desired sizes exceeding the customer demand by a predetermined amount.

7. The method defined in any one of the preceding claims, wherein the customer demand comprises consolidated orders from multiple separate customers.

8. The method defined in any one of the preceding claims, wherein the customer demand includes an allowance for a predetermined number of items of each desired size to contribute to stock inventory.

9. The method defined in any one of the preceding claims, wherein the bulk material specifications include the composition, thickness and cuttable width.

10. The method defined in any one of the preceding claims, wherein the bulk material comprises coiled steel and the capabilities of the cutting equipment include the maximum number of simultaneous cuts, including edge trimming cuts, having regard to the bulk material specifications and the cutting width of the cutting equipment

11. The method defined in any one of the preceding claims, wherein the step of selecting a combination of cutting patterns comprises the steps of (i) selecting a combination of cutting patterns that satisfies customer demand and determining the waste produced by that combination of cutting patterns and (ii) determining a revised combination of cutting patterns by replacing one or more cutting patterns in the combination of cutting patterns selected in step (i) with one or more alternative cutting patterns selected so that the revised combination produces less waste than is produced by the combination of cutting patterns selected in step (i).

12. The method defined in claim 11, wherein the step of selecting a combination of cutting patterns further comprises repeating step (ii) to determine a revised combination that produces less waste than other revised combinations determined by step (ii) until no further combination with reduced waste exists.

13. The method defined in any one of claims 1 to 12, wherein the step of selecting a 5 combination of cutting patterns is carried out by subjecting the cutting patterns

identified in step (b) to linear programming that is optimised to reduce waste.

14. A computer program adapted to control a computing device to implement the method of any one of claims 1 to 13.

o

15. A computer readable medium comprising a computer program as claimed in claim 14.