WO2001090969A1 - Method for preparing a cutting plan for semi-finished products to obtain batches assigned to orders of an order book - Google Patents

Abstract

The invention concerns a method for producing a cutting plan for semi-finished products defining how to cut off from a stock of semi-finished products one or several batches of products designed to fulfil one or several orders recorded in an order book which consists in: determining an operable cutting plan consisting of batches of semi-finished products each associated with an order. The method is characterised in that it consists, for each batch, in defining an assignment risk; assessing whether the assignment risk is acceptable or not; producing an operational cutting plan consisting only of batches whereof the assignment risk is acceptable.

Description

 PROCESS FOR DEVELOPING A CUTTING PLAN OF SEMI-FINISHED PRODUCTS TO OBTAIN LOTS ASSIGNED TO ORDERS FROM AN ORDER BOOK

The present invention relates to a method for developing a cutting plan for semi-finished products, the cutting plan defining how to take by cutting from a stock of semi-finished products one or more batches of products intended to satisfy one or more orders recorded in an order book.

Various industries, for example the paper industry, the wood industry, the glass industry, the textile industry or the steel industry, produce semi-finished products in sheet or strip form which must be cut by shearing and slitting to obtain products corresponding to customer requests. To define or even optimize these cuts, methods are used which can be computerized and which can implement algorithms for optimizing two-dimensional cutting planes. In general, these methods determine how to cut from a stock of semi-finished products batches of products having a determined format corresponding to an order, while respecting rules of geometric feasibility taking into account the possibilities of the available cutting tools and minimizing the manufacturing cost, in particular taking into account the falls generated. For various reasons, semi-finished products may have surface defects that are unacceptable to customers and which must be eliminated. For this, the cutting plan optimization methods use a mapping of the defects present on the semi-finished products and determine cutting plans which eliminate the zones carrying defects, on the edge or at the end of the semi-finished products.

Very often, the stock of semi-finished products is made up of semi-finished products of various kinds, only some of which, sometimes called "capable products", are likely to satisfy a particular order. In general, there are several possibilities for choosing a particular semi-finished product from the available capable products. In this case, the methods for developing cutting plans use substitution rules which define the possible choices, and choice strategies which define an order of priority for the choice of capable products. In all cases, the known methods define cutting planes which make it possible to satisfy all the conditions of the orders.

However, in certain industries such as the steel industry producing stainless steel strips, the allocation of semi-finished products to orders is done, in general with more flexibility. Indeed, in these industries which produce a wide variety of products to meet a wide variety of uses, certain semi-finished products are more or less equivalent for certain uses while they are less or not for 'other. In order to manage stocks effectively and respond as best as possible to customers' wishes, a semi-finished product can be assigned to a particular order which, without being exactly what was requested, nevertheless meets the customer's main requirements. This practice can generate a risk linked for example to the nature of the product or to the quality of its surface finish having regard to the intended use and the particular requirements of the customer concerned. We are thus led to consider that an assignment of a semi-finished product to a particular order is more or less acceptable depending on whether or not it leads to taking a risk and depending on whether this risk is greater or less. The known methods for defining cutting plans using optimization algorithms do not allow this notion of risk to be taken into account and, therefore, do not allow cutting plans for industries such as the steel industry, or any industry facing the same problem.

The aim of the present invention is to propose a method for optimizing a cutting plan for semi-finished products to satisfy orders, taking into account a risk associated with the choice of allocation of the semi-finished products to the orders. This process can be implemented using a computer.

To this end, the subject of the invention is a method for developing a cutting plan for semi-finished products defining how to take by cutting from a stock of semi-finished products one or more batches of products intended to satisfy one or more recorded orders in an order book according to which a feasible cutting plan is determined consisting of batches of semi-finished products each associated with an order, for each batch of semi-finished products assigned to an order, an assignment risk is defined, assesses whether the risk is acceptable or not and an operational cutting plan is drawn up consisting only of lots for which the risk of allocation is acceptable. To define the assignment risk, we can use risk assessment rules, and to determine whether the risk is acceptable or not, we can use risk acceptance rules.

In a particular embodiment, each semi-finished product corresponds to an article in a catalog of products, has a determined format and includes defects listed in a map of defects classified as "absolute defects" and "other defects". Each order corresponds to an article from the said catalog of products, has a requested format, a desired level of quality and a deadline. The cutting of semi-finished products is done using cutting tools whose physical characteristics impose rules of feasibility of cutting. An article in the product catalog may be replaced by another article in the catalog provided that the rules for substituting articles between them are observed. The choice of a semi-finished product to satisfy an order can be made from a set of semi-finished products by respecting the rules of association of semi-finished products and orders and by respecting an allocation strategy which defines priority rules for choosing semi-finished products from the stock of semi-finished products. A cutting plan has a cost that can be evaluated using cost calculation rules.

Assigning a semi-finished product to an order can lead to a risk assessed using risk assessment rules, the more or less acceptable nature of this risk being able to be assessed using risk acceptance. According to this process:

- from the stock of semi-finished products and the order book, and using the rules for substitution of items between them, we develop the rules for combining semi-finished products and orders, - from the stock of semi-finished products and order book, using the rules for combining semi-finished products and orders, the defect maps for each of the semi-finished products, the rules for calculating cost, the rules for feasibility of cutting and respecting the allocation strategy, a workable cutting plan is drawn up indicating how to take from semi-finished products the stock of semi-finished products, lots not containing

"Absolute defects" and each assigned to an order, each lot assigned to an order corresponding to a catalog item and having a format compatible with the catalog item and the format requested for the order in accordance with the rules of association of semi products - finished orders, - by using risk assessment rules, for each of the batches of products in the feasible cutting plan, the risk of allocation associated with the allocation of any part of a batch of products to the corresponding order is determined, - from this assessment of the allocation risk, using the risk acceptance rules, it is decided whether the said batch of the feasible cutting plan is acceptable or not,

- and an operational cutting plan is drawn up consisting only of acceptable batches. Preferably, to develop the feasible cutting plan, the cost is minimized.

In a preferred embodiment, the rules for substituting the items of the catalog with one another are a graph which, for any pair consisting of a first item of the catalog and a second item of the catalog, defines a risk of substitution associated with the replacement of said item first article of the catalog by said second article of the catalog. The graph of the possible substitutions of the articles of the catalog between them can, moreover, define for any couple made up of a first article of the catalog and a second article of the catalog, a difference of cost of substitution associated with the replacement of said first article of catalog by said second catalog item, this cost difference being taken into account by the cost calculation rules. The graph of the possible associations of the catalog items between them can be neither symmetrical nor transitive.

The rules for associating semi-finished products and orders are, for example, a graph of possible associations which, for each pair consisting of a semi-finished product from the semi-finished product stock and an order from the order book of order whose formats are compatible, associates a risk of association equal to the risk of substitution defined by the rules substitution of the articles of the catalog between them for the couple constituted by the article of the catalog corresponding to the said order and the article of the catalog corresponding to said semi-finished product.

Preferably, to develop the association rules for semi-finished products and orders, we set an association risk threshold and we only use in the graph of possible associations the semi-finished product / order pairs whose risk association is below said threshold. The risk assessment rules may take into account “other faults”. In this case, to assess the risk for a batch of products from the feasible cutting plan, one can, for example, proceed as follows:

- using the defect map and the rules for taking faults into account, the "other faults" present on said batch of products are determined and their degree of severity is assessed so as to establish an intrinsic quality grid for the batch of products,

- using the risk assessment rules, the intrinsic quality grid of the batch is compared to the desired quality level for the order so as to obtain a quality difference between the batch of products and the order,

- And a level of risk is determined based on the quality gap between the batch of products and the order.

To assess the degree of severity of the defects, one can, for example, classify the defects by families, and for each family, evaluate a degree of severity as a function of the density of the defects of the family.

The risk assessment rules may also take into account the risk of assigning semi-finished products to orders.

To decide whether a lot of the feasible cutting plan is acceptable or not, we can use an expert system which, by applying the risk acceptance rules, determines according to the order, the semi-finished product assigned to it and the corresponding risk, if the risk is "automatically accepted", "acceptable only after validation by an operator" or "unacceptable in all cases". If the risk is "automatically acceptable", it is decided that the lot is acceptable. If the risk is "acceptable only after validation by an operator", the question is submitted to an operator by providing him with information enabling him to make his decision, and the operator decides whether the batch is acceptable or not. If the risk is "unacceptable in all cases", it is decided that the lot is unacceptable.

According to this process, the absolute faults can be real or virtual. The allocation strategy can be chosen from several possible strategies, at least one of these strategies taking into account the deadlines to be met for orders.

Preferably, the method is implemented partially or completely using computer programs.

The invention also relates to a computer-readable medium on which a program for implementing the method is recorded. The invention will now be described in more detail, but without limitation.

The process for developing an operational cutting plan for semi-finished products such as strips from an order book on the one hand and from a stock of available semi-finished products on the other, taking into account the quality requirements associated with each order, the defects present in the semi-finished products and the possibilities of the tools that can be used, comprise three main stages:

- elaboration of the graph of the possible associations of semi-finished products available for orders, so as to determine for each order which semi-finished products are likely to be used to satisfy it, and under what conditions;

- development of a “feasible” cutting plan, taking into account the graph of possible associations, the capacities of the tools likely to be used, the mapping of major product defects, and costs, so as to determine how to cut semi-finished products available to meet orders at the best cost, possibly taking into account a substitution risk associated with the substitution of an article requested by another a priori acceptable; - validation of the “feasible” cutting plan, taking into account the quality conditions associated with each order, defects in semi-finished products and risks relating to the level of quality that can be accepted for each order, so as to produce a "operational" cutting. The last stage comprising three intermediate stages: - risk assessment,

- assessment of whether the risk is acceptable or not,

- constitution of the operational cutting plan.

By feasible cutting plan is meant a cutting plan which satisfies all the conditions imposed except those relating to the quality requirements of the orders which are not a priori prohibitive. This means that if the orders were delivered to customers by applying this cutting plan, there could possibly be risks of rejection of the products delivered by the customers.

By operational cutting plan, we mean a cutting plan that will actually be carried out in order to deliver orders to customers. In such a plan, the order quality requirements are taken into account so that the risk of not fully satisfying these requirements is taken in a measured and conscious manner.

The concept of risk is a complex concept which involves several sources of risk; it will be explained later.

This process will be explained more fully by taking the example of a workshop manufacturing stainless steel strips obtained by cold rolling as well as by various metallurgical operations such as pickling, bright annealing or any other operation intended to give the bands of the properties of use such as mechanical characteristics or characteristics of surface appearance. These strips, of rectangular shape, the thickness of which can be between a few tenths of a millimeter and a few millimeters, the width of which can exceed 1.5 meters and the length of which can reach several kilometers, are stored in the form of reels. The coils are cut by slitting (cutting lengthwise) and by shearing (cutting lengthwise) in order to obtain products having a determined width and length and corresponding to an order. These products, generally rectangular in shape, are either in the form of coils or in the form of sheets depending on the ratio of their length to their width. The products sold can also be discs or more generally blanks of any shape cut from reels or sheets which then constitute intermediate orders.

More specifically, the workshop has: - a "product catalog" made up of "articles", each corresponding to a class of products that can be produced,

- a "stock of semi-finished products" made up of all the available bands, generally in the form of reels, each band possibly having more or less acceptable defects, - an "order book" made up of the 'all of the "orders" it has received and which have not yet been fulfilled,

- a set of tools with specific possibilities.

Each item in the product catalog is characterized by: - a steel grade, corresponding to a standard targeted chemical analysis (or "commercial grade") as it appears in the catalogs offered to customers, these grades can be grouped by families corresponding to different grades but having metallurgical properties similar; - a state of the product, corresponding to a class of intended use properties, for example, high-end bright annealing or bright annealing for polishing,

- additional characteristics such as;

- format: target thickness, standard supply width,

- the standard or generic manufacturing range, determined from metallurgical rules and broken down into the manufacturing cycle according to the particularities of the factory in which it will be carried out.

Each order, which corresponds to one or more identical products ordered by a customer, is characterized by: - an article from the product catalog,

- additional characteristics such as:

- the format requested (width, length), possibly with ranges of length (for example between 1000 and 2000 m long) and width,

- the requested thickness and thickness tolerances, - the weight or number of products (especially in the case of sheets),

- surface condition, packaging, etc,

- quality requirements defined in particular by a quality level relating to defects and a tolerance on the quality level,

- a deadline, - the intended use of the product,

- the name of the client.

The customer can also be characterized by a sensitivity to quality problems depending, in particular, on the use he makes of the product.

Each semi-finished product available in the stock is characterized by:

- an article from the product catalog,

- additional characteristics such as:

- the actual format (width, length),

- the actual thickness, - a fault map giving the distribution and the nature of the faults on each side of the product; faults are divided into two categories: major faults or "absolute faults" which cannot in any case be accepted on a product, and other faults which can be accepted in certain cases, depending on the quality requirements of the order to which the product is affected.

Each tool is characterized in particular by its nature (for example, splitter or shears) and by these capacities such as: possible formats at the input, possible formats at the output, acceptable thickness, etc.

From this data, the method first determines a feasible cutting plan and then an operational cutting plan, taking into account a certain number of rules which are in particular: - rules for substituting catalog items between them; these rules make it possible to determine to what extent, with what risk of not satisfying the quality conditions, and with what cost difference, an article from the catalog can be replaced by another article from the catalog; these rules are used to construct rules for associating semi-finished products with orders which make it possible to determine which products can be assigned to which orders or which orders can be carried out by which products, with, possibly, what risk and what difference in cost ;

- metallurgical rules for taking into account any defects so as to determine the quality level of any portion of a semi-finished product to compare it to the quality requirements of an order;

- cutting feasibility rules taking into account the tools available;

- cost calculation rules making it possible to compare two possible cutting plans for the same set of orders and products in stock.

- Rules for assessing the risk associated with allocating a portion of a particular semi-finished product to a particular order;

- risk acceptance rules making it possible to determine whether a risk is acceptable or not;

- one or more allocation strategies defining priority rules for the choice of a semi-finished product from stock to assign it to an order, or for the choice of an order for which we will look in the stock of semi-finished products for a semi-finished product that can be assigned to it. More specifically: 1) - The substitution rules consist of a graph of possible substitutions for catalog items which, for each pair of catalog items, consisting of a first item and a second item, determines in which measure and with what cost gap the first item can be replaced by the second item. This possibility and the cost difference are determined by taking into account in particular the steel grade and the condition of the product. The extent to which the first item can be replaced by the second is either of the "yes", "may be" or "no" type, or a numeric indicator between 0 and 1 representing the probability with which the replacement can be made without incidents, or, what amounts to the same thing, the risk associated with replacement. The risk varying as the inverse of the probability of being able to make the replacement without incidents. In this case, 0 corresponds to “no”, zero probability of not having incidents and therefore infinite risk; 1 corresponds to "yes", the risk is zero and replacement can be done in all cases; the values between 0 and 1 correspond to “can be”, that is to say in the intermediate cases. Obviously, when the two articles are identical replacement is always possible with zero risk.

The cost difference corresponds to the cost difference between the first article and the second article. This difference can be both positive and negative. It is obviously void when the two articles are identical.

This graph is neither symmetrical nor transitive, which means that: - if a first article can be replaced by a second article with a certain risk and a certain cost difference, in general the second article cannot be replaced by the first article, and in any case, not with the same risk or with the same cost difference; - if a first article can be replaced by a second article and the second article by a third, in general the first article cannot be replaced by the third, and in any case, the risk and the cost difference associated with the replacement of the first article by the third cannot always be calculated from the risks and cost differences associated with the replacement of the first article by the second and the second by the third. 2) - The association rules consist of a graph of the possible associations of semi-finished products with orders which, for all pairs made up of a semi-finished product in stock and an order from the compatible order book between them, defines to what extent and with what cost difference, the semi-finished product can be assigned to the order.

A semi-finished product and an order are compatible if the following conditions are met simultaneously:

- the article of the catalog corresponding to the semi-finished product can be substituted for the article of the catalog corresponding to the order, in accordance with the rules of substitution of the articles between them (“yes” or “can be”),

- the format and thickness of the semi-finished product make it possible to satisfy the format and thickness requirements requested for the order,

- possibly if additional characteristics of the semi-finished product are compatible with desired characteristics (for example, surface finish, skin-past, etc.).

The extent to which a semi-finished product can be associated with an order and the cost difference are those which are defined by the rules of substitution of the products between them. In particular, the extent to which a semi-finished product can be assigned to an order defines or makes it possible to define a risk of substitution.

3) - Defects, which may be present on a strip, correspond to various manufacturing incidents such as scratches, straws, appearance defects etc. The identification of faults is done by reference to a typology comprising families broken down into classes, themselves broken down into sub-classes. This typology makes it possible to identify the nature of the defects, their origin and their gravity and their density. The gravity represents the importance of each defect, for example in the case of a scratch, the depth of the scratch or any equivalent characteristic. The density represents the number of defects per 100m of tape, for example. During the tape quality control operation, all the faults present are identified, their position and extent are identified and their severity is assessed. In particular, absolute faults and other faults are identified.

The position of each defect is defined by the face on which it is located as well as by its coordinates (distance to a reference bank and distance by relative to a reference end of the strip). Its extent is defined by the dimensions of the smallest rectangular area that contains it, it being understood that several small point defects may have been grouped together beforehand to form a single larger defect. Its severity is evaluated by a gravity coefficient which makes it possible to determine to what extent the presence of the defect can be accepted.

The face on which the defect is found is of particular importance. Indeed, the two faces of the same strip are not always identical and the desired properties are not always the same, for example one face can be polished and the other not. The importance of these differences may result from the intended use. It is therefore necessary to take this into account to assign a semi-finished product to an order.

All the information relating to the nature of the faults present on a strip, relating to their position, their extent and their seriousness, constitutes the map of the faults of the strip.

From the defect map of a strip, it is possible to draw up the defect map of any rectangular portion of the strip, called the strip area. We can then, for any area, develop an intrinsic quality grid for the area. This intrinsic quality grid consists of a table giving for each defect family a severity index determined from the faults present in the area, their density and their severity.

In addition to the real faults which have just been described, it is also possible to take into account virtual faults which can be used to identify particular zones of the bands. These particular zones may be zones comprising irregularities (for example, of thickness or width) which are not strictly speaking defects, but which must nevertheless be taken into account. They can also be areas that we want to reserve for later use (allocation in sheets, discs or narrow spools) or that we want to identify because we want to be able to perform on them an additional operation (for example, re-rolling ) or that we want to eliminate for a particular reason, this may be the case, for example, of narrow strips along the edges of the strip or of areas which contain too many "small" defects. 4 - The metallurgical rules make it possible to determine from the intrinsic quality grid of a particular area if this area can be used for a particular use (assignment to a particular order having a certain quality requirement) and with what possible risks. These rules consist in particular in defining how to compare the intrinsic quality grid of an area with the quality grid corresponding to the intended use for the area, possibly taking into account a quality tolerance grid representing for example the sensitivity of the client concerned, so as to determine the risk possibly associated with the use of the area for the intended use. These rules can take into account not only the quality grid and the intended use for the product ordered, but also other characteristics such as the catalog item corresponding to the order. These characteristics can be used in particular to determine the quality tolerance grid.

5) - The rules of feasibility of the cuts take into account geometric and operational constraints resulting in particular from the possibilities of the tools. They make it possible to identify the impossible configurations such as too little shearing of the edges, a slitting leading to too narrow strips or a laying of coating impossible to achieve. These rules make it possible not only to define the geometry of the cuts, that is to say the format of the products obtained and the position of these products in the strip, but also the manufacturing range allowing the cutting to be carried out, that is to say the succession of operations and the tools used to carry them out. In general, these rules are common to all cutting workshops equipped with shears and slitters, and they are well known to those skilled in the art. But, in their details, they depend on the tools specific to the workshop concerned.

6) - The rules for calculating the cost of a cutting plan are defined from the accounting rules of the workshop, and can take into account in particular:

- the cost of cutting operations, which may incorporate unit costs for each of the operations, fixed costs, and, more generally, all the costs involved in producing a cutting plan and which can be identified by cost accounting . - the cost of disposing of unusable scrap metal,

- the cost of stocks,

- the cost of delays in the delivery of orders,

- the cost difference associated with the substitution of an item in the catalog by another item in the catalog,

- costs associated with the risk of substitution and the risk resulting from defaults; these costs being evaluated, for example, by reference to the average cost of customer incidents, taking into account the importance of the risk, ie the probability that it will lead to an customer incident.

7) - The risk assessment rules make it possible to determine for each zone of a semi-finished product on an order, the corresponding allocation risk.

As indicated above, the concept of risk is complex and involves several sources of risk: on the one hand, a risk linked to the substitution of an article in the catalog by another article in the catalog (“risk of substitution” ) which, at the stage of associating a semi-finished product with an order, leads to the “risk of association”, on the other hand a risk linked to the level of quality of the products (“metallurgical risk”), the latter risk being itself broken down into a “risk linked to the quality grid” and a “specific expertise risk”. The overall risk is called “allocation risk”.

To the extent that we can quantify each of the elementary risks, we can quantify the overall risk called “allocation risk”. For example, if each of the elementary risks is evaluated by a risk rate TRj between 0 and 1 and representing the probability that the delivered products will be rejected by the customer, the overall risk TR _G is equal to: TR _G = 1 - _forall π i (1 - TRj). If elementary risks are assessed qualitatively, for example by "low or zero", "medium" or "high", the overall risk rate is the highest of the elementary risk rates. Note that, depending on the particular context of the application, to assess the risk of allocation, one can only take into account the risk of association or only the metallurgical risk.

The substitution risk assessment rules are defined later in the section relating to the development of rules for associating semi-finished products with orders. Taking into account the metallurgical risk may concern either the risk linked to the quality grid, either the risk of specific expertise, or the two types of metallurgical risk.

The rules for assessing the metallurgical risk component linked to the quality grid take account of faults. These rules may consist in comparing the quality grid of the area concerned with the desired quality grid, taking into account the tolerance grid defined by the metallurgical rules, so as to determine for each defect family a quality index depending on the gravity or density, and then assess the risk from this gap.

The risk assessment corresponding to each family of defects can be done, for example, by comparing the difference in severity or density with one or more thresholds defined in advance and deducing a level of risk for the family concerned. , of the type: "zero" if the difference is small, "average" if the difference is between a lower threshold and an upper threshold, "large" if the difference is greater than the upper threshold.

When there are several families of faults, the rules make it possible to define an overall risk which is for example the greatest of the risks evaluated for each family.

The rules for evaluating the metallurgical risk component linked to a specific appraisal are made up of an expert system involving either permanent rules or introduced as necessary, for example of the type "if the order is intended for the use X, and if the article corresponding to the semi-finished product chosen differs from the article specified by the customer by the characteristic Y, and if the semi-finished product must undergo the additional operation Z, then the corresponding risk is W ". These rules can also take into account faults. 8) - The risk acceptance rules is an expert system which makes it possible to determine whether the risk associated with the allocation of a particular lot to an order is "automatically acceptable", "acceptable only after validation by a expert (or operator) "or" unacceptable in all cases ". They can take into account both the substitution risk and the risk linked to faults (or metallurgical risk).

These rules are on the one hand permanent rules linked to the general characteristics of the orders, and on the other hand circumstantial rules taking into account particular situations linked for example to relations with a customer individual, for example we know that the quality requirements are very strict. These latter rules can evolve relatively quickly over time.

When these rules determine that a risk is "acceptable only after validation by an expert (or operator)", they also state the reasons for which the opinion of an expert is sought.

9) - The allocation strategies make it possible to take into account the management requirements of the workshop when, and this is the most general case, there is not a perfect match between the stock of semi-finished products available and the order book. These allocation strategies make it possible to define criteria to be satisfied as a priority for the choice of semi-finished products and orders that will be taken into account to build the cutting plan. These strategies are for example:

- a strategy favoring respect for deadlines: the choice of orders to be satisfied is made by prioritizing the most late orders if there are, or if not, the most urgent orders;

- a strategy favoring inventory management: priority is given to orders that will allow the use of a particular part of the stock whose volume is to be reduced.

- A strategy favoring the use of a particular cutting tool to saturate it, or on the contrary, avoiding the use of a particular tool which is not temporarily available.

- A strategy which takes into account quality criteria, for example we associate in priority to the most demanding orders from the metallurgical point of view the semi-finished products of better quality, and we try as much as possible to affect the semi-finished products having the lowest quality by looking for the least demanding orders.

These strategies can also take into account conditions for the priority allocation of certain semi-finished product areas to certain orders, as will be explained below.

We will now describe the implementation of the process, certain details of which will be explained below.

This implementation is done as follows: - from the stock of available tapes and the order book, taking into account the rules for substituting catalog items, we establish the graph of the possible associations of tapes in stock with orders, taking into account the compatibility of the formats of the tapes and formats requested for orders.

- We choose an allocation strategy.

- From the absolute defect map for each band, including real faults and virtual faults, we determine for each band which zones are unusable or for which certain assignments are excluded a priori, or for which certain preferential assignments must be chosen a priori, and, by difference, the map of areas usable without preferential allocations or a priori exclusions.

- From the stock of available tapes and the order book, taking into account the graph of possible associations, the map of usable areas, the rules of feasibility of cuts and the allocation strategy that has been chosen, we develop one or more possible cutting planes.

- Using the cost calculation rules, we calculate the cost of the different possible cutting plans and identify the cheapest cutting plan which then constitutes the feasible cutting plan. At this stage, we take into account the costs associated with the risk of substitution to calculate the costs of different cutting plans, but we do not take into account the costs associated with "other defects" present on semi-finished products. On the other hand, the cost calculation method can take into account the allocation strategy, for example by valuing the non-respect of deadlines. When the stock of available tapes is sufficient to satisfy a priori all of the orders in the order book, the feasible cutting plan associates with each order in the order book one or more zones of one or more reels as well as the range of manufacturing to obtain the products specified in the orders. However, in general, the stock is not perfectly suited to the order book; in this case, the cutting plan only concerns part of the orders in the order book.

- Using metallurgical rules and risk assessment rules, the risk resulting from the presence of possible faults associated with each corresponding part of the achievable cutting plan is assessed for each order taken into account in the workable cutting plan.

- Using the risk acceptance rules, it is determined whether the risk associated with the defects and possibly the substitution risk are or are not acceptable.

To do this, we compare each risk or a combination of risks to a threshold set in advance. This threshold is for example defined in a risk scale ranging from 0 to 100 and can either be a point value or correspond to an intermediate range. In the latter case, two values S _m i _n and S _{max are} defined (Smin <Smax), when the risk is less than S _m i _n , the risk is less than the threshold, when the risk is between S _m in and Sm _ax , the risk is equal to the threshold, when the risk is greater than Sm _ax , the risk is greater than the threshold. If the risk is below the threshold, the corresponding part of the feasible cutting plan is confirmed. If the risk is greater than the threshold, the assignment of the command to the zone is prohibited and the corresponding part is removed from the feasible cutting plane. If the risk is equal to the threshold, the corresponding part of the feasible cutting plan is submitted to an expert so that he can assess whether this part of the feasible cutting plan is acceptable or not. If the expert's opinion is positive, the corresponding part of the feasible cutting plan is confirmed, if not it is invalidated and the corresponding part is removed from the feasible cutting plan. All the parts of the feasible cutting plane remaining after this operation constitutes the operational cutting plane.

- In addition, the operational cutting plan can be optimized in order to minimize the cost associated with the defects, without however calling into question the cutting plan.

For this, it is possible to make permutations between certain lots. For example, if a short length batch at the start of the strip and a long length batch at the end of the strip has been provided for, these two batches can be swapped if this results in reducing the cost associated with the defects. We can also proceed in the same way with two batches of different width provided side by side, one on the right side, the other on the left side of the same strip. The only limit to these permutations which do not change the nature of the semi-finished product associated with an order, is that the cutting plan remains feasible. This gives an optimized operational cutting plan.

- Once the operational cutting plan has been drawn up, the stock of available tapes and the order book are provisionally updated. Then, we carry out the operational cutting plan so as to manufacture the products corresponding to the orders taken into account by the operational cutting plan and we confirm the update of the stock of available tapes (or available semi-finished products) and the book control. When an optimized operational cutting plan has been drawn up, this optimized operational cutting plan is executed.

We will now explain certain steps of the method, corresponding to a particular embodiment, given by way of example.

1) Development of the rules for possible association of products with orders. This is done using the substitution rules for articles in the product catalog, taking into account the compatibility of the formats requested for orders and the formats of products in stock.

The rules for the substitution of articles consists of a graph of substitution of articles which depends only on the catalog of products and which, generally, is updated only when the catalog of products is modified. This graph, which can be represented in the form of two square tables having as many rows and columns as there are articles in the catalog, consists of all the links L (aι, a _j ) = {F (aι, a _j ), G (aj, a _j )} indicating whether it is possible to replace the article a _\ by the article a _j , and with what additional cost. F (aι, aj) which corresponds to the value entered in the box of a table at the intersection of the row of row i and the column of row j, is an index which represents the possibility of replacing item a _\ by article aj; it is of the "yes", "may be" or "no" type, or more generally it has a numerical value between 0 and 1; 0 corresponding to "no", 1 corresponding to "yes", and the intermediate values to "may be". G (aj, a _j ), which corresponds to the entered value in the box of the second table at the intersection of the row of rank i and the column of rank j, is a quantified indicator of the cost difference associated with the replacement of a-, by aj.

Each link L (aι, aj) is developed as follows:

- Generally, an article of the catalog is characterized by n characteristics Ki, K _2> ... K _n and each article a-, is defined by a set of n values: {Kι (aj), K ₂ ( aι) K _n (aι)}; for any index k between 1 and n, K _k (aι) is the value of the characteristic K _k for the article a-, (in general this value is not a numerical value, but for example the name of the steel grade, the name of the type of surface finish, etc.).

- To each characteristic K _k we associate a filter F which is a function F _k (aj.aj) allowing to evaluate the possibility of replacing an article a whose characteristic K _k has the value K _k (aι), by an article a _j whose characteristic K has the value K _k (a _j ); this evaluation being made without taking into account the other characteristics. This function takes a value between 0 and 1 (0 <F _k (aj, a _j ) <1) which indicates whether, as far as the characteristic K _{k is concerned} , the article a _\ can be replaced by l item a _j , and also makes it possible to calculate an associated risk R _k (aj, a _j )> 0. - If F _k (aj, a _j ) = 1, replacement is possible with zero risk, this is the case in particular when K _k (aι) = K _k (a _j ). If F _k (ai, a _j ) = 0, replacement is not possible and the risk is very large (even infinite). For intermediate values, replacement is possible but with a non-zero risk, which means that replacement will not always be possible or desirable. From the values F _k (aj, a _j ), the global indicator F (aι, a _j ) of the possibility of replacing the article a _\ by the article a _{j is determined} , as well as the associated global risk R (aι , a _j ). F (aj, a _j ) is a function of all F (aj, aj) whose values are such that:

- F (aj, a _j ) = 1 if all the F _k (aj, aj) are equal to 1,

- F (aι, aj)> 0 and <min _p0U r all {F _k (ai, aj)}, and for example equal to min _for all k {F _k (aι, a _j )}, in other cases, which means that only one value is sufficient

F _k (ai, a _j ) is zero so that F (aj, a _j ) is zero.

R (ai, a _j ) is a function of all R _k (aι, aj) whose values are such that:

- R (aι, a _j ) = 0 if all the R _k (aj, a _j ) are equal to 0, - R (aj, aj)> Max _p0U r all k {R _k (ai, aj)} in the other cases, and for example equal to Max for all k {Rk (aι, aj)}.

Note that the value of F _k (aj, aj) can, for example, represent the probability that the substitution of a-, by a _j , having regard to the characteristic K _k , is done without problems, (F _k ( aj, aj) = 0 if substitution is impossible, i.e. zero probability of success; F _k (aι, aj) = 1 if substitution can be considered without risk). In this case, and if all the characteristics are independent, the global indicators

F (aι, aj) and R (aι, aj) can be calculated as follows: - the overall probability that the substitution of a _\ by a _j is done without problems is equal to F (aι, aj) = π _for all k F _k (ai, aj),

- the associated risks can be assessed by the following formula:

Rk (aι, aj) = 1 / (F _k (aι, aj) + α) - 1 / (1 + α) which means that, when substitution can be envisaged without problems, the risk is zero; when substitution is impossible, the risk is very great (α is an arbitrary positive coefficient very small before 1, intended to avoid the problems linked to the division by 0).

The overall risk can be calculated by the formula:

R (a _il aj) = 1 / (F (a _i , a _j ) + α) - 1 / (1 + α)

Also note that the functions

instead of taking numerical values, can take values of the type "yes", "no" or "can be". In this case, the result of taking into account two filters relating to two different characteristics is done by applying “multiplication” rules of the type “yes” * “yes” = “yes”; "Yes" * "may be" = "may be" * "may be" = "may be";"Yes" * "no" = "may be" ^* "no" = "no" * "no" = "no".

- We also define, from the economic data specific to the activity concerned, cost differences G _k (ai, a _j ), associated with the replacement of an article a _\ having the characteristic K _k (aι) by an article aj having the characteristic K _k (aj) without taking account of the other characteristics, then a global cost difference G (aι, a _j ) is calculated as a function of all Gk (aj, aj). Each cost difference G _k (aj, a _j ) is zero if K _k (aj) = Kk (aj), and positive or negative in the other cases. The overall cost difference G (aj, aj) is by example equal to the sum of G _k (aι, aj) when the different characteristics are obtained by operations independent of each other.

In the example described above, the substitution graph for catalog items takes into account only two characteristics: the shade and the condition of the product. However, there is nothing to prevent a greater number of parameters from being taken into account, and the method which has just been described applies to such a case.

2) Development of the possible association rules for semi-finished products when ordering, these rules are presented in the form of a graph of possible associations:

- From the substitution graph for the items in the catalog, we construct the graph of the possible associations of products (strips in stock) with orders, taking into account the characteristics specific to the products in stock and specific to unfilled orders, in particular the characteristics relating to the formats available for products in stock and the formats requested for unfilled orders, so as to check the compatibility of these characteristics. This graph consists of all the links Lpc (Pi, C _j ) of the possible associations of a product Pj with an order Cj: such a link exists if the product Pj can be used to satisfy the command Cj. It is made up of a pair of values Rpcjj and Gpcy corresponding respectively to the risk and the cost difference associated with the assignment of product Pj to the order C _j .

- To build the graph of the possible associations of the products with the orders, one examines all the possible couples made up of a band available in the stock and an order of the order book, and one proceeds in the following way:

- each strip in stock Pj is characterized by:

- an article from the product catalog a (Pj),

- a width l (Pj), - a thickness e (Pj),

- possibly, a “complementary state” resulting from complementary operations such as surface preparation having already been carried out.

- each order C _j in the order book is characterized by: - an article from the product catalog a (Cj),

- a width l (C _j ),

- a minimum thickness em (Cj) and a maximum thickness eM (C _j ),

- possibly a "complementary state". - using the graph of the substitutions of the articles of the catalog one determines if the article a (Pj) can be substituted for the article a (C _j ), ie if F (a (C _j ), a (Pj)) is strictly greater than 0, and we determine the associated risk R (a (C _j ), a (Pj)), as well as the additional cost G (a (C _j ), a (Pj)),

- If F (a (Cj), a (Pι))> 0 and if l (P,)> l (C.) And if em (Cj) <e (Pι) <eM (Cj) and if the " additional state "of the order can be obtained from the" complementary state "of the product, it is considered that the product in stock Pj can be assigned to the order Cj and a link Lpc (Pj, Cj) = {RpQ is established _j , Gpq, j}, with RpQj = R (a (Cj), a (Pj)) and GpQj = G (a (Cj), a (Pj)); which means that the risk associated with the association of the product Pj and the order C _j , called “association risk”, is equal to the risk corresponding to the substitution of the article characterizing the order by the article characterizing the stock product associated with the order; similarly, the additional cost associated with the association of the product Pj and the order Cj is equal to the additional cost associated with the substitution of the article characterizing the order by the article characterizing the product in stock assigned to the order; the risk and the additional cost being those defined in the substitution graph for the items in the catalog. Note that the term "substitution" also covers the case in which the article requested in the order is the same as that which characterizes the product available. - If at least one of the conditions defined above is not fulfilled, no link is established (the association of the product and the order is not possible).

It will be noted that this process generally leads to the creation of links between the same product and several orders and between several products and the same order.

3) Development of one or more possible cutting plans: There are several ways to develop a workable cutting plan. These means can be well-known algorithms in the technical field of optimizing two-dimensional cutting of strips. It can also be a manual method implemented by an operator.

In particular, a possible cutting plan can be developed as follows:

- by applying the rules resulting from the choice of the allocation strategy, and taking into account the graph of the possible associations of the coils to the orders, a first order is chosen in the order book, and in the stock of bands a band assignable to this ordered. When several bands are assignable, the one that best corresponds to the command is chosen, that is to say the one for which the risk of substitution is the lowest.

- From the map of the usable areas of the strip and the format requested for the order, taking into account the rules of feasibility of cuts, we define in the strip one or more areas that are assigned to the order, one or more areas to be scrapped because unusable, and possibly one or more areas not affected but reusable. The corresponding cutting range is also defined, and the part of the cutting plane thus obtained is memorized.

- We update the stock of available tapes and the order book.

To update the stock of available tapes, it is possible, if necessary, to introduce new virtual defects into the tape defect map to mark the areas that have just been defined in the cutting plan.

And we repeat the previous three operations until we can no longer assign bands to commands. 4) Use of metallurgical rules to assess the relevance of a workable cutting plan:

This assessment is made command by command, band zone by band zone, so as to determine for each band zone the risk associated with its allocation to the command concerned.

This risk is determined by reference to quality grids as defined above and which consist of a table comprising as many rows as there are families of defects defined by the typology of defects; this table giving each family a degree of seriousness. A distinction is made between the actual quality grids established from the map of actual faults in an area of a strip, and the reference quality grids corresponding to the quality desired for each order.

A reference quality grid is obtained by adding to a standard quality grid depending on the type of order (nature of the product, intended use, etc.) a tolerance grid depending on the format of the order and possibly the sensitivity of the customer ( or any other relevant parameter). This addition is done, for example, line by line, the degree of severity of the reference grid for a given family of faults being the sum of the corresponding degrees of severity of the standard grid and the tolerance grid. The grid thus obtained gives for each family the degree of gravity which it is desirable not to exceed. However, a higher degree of severity can in some cases be accepted, but with a certain risk.

To assess the risk associated with assigning a zone of a band to an order, using the band's defect map, we determine the intrinsic quality grid for the zone, then compare line by line. this intrinsic grid and the reference quality grid so as to determine the deviations, and in particular the lines, that is to say the families of defects, for which the degree of severity of the zone of the strip is greater than the degree of gravity defined by the reference grid.

Using rules known as “metallurgical rules” and the characteristics of the defects recorded in the defect map, we then evaluate, family of defect by family of faults, the associated risk, and we indicate the rule that was used. Obviously, when the degree of gravity of the intrinsic quality grid is less than the degree of gravity of the reference quality grid, the risk is zero. In other cases, the risk is assessed, for example, by an assessment of the “low”, “medium” or “high” (or “infinite”) type. This risk assessment is made by reference to three situations corresponding to: “risk accepted automatically”, “risk acceptable only after validation by an operator” and “risk unacceptable in all cases”.

The metallurgical rules are for example of the type “if the zone contains a defect of such a family, and if its density is greater than a certain value, and if its extent is greater than a certain value, then the zone can be assigned to the command with a risk of such level ".

These rules are of two types which depend on the nature of the defect:

- on the one hand, the rules included in the quality grid and which are valid for all orders,

- on the other hand, rules which may depend on the customer or on any other parameter specific to an order and which are defined on a case-by-case basis; these particular rules can be applied by using for example an expert system possibly dialoguing with an operator.

This assessment may also be supplemented, if necessary, by an indication relating to the risk associated with the catalog item corresponding to the strip area. This risk is that which is assessed using the substitution graph of the catalog items.

It is this information relating to the risks and metallurgical rules taken into account that is submitted to an expert for decision on the acceptability of the allocation of the zone to the strip.

The method as just described can be implemented by computer means which then include files on the one hand, and program modules on the other hand each fulfilling a particular function. The files are in particular: a file of orders in the order book (the order book), a file of the available bands (the stock of semi-finished products available), a file of the faults of each band (corresponding to the fault card), a file of substitution rules representing the substitution graph for items in the product catalog, a file of cutting rules, a file of economic data, a file of metallurgical rules and a file of cutting plans.

The program modules are in particular: - an association module which determines, from the order book file, the available tapes file and the substitution rules file, the links between the order book file and the order file bands available to identify possible associations.

- A cutting module allowing, from the order book file, the available bands file, links between these files, the defect file, the cutting rules file and the economic data file, to determine a plan cutting plan which will feed the cutting plan file. This module can be configured by the allocation strategy chosen. - A module for calculating the intrinsic quality grid for the quality of an area of a strip. This module uses the defect file and the cutting plan file to find out where the area is located, as well as the metallurgical rules file to determine the calculation rules to apply.

- A metallurgical risk assessment module which, from the defect file, the metallurgical rule file and the cutting plan file, assesses the risk associated with assigning a zone to an order.

- A dialogue module with the expert who presents the cutting plans with the associated risks, for validation.

- A cutting plan management module which updates the order files, stock and cutting plans according to the validation decisions of the cutting plans.

These computer means can take various forms that the skilled person can construct according to each particular situation, and the invention is not not limited to the embodiment which has just been described. The invention can, in particular, be applied to any type of material produced in the form of strips, the characteristics described here with reference to stainless steels being able to be replaced by any corresponding characteristic for another material. The method, which consists in particular in taking into account the concept of risk, can also be applied to products in the form of bars or profiles, subject to adaptations that a person skilled in the art will be able to make.

The implementation of the method is done in particular by introducing the necessary input data on suitable electronic media known in themselves and by recovering the output data also on suitable electronic media. These data exchanges can be done via terminals such as a personal computer, or by links between computers using networks. When you have developed an operational cutting plan, you realize it. For this, we take from the stock of semi-finished products the strips assigned to orders, we cut them using the cutting tools according to the cutting plan, and we combine the lots assigned to each order, as usually does.

Claims

1 - Process for developing a cutting plan for semi-finished products defining how to cut by cutting from a stock of semi-finished products one or more batches of products intended to satisfy one or more orders recorded in an order book according to which it is determined an achievable cutting plan consisting of batches of semi-finished products each associated with an order, characterized in that for each batch, a risk of allocation is defined, the acceptability or otherwise of the risk of allocation is assessed and a operational cutting plan consisting only of lots for which the risk of allocation is acceptable, at least one step of the process being implemented using a computer.

2 - Method according to claim 1 characterized in that, to define the risk of allocation, using risk assessment rules.

3 - Method according to claim 1 or claim 2 characterized in that, to determine whether the risk is acceptable or not, using risk acceptance rules.

4 - Method according to any one of claims 1 to 3 characterized in that there is a catalog of products and rules for substitution of an article from the catalog by another article from the catalog defining in particular, for each couple consisting of 'a first catalog item with a second catalog item, a substitution risk corresponding to the risk associated with the replacement of a first catalog item with the second catalog item. 5 - Method according to claim 4 characterized in that the rules for substitution of an item in the catalog by another item in the catalog constitute a graph which is neither symmetrical nor transitive.

6 - A method according to claim 4 or claim 5 characterized in that to determine a workable cutting plan is determined rules of association of semi-finished products and orders using the rules of substitution of a catalog item by another item from the catalog, and we define for each pair consisting of a semi-finished product and an order whose formats are compatible, a risk of association equal to the risk of substitution of the item of the catalog requested in the order by catalog item corresponding to the semi-finished product, these association rules constituting a graph of the possible associations of a semi-finished product with an order.

7 - Method according to claim 6 characterized in that to develop the association rules for semi-finished products and orders, we set an association risk threshold and we retain in the graph of possible associations that the product pairs semi-finished / order whose risk of association is lower than said threshold.

8 - Method according to claim 6 or claim 7 characterized in that the risk assessment rules take into account the risk of association. 9 - Method according to any one of the preceding claims, characterized in that each semi-finished product in stock is associated with a defect map which lists the defects present on said semi-finished product as well as their position.

10 - A method according to claim 9 characterized in that the defects are classified as "absolute defects" and "other defects" and in that, to develop a workable cutting plan, eliminating the areas of semi-finished products with " absolute defects ”.

11 - Method according to claim 10 characterized in that the "absolute defects" can be virtual defects generated in order to reserve certain areas of a semi-finished product.

12 - A method according to claim 10 or claim 11 characterized in that to assess the risk of allocation we take into account "other faults".

13 - Method according to claim 12 characterized in that to assess the risk of allocation resulting from the presence of defects in an area of a batch of semi-finished product associated with an order:

- using the fault map, the “other faults” present in said area are determined,

- using rules for taking account of faults, their degree of gravity and their density are evaluated,

- using rules for assessing the allocation risk resulting from the presence of faults, the corresponding allocation risk is evaluated.

14 - Method according to claim 13 characterized in that using the rules for taking into account the defects is developed a grid of intrinsic quality of said zone, and with the aid of the risk assessment rules, said intrinsic quality grid is compared to a reference quality grid defining the level of quality desired for the order.

15 - Method according to claim 13 or claim 14 characterized in that the rules for taking account of faults and the rules for assessing the risk of allocation constitute an expert system.

16 - Method according to any one of claims 1 to 15 characterized in that to decide whether a batch of the feasible cutting plan is acceptable or not, using an expert system using the risk acceptance rules d assignment, it is determined according to the order, the semi-finished product assigned to it and the corresponding assignment risk, if the risk is "automatically accepted", "acceptable only after validation by an operator" or " unacceptable in any case ",

- if the risk of allocation is "automatically acceptable", it is decided that the lot is acceptable,

- if the allocation risk is "acceptable only after validation by an operator", the question is submitted to an operator by providing him with information allowing him to make his decision, and the operator decides whether the batch is acceptable or not, - if the risk of allocation is "unacceptable in all cases", it is decided that the lot is unacceptable.

17 - Method according to any one of claims 1 to 16 characterized in that to develop the feasible cutting plan, the cost is minimized using cost calculation rules. 18 - Method according to claim 17 characterized in that to minimize the cost, when developing the feasible cutting plan, the cost is minimized without taking into account the cost associated with other defects.

19 - A method according to claim 17 or claim 18 characterized in that, after having developed the operational cutting plan, the cost associated with other faults is minimized so as to obtain an optimized operational cutting plan.

20 - The method of claim 19 characterized in that to minimize the cost associated with other faults is carried out permutations between batches of the operational cutting plan. 21 - Method according to any one of claims 1 to 20 characterized in that to develop the feasible cutting plan, one chooses an allocation strategy from among several possible strategies, at least one of these strategies taking into account the deadlines to respect for orders.