Method for planning and scheduling the production for a continuous casting installation, and associated electronic system

Abstract

A method for determining a production schedule for continuously casting an ensemble of steel slabs, which are gathered into batches of slabs called orders, the method comprising iteratively executing the following steps: - a casting simulation module: receives data specifying which of said orders is selected for keeping on the casting of said ensemble; determines an instant for which a casting of the selected order will be completed; and then send to a constructive optimization module a request for data specifying a next order to be casted, which comprises constraints to be met by the next order, - selection of the next order to be casted by the constructive optimization module, which is configured for optimizing at least one or more of: a number of tundishes needed for casting said orders, a casting productivity, compliance with requested delivery dates.

Description

Method for planning and scheduling the production for a continuous casting installation, and associated electronic system

[0001] The technical field is that of continuous casting, in particular steel continuous casting. It is more specifically that of planning and scheduling, that is ordering the production for a continuous casting installation, and producing steel slabs according to such a schedule. Technical background

[0002] Steel slabs, widely produced semi-finished product, are produced by continuous casting. In practice, in spite of a huge production volume, steel slabs are products that are produced on-demand, usually with individual, distinct characteristics that differ from slab to slab. As the production process is continuous, and as a single steel ladle contains steel for several slabs, the order in which the slabs are produced is very important. The ressources necessary for producing a given list of slabs, and even the feasibilty of the production depends directely on the planned production schedule, which specifies in which order the steel slabs are to be produced by continuous casting.

[0003] Methods for determining an industrial production schedule for a continuous process exist, for instance for optimizing a steel coils processing schedule for continuous annealing and coating lines.

[0004] Still, in the case of continuous casting, the scheduling is made harder as the quantities manipulated are continuous (and divisible) ones, namely amounts (tons) of liquid steel, instead of corresponding to a set of discrete elements such as discrete steel coils. Besides, there are numerous technical constraints, some of them related to upstream operations, to be met during such a casting operation.Summary

[0005] In this context, the instant technology provides method according to claim 1 for determining a production schedule which specifies in which order steel slabs, listed in an order book, are to be produced by continuous casting.

[0006] More generally, the instant technology concerns a method for determining a production schedule for continuously casting an ensemble of steel slabs, which are gathered into batches of slabs called orders, the method comprising iteratively executing the following steps:a casting simulation module: receives data specifying which of said orders is selected for keeping on the casting of said ensemble; determines an instant for which a casting of the selected order will be completed; and then send to a constructive optimization module a request for data specifying a next order to be casted, which comprises constraints to be met by the next order,- selection of the next order to be casted by the constructive optimization module, which is configured for optimizing at least one or more of: a number of tundishes needed for casting said orders, a casting productivity, compliance with requested delivery dates.

[0007] In this method, using an optimization of the sequence of the constructive type is very fruitful, as the step-by-step (order by order) construction of an optimal sequence allows for transferring the management of the numerous physical constraints to be met to a temporal simulation module (namely the continuous casting module), thus simplifying the optimization procedure itself and rendering feasible, practicable and more efficient, while respecting the constraints in questions.

[0008] This method may comprise one or more additional features, defined in claims 2 to 16, considered alone or in combination.

[0009] The instant technology also concerns an electronic scheduling system according to 17 and a continuous casting installation according to claim 18. It concerns also a computer program comprising instructions whose execution on a computer (possibly connected to relevant sensors and / or actuators and / or monitoring or control devices) make the computer to execute the instant method.Detailed description

[0010] The instant technology will now be described in more detail and illustrated by examples without introducing limitations, with reference to the appended figures.

[0011] Figure 1 represents schematically and partially a continuous casting installation.

[0012] Figure 2 is a block diagram representing schematically some steps of a method for determining a production schedule for the continuous casting installation of figure 1.

[0013] Figure 3 is a block diagram representing schematically another step of the method.

[0014] Figure 4 schematically represents an interaction between a continuous casting simulation module and a constructive optimization module employed to execute this method.

[0015] Figure 5 is a schematic sequence diagram representing the interaction between the continuous casting simulation module and the constructive optimization module.

[0016] Figure 6 schematically represents a portion of a casting sequence determined when executing this method.

[0017] Figure 7 schematically represents the result of a cutting plan applied to a continuous steel strand produced according to the casting sequence of figure 6.

[0018] Figure 8 schematically represents the scheduled operation of the continuous casting installation of figure 1 , including secondary metallurgy scheduling, for an exemplary sequence determined according to the instant method.

[0019] Figure 9 schematically represents the cutting plan for part of a double continuous steel strand, determined according to this method.

[0020] Figure 10 schematically represents production costs and service costs for difference candidate processing sequences determined according to this method.

[0021] Figure 11 schematically represents a proportion of buffer slabs produced during the operation of the continuous casting installation of figure 1.

[0022] Figure 12 schematically represents an average number of ladles per tundish, for different weeks of exploitation of the continuous casting installation of figure 1.Continuous casting installation

[0023] Figure 1 represents schematically some elements of a continuous casting installation 1 which comprises one or more continuous casters, here two continuous casters CC1 and CC2 (CC1 only being represented in figure 1). Each of the continuous casters comprises a replaceable tundish 4 feeding one, or like here two continuous casting lines L1 , L2 for the casting of two respective steel strands (L2 and the steel strand it produces are note represented, in figure 1).

[0024] Each tundish 4 is supplied with liquid steel 7 provided by a steel ladle 3. The tundish 4 plays, inter alia, the role of a kind of liquid steel buffer allowing for continuously casting the steel strand 8, with no interruption of the casting when the ladle 3, once emptied, is replaced by another ladle. Here, the tundish 4 distributes the liquid steel to the two parallel continuous casting lines L1 , L2. The liquid steel distributed by the tundish is introduced in a mould 5 (one mould for each casting line L1 , L2) which gives a rectangular shape to the cross section of the continuous strand 8. The mould 5 has an adjustable width, thus allowing for controlling the width of the steel strand 8 (which can thus be adjusted continuously). Downstream of the mould 5, the steel strand is guided by a set or rolls of the continuous casting line L1 and is cooled down, here by waterjets. The steel strand 8 thus gradually solidify. It is then cut into lengths to obtain slabs 9, using a torch cutting device 9.

[0025] The tundish 4 has a limited lifetime, in terms of liquid steel amount it can transfer before being out of order. This lifetime corresponds typically to the volume of 4 to 10 steel ladles. Besides, during its use, a contamination status of the tundish may evolve, depending on the steel grades that are casted using the tundish. For instance, if a chromium-rich steel grade is casted using the tundish, a chromium contamination level of the tundish increases, and afterwards, a chromium-lean steel grade cannot be casted anymore using this tundish. The contamination status of the tundish may be defined by a type of chemical elements contaminating the tundish (e.g.: chromium, copper, nickel, molybdenum) and corresponding levels of contamination.

[0026] The continuous casting installation 1 may, like here, comprise also one or more secondary metallurgy processing units. In this example, it comprises three such units, namely:a first unit, labelled as CAS, for Composition Adjustment by Sealed argon bubbling, an second unit, labelled as RH, for steel composition adjustment using the Ruhrstahl-Heraeus process, also called Vacuum Circulation Process, and a third unit unit, labelled as STAD (configured for decarburizing pig iron).

[0027] The continuous casting installation 1 comprises a computer system 10 for managing slab production by the continuous casting installation 1. The computer system 10 comprises at least:an electronic scheduling system 11 , configured for determining a production schedule which specifies in which order steel slabs, listed in an order book OB, are to be produced using the continuous casting installation 1 ; electronic scheduling system 11 is configured (here, programmed) for executing the method described further below,and an electronic control system 12, configured for controlling and monitoring the operation of the continuous casting installation 1.

[0028] The electronic scheduling system 11 comprises: one or more memories, including a non-transitory memory; one or more processors; one or more communication interfaces, such as a network of bus interface card or chip, for receiving and emitting data. Here, the electronic scheduling system 11 comprises also a Human-Machine Interface (including for instance one or more screens or indicators and input devices like a keyboard, buttons or selectors). The electronic scheduling system 11 may take the form of a standalone computer (such as a server). Still, all or part of electronic scheduling system 11 may be implemented in a distributed manner (“virtually”), using so-called “cloud” resources (computing and storing resources distributed among distinct, and possibly remote physical systems in a network).

[0029] The communication interface(s) allows the electronic scheduling system 11 to receive an order book OB (in the form of digital data) specifying a list of steel slabs to be produced (the information specified in the order book is presented in more detail further below).

[0030] The one or more memories of the electronic scheduling system 11 contain data specifying constraints CSTR forthe casting operation and / or regarding compatibilities between different steel grades in terms of in-use properties and / or client requests. The constraints for the casting operation may, like here, specify:- manufacturing constraints, specifying which grades are achievable using a tundish having a given contamination status (status indicating the nature of the contaminant and a level of contamination);- a width variation rate constraint, forthe casted strand;- steel grades compatibility constraints at the junction of two successively casted portions of the casted strand.

[0031] Each of the constraints CSTR may be received by the electronic scheduling system 11 from another computer device (through its communication interface(s)), or may be entered by an operator 20 using the human-machine interface, or adjusted by the operator using the human-machine interface.

[0032] The electronic scheduling system 11 is connected, through the communication interface(s), to one or more monitoring devices monitoring a status of the continuous casting installation. The information, LS_cap, received from the monitoring device(s) may, like comprise:an amount of available pig iron at the current instant,a planned temporal evolution for the amount of available pig iron, given a current status (an planned operation) of a blast furnace installation or electric furnace installation;a number of operational ladles at the current instant;a list of operational secondary metallurgy units at the current instant (and possibly, an amount of available steel for each of these units and / or an instant at which the unit will be available for a next heat).

[0033] The monitoring device(s) may be a device distinct from the electronic control system 12 and comprising one or more sensors and computation means (this device being connected to the electronic scheduling system 11). Instead of, or in complement to one or more distinct monitoring devices, the electronic control system 12 may play the role of such a monitoring device, the electronic control system 12 being connected to sensors of the continuous casting installation 1 and being configured for estimated the above-mentioned quantities (instant and foreseen amount of pig iron, number of available ladles, ...), and to transmit them to the electronic scheduling system 11.

[0034] The electronic scheduling system 11 is configured for displaying the production schedule, which specifies in which order the steel slabs listed in the order book OB are to be produced, using the human-machine interface.

[0035] The electronic scheduling system 11 may be configured for transmitting this production schedule Ssoito the electronic control system 12 (possibly after a validation by the operator 20, or after that the operator 20 had selected one schedule among different possible schedules determined by the electronic scheduling system 11 , or possibly after that the operator had modified the schedule determined by the electronic scheduling system). The electronic control system 12 may in turn be configured for controlling the continuous casting installation so as to produce the steel slabs listed in the order book OB according to the production schedule Ssoiit received from the electronic scheduling system 11 .

[0036] The electronic control system 12 comprises also: one or more memories, including a non-transitory memory; one or more processors; one or more communication interfaces, suchas a network of bus interface card or chip, for receiving and emitting data. Here, the electronic control system 12 comprises also a Human-Machine Interface (including for instance one or more screens or indicators and input devices like a keyboard, buttons or selectors). The electronic control system 12 may take the form of a standalone computer or the form of an ensemble of computer devices, some of them being for instance industrial computers like Programmable Logic Controllers or like modules of a Distributed Control System. The electronic control system 12 receives information relative to the operation and status of the continuous casting installation 1 (such as a liquid steel level in the tundish and the mold, a current width of the casted strand, a casting speed, a temperature of the liquid steel, or all or part of the information LS_cap above-mentioned, ...). This information is received by the electronic control system 12 through its communication interface(s), from sensors or monitoring devices of the continuous casting installation 1. Here, the electronic control system 12 is configured for controlling the continuous casting installation 1 , based, inter-alia, on the information relative to its operation and status. To this end, the electronic control system 12 sends instructions and / or setpoints to actuators (motors, valves, controllable cranes, ) or to low level controllers of the continuous casting installation 1.Scheduling method

[0037] The production schedule Ssoiis determined by the electronic scheduling system 11 based on the order book OB which lists the steel slabs to be produced.

[0038] In the order book OB, the slabs are gathered into batches of slabs, herein designated as orders (they correspond each to a client order, here), each order gathering one or more of the slabs that have a same steel grade. Such an order typically gathers together 1 to 10 slabs (frequently, from 1 to 6) of a same steel grade. For each slab, the order book OB specifies:a requested steel grade, with some potential and more expensive alternatives, a requested width (a target width), completed by an acceptable width range, defined for instance by a minimum width and a maximum width,indications regarding the requested weight or volume of the slab; here, this indication takes the form of a target weight, completed by an acceptable weight range defined by a minimum weight and a maximum weight, here ; it is noted that, in alternative embodiments, a length target could be used instead of a weight target (steel density being known or assumed constant, and given that the thickness of the slabs is assumed to be standardized - for instance equal to 270 mm for all the slabs),

[0039] The order book OB may also specify, like here:a requested length, completed by an acceptable length range,a requested delivery date which is a latest acceptable; delivery date (maximum acceptable delay).

[0040] The order book OB may further specify a priority level for each slab, as having a standard priority level or a high priority level.

[0041] Some general features of the method for determining the production schedule Ssoiare first presented below in a general manner, and the method is then described in more detail further below.

[0042] Feature A. In this embodiment, the method for determining the production schedule Ssoicomprises the determination of multiple candidate processing sequences Ssoi,i, with i from 1 to m, each candidate processing sequence specifying a possible casting order for producing the steel slabs listed in the order book. The production schedule Ssoi, to be employed for casting these slabs, is then determined from this set of candidate processing sequences Ssoi,i, i=1 ,...,m (during step s3; see figure 3). m is typically from 100 to 5000, for instance from 700 to 1500.

[0043] Feature B. For each candidate processing sequence Ssoi.i (or for the single processing sequence, should only one be determined, in alternative embodiments), the sequence Ssoi,i is determined by executing two main steps, s1 and s2 (figure 2):- first, a so called “liquid sequence” determination step, s1 , during which a casting sequence Siiq,i, for successively casting the orders listed in the order book OB in the form of one or more continuous steel strands, is determined; Siiq,i is called indifferently the casting sequence or the liquid sequence, in this document;- then, a so-called “solid sequence” determination step, s2, during which a cutting plan, for cutting the one or more continuous strands determined in step s1 in order to obtain the steel slabs listed in the order book, is determined; the candidate processing sequence Ssoi,i is the sequence of slabs (the ordered list of slabs) resulting from cutting the continuous strand(s) according to the cutting plan (i.e.: it is specified by the casting sequence determined in step s1 and the cutting plan for cutting the continuous strand corresponding to that casting sequence, determined in step s2).

[0044] Feature C. In step s1 , each “liquid sequence” Siiq,i is determined using a casting simulation module Sim interacting with a constructive optimization module Optm (figure 4). Siiq,i is constructed gradually, order by order. The casting simulation module Sim starts with an initial, first order to be casted, determines an instant at which the casting of this order will be finished (and also determines a status of the continuous casting installation at this instant, here), and then asks for the constructive optimization module Optm to determine a next order to be casted then, the casting simulation module Sim specifying, to the constructive optimization module Optm, constraints to be met by this next order. This procedure is executed iteratively. In other words, the casting simulation module Sim is in charge of determining the temporal evolution of the casting operation, detecting end-of-order events (and also end-of-ladle, end-of-tundish and end-of-sequence events), and determining the constraints to be metby the next order in order to obtain a physically feasible sequence. While the constructive optimization module Optm is in charge of selecting optimally the next order (optimally with respect to an objective, cost function), among the orders not casted yet. By module, it is meant here a dedicated group of computer instructions (a distinct routine, program or sub-program) implementing the functions (and algorithms) herein described.

[0045] Feature B simplifies significantly the complex problem of finding an optimal sequence for the casting of the slabs listed in the order book, as the determination of this sequence is divided into two successive steps. Besides, this simplification does not lead to less optimal sequences. Indeed, during the “solid sequence” determination step s2, when determining how to distribute the slabs along the continuous steel strand, the slabs sequence can be modified using both intra-order slab rearrangement (slabs re-arrangement within a given order ord1 , ord2, ord3,...) and inter-order rearrangement. In other words, positioning a slab belonging to a given order, along the strand, outside of a zone of the strand occupied by that order in the “liquid sequence” Siiq,i, is allowed. This allows for exploring efficiently the solution space without being significantly constrained by the two steps (step s1 , then step s2) structure of the method.

[0046] Feature C allows for efficiently solving the complex problem of finding an optimal sequence for continuously casting an ensemble of slabs. Finding a solution to this problem is complex because, contrary to other types of industrial scheduling optimization problems, here: there are numerous technical constraints to be met during such a casting operation, a slab of order selection has a very strong influence of on the rest of the casting, and the quantities manipulated are continuous (and divisible) ones, namely amounts (tons) of liquid steel, instead of corresponding to a set of discrete elements. In this context, using an optimization of the constructive type is very fruitful, as the step-by-step (order by order) construction of an optimal sequence allows for transferring the management of the physical constraints to a temporal simulation module, thus simplifying the optimization procedure itself and rendering is feasible, practicable.

[0047] Steps s1 , s2 and s3 are now described in more details.Step si: determination of the casting sequence Sna.i

[0048] Step s1 comprises the following steps (figure 5):s11 : the casting simulation module Sim:o receives data, next_ord_rtrn specifying, among the list of orders in the order book, one selected order (for example the order labelled as ord1 , in figure 6), selected for keeping on the production of the order book, o determines an instant (tein figure 6) at which a casting of the selected order (ord1) will be completed,o then, sends a request, next_ord_rqst, for data specifying a next order to be casted, said request being sent to the constructive optimization moduleOptm and specifying constraints to be met by the next order, said constraints comprising at least width and steel grade constraints,s13: the constructive optimization module Optm selects the next order (ord2, in the example of figure 6) to be casted, among the non-already casted orders, the next order being selected so as to meet the constraints specified by simulation module Sim, the constructive optimization module being configured for optimizing at least one of the following features, or a combination thereof: a number of tundishes needed for casting the orders according to the sequence Siiq,i; an amount of steel needed for one or more buffer slabs (labelled as e_slb and t_slb in figure 6) that are not in the order book OB but that are needed for producing the orders of the order book according to the sequence Siiq,i ; a casting productivity achieved when casting the orders according to said sequence; compliance with the requested delivery dates (specified in the order book).

[0049] The set of steps comprising steps s11 and s13 is executed iteratively until the sequence Siiq comprises all the orders of the order book OB. For instance, if there are N orders in the order book OB, this set of steps is executed N times successively (figure 5). The number N of orders in the order book is typically above 100, or above 500 or even above 1000. It is for instance from 500 to 10000.

[0050] During some executions of step s11 , the casting simulation module may receive, from the constructive optimization module, an “empty” next order, that is a message specifying that no feasible next order has been identified among the remaining, not yet casted orders. In this case, the casting simulation module decides to cast an inventory slab (t_slab, e_slab), as a next order. Anyhow, during at least some of the iterations of step s11 , the casting simulation module receives from the constructive optimization module a non-empty next order.

[0051] It is noted that this procedure is applicable to continuous casting installations comprising not just one, but also more than one continuous casters, each continuous casting being possibly a dual-line caster. In such a case, the casting simulation module Sim computes the temporal evolution of the casting operation (casting process) for all the continuous casting lines (and the evolution of the casting installation status), using possibly different simulation sub-modules, and each time an end-of-order event occurs (whatever the line), requests the constructive optimization module to select a next order to be casted. When the continuous casting installation comprises more than one continuous casting lines, the casting simulation module also determines, in step s11 , which of the casting lines to use, to cast the next order. Casting simulation module Sim

[0052] In step s11 , after having received the data specifying the order selected for keeping on the production, in the form of the returned data next_ord_rtrn, the casting simulation module Sim determines not only the instant predicted for the end of the casting of the selected order(called end-of-order instant), but also a status of the continuous casting installation 1 , at least at this end-of-order instant. The status of the continuous casting installation 1 , determined step by step by the casting simulation module Sim, may comprise one or more of the following information:the contamination status for the tundish(es) in use at the instant considered; a remaining time-life for the tundish(es) in use at the instant considered; a number of operational ladles at the current instant;a list of operational secondary metallurgy units at the current instant (and possibly, an amount of available steel for each of these units and / or an instant at which the unit will be available for a next heat;an amount of available pig iron at the current instant (in particular, at the end- of-order instant).

[0053] The casting simulation module Sim determines (computes) the predicted evolution of the status of the continuous casting installation 1 , during the casting operation, starting from an initial status of the continuous casting installation 1. Here, this initial status is set based on the monitoring data LS_cap received by the electronic scheduling system 11 , which are representative of the actual status of continuous casting installation at the initial instant (or from which the initial status, at the initial instant, can be computed).

[0054] Example of casting sequence

[0055] Figure 8 represents, for the exemplary embodiment considered here, and for a given sequence, the operation of the continuous casting installation 1 as planned by the casting simulation module Sim (with the help of the constructive optimisation module Optm). Figure 8 shows some of the information displayed by the electronic scheduling system 11 using its human-machine interface.

[0056] In figure 8, the horizontal direction represents time t. As above mentioned, the continuous casting installation 1 comprises two continuous casters CC1 and CC2, here, each comprising two continuous lines, L1 , L2, and LT, L2’ respectively.

[0057] In figure 8, the temporal evolution of the available amount of pig iron PIL (Pig Iron Level) is represented (in arbitrary units) by a thick line. Forthe secondary metallurgy units CAS, STAD and RH, each rectangular block represents the preparation of a steel ladle (more specifically, the preparation of the content of a steel ladle, that is of a ladle volume of refined liquid steel). For instance, the rectangle in the top-left corner of figure 8, labelled as Idl, represents the preparation of a ladle with a type of steel grade of reference A247. The right side of the rectangle corresponds to the instant at which the ladle has been prepared and is ready for being used by the continuous casters. In this embodiment, all the ladles have the same capacity (in terms of volume of liquid steel).

[0058] For the continuous casting lines L1 , L2, L1 L2’, each of the smaller-size rectangle represents an order. The successive orders casted using a same ladle are grouped in a bigger rectangle representing the ladle, whose steel grade reference is specified in the figure (e.g.: A247-3488866, A231-5488877, A743-4488843,...). For instance, in the bottom-left of figure 8, the ladle Idl is employed for casting, in parallel: three orders using the continuous casting line L1 ’, and also three orders using the continuous casting line L2’. This ladle Idl is the one above-mentioned, who was produced at the CAS unit and is represented by the rectangle at the topleft of figure 8. Each tundish is employed for continuous casting the steel contained in a number of successive ladles. A group of ladles, whose steel is casted using the same tundish, is represented as a rectangular block gathering the ladles in question. For instance, in figure 8, for the continuous caster CC2, the tundish tdsh’ is employed for casting five successive ladles, before being replaced. For the continuous caster CC2, the tundish tdsh is also employed for casting five successive ladles, before being replaced.

[0059] In figure 8, the casting sequence Siiq,i, determined by electronic scheduling system 11 for the successive casting of the orders listed in the order book OB, corresponds to the temporal succession of orders, for the set of casting lines L1 , L2, L1 ’, L2’, represented in this figure.

[0060] In figure 6 another example of the casting sequence Siiq,i is partially represented. The representation in figure 6 is of the same type as that in figure 8, but shows the sequence for the continuous caster CC1. In figure 6, the tundish tdsh is employed for casting the content of six ladles successively, the tundish tdsh being then replaced. The steel grade grd for each lalde is specified by the reference in thrtop of each rectangle representing a ladle. In figure 6, the ladle Idl1 is used for casting the order ord1 and then the order ord2 using the continuous casting line L1 , and for casting two other orders, in parallel, using the continuous casting line L2. The ladle Idl1 , thus emptied, is then replaced by the ladle Idl2, employed for casting the order ord3 and then the order ord4 using the continuous casting line L1 , and for casting a single order, in parallel, using the continuous casting line L2. The instant terepresents the instant predicted by the electronic scheduling system 11 for the end of the casting of the order ord1.

[0061] In figure 6, two special types of ‘orders’ e_slab and t_slab, are also represented. These ‘orders’ are buffer slabs that are not in the order book OB but that are employed for producing the orders of the order book OB according to the casting sequence Siiq,i.

[0062] Such a buffer slab may be transition slab t_slab, inserted in the sequence Siiq,i by the casting simulation module Sim for making possible a transition between two successive orders of the sequence Siiq,i. Indeed, a transition between two successive orders may turn out to be impossible as such, due to a steel grade incompatibility between these two successive orders (some steel grades cannot be casted one after the other, due to an incompatibility betweenthese two grades at the tundish or ladle level - using the same tundish, a chromium lean grade cannot be casted after a chromium rich grade using the same tundish, which may cause to introduce a transition slab to finish using the in-use tundish), or due to non-overlapping width ranges between these two orders (with requiring to insert a transition slab, of varying width, for doing the width transition between the two orders). Preferably, when the casting simulation module Sim determines that a transition slab t_slb is to be inserted, it selects the transition slab within a catalogue of (optimized) standardized slab formats (in other words, it uses an inventory slab format / type, for the transition slab), to optimize the chances that this non ordered slab be then employed or sold, and to facilitate the subsequent storage and management of this slab.

[0063] Such a buffer slab may also be an emptying slab e_slab, inserted in the sequence Siiq,i by the casting simulation module Sim for emptying an in-use ladle when the remaining amount of steel in that ladle is too small to allow for casting a next order.

[0064] Casting simulation

[0065] Here, the casting simulation module Sim comprises: one casting submodule for the simulation of each continuous caster CC1 , CC2, a secondary metallurgy submodule and an orchestration submodule coordinating the operation of the above-mentioned submodules.

[0066] The casting simulation module Sim computes the temporal evolution of the status of the continuous casting installation and of the casting operation and detects some key events occurring during this evolution; these key events comprise at least:end-of-order events (when the casting of an order is completed), end-of-ladle events (when a ladle has been emptied, and thus cannot supply liquid steel anymore),end-of-tundish (when the lifetime of the tundish considered is reached, orwould be exceeded should one more ladle be tapped though this tundish).end-of-sequence (when a sequence ends and then a setup time is necessary before casting a new tundish).

[0067] When an end-of-order event E occurs (figure 5), the casting submodule for which the event occurs call the constructive optimization module Optm, requesting the constructive optimization module Optm to specify the next order to be casted (next_ord_rqst).

[0068] When an end-of-ladle event occurs, the casting submodule for which the event occurs notifies the secondary metallurgy submodule that a new ladle, having a prescribed steel grade, is needed. The secondary metallurgy submodule then determines a production route for producing this new ladle; in particular, it selects the secondary metallurgy unit (CAS, RH, STAD) to be used.

[0069] More generally, the secondary metallurgy submodule check the feasibility of the casting sequence Siiq,i , from the point of view of the secondary metallurgy facility.

[0070] It is noted that the continuous casters CC1 , CC2 use the same secondary metallurgy resources (somehow in parallel) and the same Pig Iron coming from the Blast Furnace(s), including the same collection of steel ladles and the same secondary metallurgy units. The continuous casters CC1, CC2 are thus in competition for these common resources. It is thus even more useful that a common module, the secondary metallurgy submodule, checks that the requested steel ladles can indeed be produced, and even determines an optimal way for producing them.

[0071] In this embodiment, the casting simulation module Sim implements a Discrete Event Simulation (DES): the status of the continuous casting installation evolves over time t according to a sequence of discrete events (still, the pig iron level temporal evolution is continuously estimated overtime). Each event occurs at a particular instant in time and marks an update of the status of the continuous casting installation.

[0072] More particularly, the continuous casting simulation module Sim executes iteratively the group of steps a, b and c below:step a: Evaluate Current Status. The continuous casting simulation module Sim evaluates a status of each continuous caster to determine Resource Availability (to ensures that required resources, such as ladles and tundishes, are ready);step b: Select Next Action. Based on the evaluation of step a, the continuous casting simulation module Sim decides the next action for each continuous caster: if all conditions are met, the caster continues its current sequence;step c: Update Status. Updates to the status of the continuous casting installation are applied to reflect the chosen actions.

[0073] The simulation switches from step b to step c in particular at an end of the casting of an order (when there is an end-of-order event or, more generally, a key event), which triggers also the request for specifying the next order to be processed is sent to the constructive optimisation module.

[0074] Optionally, possible maintenance needs, the presence of multiples order books to be executed (that is, multiple production campaigns to be achieved), and / or the fact that the instant order book contains a limited number of orders is taken into account in the loop comprising the steps a, b and c. In this case:in step a, the continuous casting simulation module Sim also determines:o Active Campaigns: identifies which campaigns are running and their respective progress;o Maintenance Requirements: checks if any of the continuous casters is due for maintenance, scheduling downtime if necessary;in step b, the continuous casting simulation module Sim also determines:o Initiate Transition: If a campaign ends, the caster transitions to the next campaign or enters a waiting state;o Enter Maintenance: If required, the caster is taken offline for maintenance;in step c, the continuous casting simulation module Sim progresses the timeline of active campaigns and maintenance schedules and Records significant changes, such as the start of a new campaign or completion of maintenance.

[0075] The continuous casting simulation module Sim decides to introduce an emptying slab e_slb for instance when the in-use ladle is not empty and contains a liquid steel whose grade is not compatible (in terms of in-use properties and / or client acceptable) with any of the remaining, not casted yet orders.

[0076] Besides, in step s11 , the casting simulation module Sim decides to add a transition slab t_slab to allow for the junction of the selected order with a previously casted order, when given conditions regarding the selected order and the previously casted order are met (in terms of grade compatibility and / or width transition, as above explained with reference to figure 8).

[0077] It is noted that the casting simulation achieved by the continuous casting simulation module Sim takes into account many physical constraints. Some physical constraints are taken into account by the second metallurgy submodules, when checking that the requested ladles can actually be prepared. And when a new ladle is requested by one of the casting modules, the grade for the new ladle is selected taking into account the manufacturing constraints that specify which grades are achievable using a tundish having a given contamination status (and which are part of the above-constraints CSTR stored in the one or more memories of the electronic scheduling device 11). Besides, when a transition slab is inserted, this is achieved based on the width variation rate constraint, and on the steel grades compatibility constraints at the junction of two successively casted portions of the casted strand.

[0078] The constraints CSTR, for the casting operation and regarding steel grades compatibilities, are also taken into account by the continuous casting simulation module Sim when elaborating the request for a next order, next_ord_rqst, to be sent to the constructive optimization module Optm.

[0079] Indeed, this request comprises constraints to be met by the next order, said constraints comprising at least width and steel grade constraints.

[0080] The width constraint is based on the width ranges for the slabs contained in the selected order, whose casting has just finished, in the simulation of the casting. Indeed, the width of the steel strand must be continuous at the junction between two successive orders.Here, the width constraint takes the form of the width range for the slab of the selected order planned to be the last casted on. In practice, when testing if a candidate next order is acceptable, the constructive optimization module checks if taking into account the width range of the previous order together with the constraints set by the width evolution of the sequence itself, at least one slab within the candidate next order has a width range which has a non-zero intersection with the with range of the last slab (last one casted) of the selected order. Taking into account the constraints set by the width evolution of the sequence itself is very useful. Indeed, in practice, after having casted the previous order, the width constraint may be more stringent than just the width range of previous order, because of the limited rate of width change of the casters (because of this limited rate of change, orders casted prior to the previous order also influence the possible width range for a next order).

[0081] This is illustrated by the following example, in which a first order contains a single slab, with a width range (in mm) of [1000 - 1100], a second order (second in the sequence) contains a single slab with a width range of [1100 - 1200], and there is a capability of widening or narrowing of 50 mm per slab. In this case, once the first order has been casted, the possible (i.e.: the acceptable and achievable) width range, during the casting of the second order, start as being [1000 - 1100] (immediately after the casting of the first order) and ends as being [950 - 1150], As the width for the slab of the second order has to be in the range [1100 - 1200], the width of the steel strand thus has to start, at the beginning of the casting of the second order, as being equal to 1100 mm, and ends, at the end of the casting of the second order, in a possible end range [1100 - 1150], This end range is the intersection of the width range for the second order (that is [1100 - 1200]) with the constraints set by the width evolution of the sequence, here the range [950 - 1150], For a third order, containing one slab, the width range for that slab has to be have a non-zero intersection with the range [1100 - 1150] (which is smaller than the width range for the second order), to be able to cast that slab after the second order. And if the slab of the third order has a width range of [1150 - 1250], for instance, then, at the end of the casting the third slab, the constraints set by both by the width range for the third order, and by evolution of the sequence correspond to the range [1150 - 1200], with which a fourth order should have a non-zero intersection, to be achievable after the third order.

[0082] Regarding the steel grade constraint, if the in-course ladle is not emptied (and can thus supply steel for the next order), it is then based:on the steel grade in the in-course ladle,and on steel grade compatibility rules, in terms of in-use properties and / or client acceptance; here, these compatibility rules are listed in a grade book (in the form of a two-dimensional matrix specifying compatibilities between grades) stored in the one or more memories of the electronic scheduling system 11.

[0083] If the in-course ladle is empty once the selected order is casted (or emptied in the form of an emptying slab), the steel grade constraint may be determined based directly on a steel grade planned (by the casting simulation module) for the next ladle. Alternatively, instead of a single grade, a list of possible steel grade(s) for the next ladle may be determined (based on constraints regarding tundish contamination, and junction between successively casted orders), the steel grade constraint for the next order taking then the form of the list of grades that are compatible (according to the steel grade compatibility rules) with the list of possible grades for the next ladle.

[0084] In this embodiment, the width and steel grade constraints take directly the form of an acceptable width range and a list of acceptable steel grades for the next order. Still, in alternative embodiments, these constraints may be transmitted as features of the last order casted (width ranges, steel grade), the acceptable width range and the list of acceptable steel grades being then determined (using the grade book) by the constructive optimization module Optm (instead of being determined by the casting simulation module). Still alternatively, a compatibility check may be achieved candidate by candidate, for the candidate next orders, instead of computing a list of acceptable steel grades.Constructive Optimization module Optm

[0085] In this embodiment, the constructive optimization module Optm has five modes of operation:ml . New first order: when an order is to be selected to start a sequence Siiqj, with no previously casted order to match, and no prior production constraint to match with;m2. New Sequence: when an order is to be selected to start a new tundish that is the first in a sequence and it means with no constraints in terms of starting width (except for intrinsic constraints due to operation limits for the continuous casters - maximum width, possibly maximum length);m3. New tundish: when an order is to be selected to start a new tundish but not to start a new sequence of tundishes, that is to start a new tundish connected to a previous tundish in terms of width;m4. New Ladle: when an order is to be selected to start a new ladle in a tundish already started;m5. In Ladle: when an order is to be selected to be the next casted order in a ladle already started.

[0086] In other words, the constructive optimization module Optm is employed not only for selecting a next order to be adjoined to a previously casted order (which the case for the modesof operation m3 to m5), but also for selecting a first order to be casted as the first, head portion of a new steel strand.

[0087] For the modes of operation m3 to m5, the constructive optimization module Optm selects the next order to be casted, among the non-already casted orders of the order book OB, so as:to meet the width and steel grade constraints transmitted by the casting simulation module Sim,and to optimize an amount of consumed resources and / or a degree of compliance with the requested delivery dates (specified in the order book).

[0088] For the modes of operation ml and m2, the constructive optimization module Optm also selects an order among the non-already casted orders of the order book OB, so as meet applicable manufacturing constraints (if any), and to optimize an amount of consumed resources and / or a degree of compliance with the requested delivery dates. The constraints taken into account in this case comprises for instance intrinsic manufacturing constraints for the continuous casters, such as a maximum width achievable with the installation. A difference with modes of operation m3 to m5 is thus that the constraints taken into account are different (and, generally, less numerous, less stringent. Another difference is that a dedicated score (a starting-order score) may be taken into account for selecting such starting orders, contrary to the operating modes m4 and m5 (more details regarding this starting-order score are given further below).

[0089] Anyhow, the consumed resources may comprise, like here: the number of tundishes needed for casting the orders listed in the order book according the sequence Siiq,i, the amount of steel needed for casting the one or more buffer slabs e_slb, t_slb, if buffer slabs are inserted in the sequence Siiq , a total duration needed for casting the order book (in other words, an inverse of a casting productivity). Here, the amount of consumed resources is represented by a quantity called production cost (which is the inverse of a production performance, or production score). The production cost is all the higher than the above-mentioned quantities are high, here.

[0090] Among the resources consumed for producing the orders of the order book, the tundishes is a key one (as preparing a new tundish, ready for casting, is very resource demanding, and in particular very expensive). Minimizing the number of tundishes is thus key. In this regard, it is noted that maximizing a (average) number of ladles casted using each tundish is a criterion that can be used instead of minimizing the total number of tundishes required for producing the order book. Indeed, if the sequence allows for optimally using the tundishes, for instance with an average of six ladles casted by tundish (instead of three or four), the total number of tundishes needed will be all the smaller.

[0091] Regarding the degree of compliance with the requested delivery dates, it is represented here by a quantity called service cost (which is the inverse of a service performance, or service score). The service cost increases when an order is overdue (and increases all the more than the time lapse between the predicted delivery date and the requested delivery date is high, possibly with a penalty factor for orders having a high priority level).

[0092] The constructive optimization module Optm is configured here for minimizing a total cost, which a sum of the production cost and service cost.

[0093] The constructive optimization module Optm implements a constructive optimization algorithm (employed for the modes of operation ml to m5), that is an algorithm building a solution, here an optimal sequence, gradually, element by element (here: order by order), by adding an additional, subsequent element to the sequence, iteratively, until the sequence comprises all the elements in the initial list; except possibly for unmanufacturable orders. This is markedly different from an algorithm starting from a complete sequence comprising all the orders, and then modifying the sequence to optimize it. Such a constructive optimization algorithm can be for instance an Ant Colony Optimization algorithm (like the Ant System of Ant Colony System algorithms), another type of particle swarm optimization algorithm, ora Greedy Randomized Adaptive Search Procedure, also called GRASP.

[0094] In the embodiment described here, the optimization algorithm is a GRASP: each time an order is to be selected (should it be a first order, or a next order), it is selected by random selection, with a probability of being selected all the higher than a cost for that order is high. This cost is the total cost, here, except in the case of a first order in which case the startingorder score is taken into account.

[0095] The optimization algorithm comprises here the following steps, executed each time an order is to be selected (should it be a first order, or a next order):a. Identification of valid orders, among the non-already casted orders of the order book OB, a valid order being an order meeting the applicable constraints (intrinsic manufacturing constraints - if any - if it is for the selection of a first order; width and steel grade constraints if it is for the selection of a next order);b. Selection of one order, among the list of valid orders (possibly further filtered), the selection being a random selection with a probability of being selected all the higher than the cost of the order considered is low.

[0096] In a first version of the instant embodiment, in step a., the list of valid orders comprises all the non-already casted orders of the order book OB that meet the applicable constraints.

[0097] In a second version of the instant embodiment, in step a., the list of valid orders is limited to some orders using an iterative procedure explained below.

[0098] The orders of the order book are grouped into sets of orders depending on the requested delivery dates for the slabs therein (orders with close requested delivery dates aregrouped together in a set of orders). The set of orders are ranked, with respect to each other, in a descending order with respect to the requested delivery dates of the corresponding slabs. The set of orders whose slabs have the earliest requested due dates is attributed the highest priority rank.

[0099] Then, in step a., for determining the list of valid orders (to be used in step b.) the following steps are executed successively for the different sets of orders, one set of order after the other, in a descending order with respect to their priority rank:the valid orders in the set of orders are identified, if any,if at least one valid order is identified in the set of orders, the iterations stop and the list of valid orders, to be used in step b, is constituted by the ensemble of valid orders in the current set of orders.

[0100] Restricting the list of valid orders in this way (by giving priority to early due dates), makes the determination of the casting sequence Snq,i more efficient. Indeed, it reduces the number of orders for which validity has to checked. Besides, this strategy reduces the possibility to select a next order having a very late due date while other orders have early due dates. In other words, it guides and constraints adequately the subsequent random choice of one of the valid orders.

[0101] In this embodiment, in step b, among the list of valid orders (restricted as above explained), the orders that have a probability of being selected which is below a fixed threshold are further eliminated before achieving the random selection itself. This is useful in particular in cases where there are very numerous valid orders each having a low probability of being selected. Indeed, in such a case, these high cost though numerous valid orders may bias the selection towards an order with a very high cost, which would not be an adequate selection (even for a random selection).

[0102] Here, the probability an order has to be selected is proportional to the inverse of the cost forthat order.

[0103] In this embodiment, several “liquid” sequences Siiq,i, with i from 1 to m, are determined using this randomized procedure.

[0104] In the course of determining these sequences Siiq,i, results of the previously determined sequences are exploited for improving the optimization process for the remaining sequences.

[0105] More specifically, each order in the order book is attributed a starting-order score. Before determining the sequences Siiq,i , i=1 ,...,m , the starting-order scores of all the orders are initiated with a same initial, default value.

[0106] Then, each time a sequence Siiq,i has been determined, for each tundish in that sequence, the starting-order score for the first order of that tundish is updated. To this end, a performance score for the whole tundish is computed, depending on service performance (duedates for the orders within that tundish) and production performance, here the length of the tundish in terms of number of ladles. For instance, a long tundish (5, or even 6 or more ladles) with high priority orders inside has a high-performance score. When the performance score for the whole tundish is high (above a given threshold), the starting-order score for its first order is increased. Conversely, if the performance score for the whole tundish is low (above the above-mentioned threshold), the starting-order score for its first order is decreased.

[0107] In step b, when selecting a first order (to start a new tundish), the order is randomly selected among the list of valid orders, with a probability all the higher than its starting-order score is high.

[0108] Thanks to this procedure, an order, which turned out to a good starting point for a tundish during a previous sequence determination, will be more likely to the be selected for starting a tundish in future sequence determinations.

[0109] This procedure is very useful. Indeed, the choice of a first order, for starting a tundish, influences the whole tundish, due to steel grades and width constraints. An inadequate choice for the first order of a tundish may impair completely the performance for that tundish. The procedure above allows for capitalizing the results of past attempts for finding an optimal casting sequence, and to gradually improve the quality of the casting sequences. In a way, it is alike an Adaptative Memory technique (adapted to the instant sequence determination problem), and provides benefits similar to the ones of Adaptative Memory techniques.Step s2 determination of the solid sequence

[0110] In step s2, the electronic scheduling system 11 determines one “solid sequence” Ssoi,i for each casting sequence Siiq,i determined in step s2. Ssoi,i is also called the candidate processing sequence, in this document. As above mentioned, it is the result of a cutting plan applied to the continuous steel strand(s) produced according to the casting sequence Siiq .

[0111] The candidate processing sequence Ssoi,i is determined, from the casting sequence Siiq,i and from the order book OB, so as to find an optimal set of widths, weights and lengths for the ensemble slabs according to a predefined fitness function (for instance a sum of squared deviations) that assesses the deviations from the target widths and weights for each slab. Optionally, the optimization may be further achieved so as to try to eliminate, or at least minimize buffer slabs, in particular emptying slabs e_slb. In practice, adjusting the slabs’ length (while complying with requested length ranges, and not getting too far from the target lengths) allows for suppressing or minimizing such buffer slabs. Besides, the optimization procedure in question may be an optimization with constraints, the constraints being to comply with the dimension ranges (width range, lengths range, weight range), and / or steel grades compatibility rules (as specified in the grade book), and / or with requested delivery dates.

[0112] This optimization can be achieved using a linear optimizer based on the simplex algorithm (like the commercially available Cplex software), or possibly using commercially available nesting optimizers.

[0113] Figure 7 and figure 9 show two examples of such candidate processing sequences Ssoi,i.

[0114] The candidate processing sequence Ssoi,i of figure 7 corresponds to the casting sequence Siiq,i of figure 6, with its two continuous strands (one for line L1 and the other for line L2) cut into slabs. In figure 7, within each order (which is represented by a thick-line rectangle), the slabs to be cut are represented by thin rectangles. For instance, it is planned to cut the order ord2 into three slabs slb1 , slb2, slb3. Some of the slabs to produce correspond directly to one of the orders, the order in question being then cut as whole, to form a single slab (it is the case for instance for the orders ord1 and ord3 of figure 6).

[0115] Figure 9 represents the candidate processing sequences Ssoi,i for one complete tundish tdsh. For the two continuous strands casted using that tundish, the plain continuous line with the reference w shows the evolution of the width of the strand, along the strand (width which is varying continuously, with no abrupt jump), as determined by the continuous casting simulation module Sim. Each rectangle represents a slab cut in these strands, like the ones labelled as slb11 , slb12, slb13. The plain step-like line low_w represents the minimum width of the width range for the slabs considered, while the dashed step-like line upp_w represents the maximum width of the width range for the slabs considered. As illustrated on figure 7, the cutting plan determined in step s2 complies with the requested widths ranges for the slabs to be cut in these two steel strands.Step s3: selection of the production schedule Ssoi

[0116] As above explained, multiple candidate processing sequences Ssoi,i, i=1,...,m are determined, by iterating steps s1 and s2. This is useful, given the partially random approach employed for determining each candidate processing sequence. Repeating steps s1 and s2 multiple times indeed allows for exploring the solution space and thus to get closer to an optimal solution. Besides, thanks to the adaptative-memory-like technics above presented (updates of the starting-order scores after each iteration), the candidate processing sequences get gradually better in the course of these iterations of steps s1 and s2 (learning capabilities). Determining multiple candidate processing sequences also allows for obtaining varied solutions corresponding to different compromises between an optimization of the production cost and an optimization of the service cost.

[0117] Figure 10 represents schematically the production cost Cprod_i and the service cost Cservj for some of the candidate processing sequences determined when iterating steps s1 and s2. In figure 10, each candidate processing sequence Ssoi,i is represented by a dot (onlya fraction of the candidate processing sequences are represented, in this figure). The best schedules are the one surrounded by a dotted line (they are on an approximate Pareto front).

[0118] In step s3, the final production schedule Ssoiis selected, among the different candidate processing sequences Ssoi,i, i=1 ,...,m.

[0119] In this embodiment, this selection is achieved automatically by the electronic scheduling system which selects the candidate processing sequence having the lowest total cost, or, alternatively, the one having the lowest total weighted cost, the total weighted cost being a weighted sum of production cost and service cost (the corresponding, respective weights being for instance adjustable by the operator 20).

[0120] In other embodiments, the final production schedule Ssoimay be selected directly by the operator 20 using the human-machine interface of the electronic scheduling system 11 .

[0121] In any case, a two-dimensional graph like the one of figure 10 may be displayed by the electronic scheduling system 11 , to allow the operator as decision maker to apprehend the expected performances of the candidate processing sequences and / or to enable him selecting one of the candidate processing sequences.

[0122] Once the production schedule Ssoihas been selected, a prompt is displayed by human machine interface to allow the operator to validate the production schedule Ssoi, here. Once the production schedule Ssoihas been validated by the operator 20, the electronic scheduling system 11 transmits it to the electronic control system 12 which then controls the continuous casting installation 1 so as to produce the steel slabs listed in the order book OB according to the production schedule Ssoi.Exemplary results

[0123] Figure 11 represents a proportion b% of buffer slabs, among the overall slabs produced (as a weight %), for 22 successive weeks of operation of the continuous casting installation 1. Each bar corresponds to one week of operation. During the 14thfirst weeks, the operation is carried out based on production schedule set up by human experts, without using the instant method. During the last 8 weeks, the operation is carried out based on production schedules set up using the instant, computer-implemented method. In average, during the 14thfirst weeks, the proportion b% of buffer slabs is of about 4.1%, and is reduced to an average of 3.6% when using the instant method, which illustrates one of the benefits of this method.

[0124] Figure 12 represents an average number of ladles per tundish, nL, for 14 successive weeks of operation of the continuous casting installation 1. Each bar corresponds to one week of operation. The plain bars (grey-filed ones) correspond to the number of ladles per tundish observed when the operation is carried out based on production schedule set up by human experts, without using the instant method. The white-filed bars (which are higher than the plain ones) correspond to the number of ladles per tundish predicted for an operationbased on production schedules set up using the instant, computer-implemented method (the orders produced being the same). This example illustrates that a particularly efficient usage of tundishes is obtained thanks to this method (in particular, a more efficient usage than when the schedule is set by human experts).

[0125] Table 1 gathers results regarding delivering delays, for seven production periods labelled from 1 to 7. The values indicated in table 1 are, for each period, the (average) delay between the delivery date and the requested delivery date (as specified in the order book), expressed in days. The last column is an average for these seven periods. As can be seen in this example, the instant method allows for delivering the ordered slabs more in advance than when the production schedule is set up human experts (4.4 days in advance, in stead of 3.6 days in advance). Besides, non-respected delivery dates (corresponding to a positive delay, that is a positive value corresponding to a late delivery compared to the requested delivery date), are avoided, thanks to the instant method.

[0126] Table 1

Claims

CLAIMS1. A method for determining a production schedule (Ssoi; Ssoi,i) which specifies in which order steel slabs (slb1 , slb2, slb3), listed in an order book (OB), are to be produced by continuous casting, the steel slabs being gathered, in the order book, into batches of slabs (ord1 , ord2, ord3) herein designated as orders, each gathering one or more of the slabs, which have a same steel grade, the method comprising a step s1 of determining a casting sequence (Siiqj) for casting said orders successively, step s1 during which:- s11 : a casting simulation module (Sim):o receives data (next_ord_rtrn) specifying, among said orders, one selected order (ord1), selected for keeping on the production of the order book, o determines an instant (te) at which a casting of the selected order will be completed,o then, sends a request (next_ord_rqst) for data specifying a next order to be casted, said request being sent to a constructive optimization module (Optm) and specifying constraints to be met by the next order, said constraints comprising at least width and steel grade constraints,- s13: the constructive optimization module (Optm) selects the next order (ord2) to be casted among said orders, so as to meet said constraints, the constructive optimization module being configured for optimizing at least one of the following features, ora combination thereof: a number of tundishes (tdsh) needed for casting said orders (ord1 , ord2, ord3) according to the casting sequence (Siiq,i); an amount of steel needed for one or more buffer slabs (e_slb, t_slb) that are not in the order book (OB) but that are employed for producing the orders of the order book according to the casting sequence (Siiq,i); a casting productivity achieved when casting said orders according to the casting sequence; compliance with requested delivery dates (specified in the order book),the set of steps comprising steps s11 and s13 being executed iteratively to determine the casting sequence gradually, order by order.

2. A method according to claim 1 , wherein the succession of orders casted according to the casting sequence (Siiq,i) forms one or more continuous strands, the method further comprising a step s2 of determining a cutting plan for cutting the one or more continuous strands in order to obtain the steel slabs listed in the order book, the production schedule (Ssoi.i), which specifies in which orderthe steel slabs listed in the order book are to be produced, being the sequence of slabs resulting from cutting the one or more continuous strands according to the cutting plan, the cutting plan being determined so as to optimize at least oneof the following features or a combination thereof: the number of buffer slabs (e_slb); compliance with requested dimensions for the slabs listed in the order book.

3. A method according to claim 2 wherein, in step s2, during the optimization achieved for determining the cutting plan, positioning a slab belonging to a given order, along one of the one or more strands, outside of a zone of the strand occupied by that order according to the casting sequence (Siiq,i), is allowed.

4. A method according to anyone of the preceding claims wherein, in step s11 , the casting simulation module (Sim) also determines a status of a continuous casting installation employed for casting said orders, at least at the instant (te) predicted for the end of the casting of the selected order, said status comprising one or more of: an available amount and / or a steel grade for a liquid steel in a ladle whose tapping is in progress or for a ladle achievable at a steel shop at that instant (te); an available amount of pig iron (PIL); a contamination status for an in-use tundish ; a remaining time-life for the in-use tundish.

5. A method according to claim 4 wherein, in step s11 , the casting simulation module (Sim) determines one or more of the constraints to be met by the next order depending on the status of the continuous casting installation.

6. A method according to claim 4 or 5 wherein, in step s11 , the casting simulation module (Sim) adds a buffer slab (e_slab) to empty the ladle whose tapping is in progress, when a steel grade of the liquid steel in said ladle is not compatible with any of the steel grades of the non-already casted orders.

7. A method according to claim 4, 5 or 6, comprising acquiring monitoring data (LS_cap) transmitted by one or more monitoring device(s) of the continuous casting installation, the monitoring data being relative to a status of the continuous casting installation at a given time.

8. A method according to anyone of the preceding claims wherein, in step s11 , the casting simulation module (Sim) determines one or more of the constraints to be met by the next order taking into account one or more of (CSTR): manufacturing constraints specifying what grades are achievable using a tundish having a given contamination status ; a width variation rate constraint, for the casted strand; steel grades compatibility constraints for the junction of two successively casted portions of the casted strand; compatibilities between different steel grades, in terms of in-use properties and / or client requests, specified by steel grades compatibility data.

9. A method according to anyone of the preceding claims wherein, in step s11 , the casting simulation module (Sim) determines the width constraint for the next order in the form of a width range, which is determined from acceptable width range(s) specified in the order book for the one or more slab(s) contained in the selected order, and from constraints set by a width evolution for the casting sequence (Siiq,j).

10. A method according to anyone of the preceding claims, wherein step s1 is executed multiple times to determine a respective multiplicity of casting sequences (Siiq,i , Siiq,i, Siiq,m) each specifying a casting order for producing the orders listed in the order book.

11. A method according to anyone of the preceding claims wherein, in step s13, the constructive optimization module executes a Greedy Randomized Adaptive Search Procedure for selecting the next order.

12. A method according to claim 11 , taken in the dependency of claim 10, wherein:- the orders in the order book (OB) are each attributed a quantity called starting-order score, the starting-order scores of all the orders being initiated with a same default value before the executions of step s1 , after each execution of step s1 , for each tundish of the casting sequence (Siiq ) determined during the execution of step s1 ,o a performance score is computed for the tundish, all the higher than requested delivery dates and possibly an order priory level are met, and than the number of ladles casted with said tundish is high,o the starting-order score for the first order of the tundish is increased if the performance score of the tundish is above a given threshold, is decreased if the performance score of the tundish is below the given threshold,- during subsequent executions of step s1 :o a first order of the casting sequence is selected with a probability all the higher than its starting-order score is high, ando in step s13, when the next order to be selected is a first order of a new tundish, it is selected with a probability all the higher than its starting-order score is high.

13. A method according to claim 11 or 12 wherein:- The orders of the order book are grouped into sets of orders depending on the requested delivery dates for the slabs in the orders, the set of orders being ranked with respect to each other, and attributed a corresponding priority rank all the higher than the requested delivery dates, of the slabs in the set of orders considered, are early, and wherein, in step s13:o the following steps i and ii are executed, for the different sets of orders successively, one set of orders after the other in a descending order with respect to the priority rank:- i. it is determined if the set of orders contains at least one valid order, a valid order being an order meeting the width and steel grade constraints,- ii. if the set of orders contains at least one valid order, a list of valid orders, containing all the valid orders in the set of orders, is formed, and the iteration of steps i and ii is stopped,o the next order is randomly selected among the list of valid orders, with a probability of being selected all the higher than a score associated to said next order is high, said score depending on an amount of resources needed to cast said order, or on a compliance with or even an anticipation of the requested delivery date for the next order, or on a combination thereof.

14. A method according to claim 10, or according to anyone of claims 11 to 13 in its dependance of claim 10, wherein a multiplicity of processing sequences (Ssoi,i, Ssoi,i, Ssoi,m) is determined from the multiplicity of casting sequences (Siiq,i, Siiq,i, Siiq,m) respectively, the method comprising a step s3 of selecting the processing schedule (Ssoi) among the multiplicity of processing sequences (Ssoi,i, Ssoi,i, Ssoi,m), the selection of the processing schedule being achieved by an operator (20) using a human-machine interface, or being achieved automatically by an electronic scheduling system (11) based on one or more selection rules.

15. A method according to anyone of the preceding claims wherein, in step s11 , the casting simulation module determines the instant (te) at which the casting of the selected order will be completed by executing a Discrete Event Simulation.

16. A method for producing an ensemble of steel slabs listed in an order book (OB), by continuous casting, the method comprising:- determining a production schedule (Ssoi; Ssoi,i) which specifies in which order the steel slabs (slb1 , slb2, slb3) are to be produced, by executing a method according to anyone of the preceding claims,- producing the ensemble of steel slabs by continuous casting, according to said production schedule (Ssoi; Ssoi,i).

17. Electronic scheduling system (11), comprising at least a processor and a non-transitory memory, configured for executing the method according to anyone of claims 1 to 15.

18. Continuous casting installation (1) comprising:one or more continuous casters (CC1 , CC2) each comprising a tundish (4) and one or two continuous casting lines (L1 , L2),- an electronic scheduling system (11) according to the preceding claim.

19. Computer program comprising instructions whose execution on a computer make the computer to execute the method according to anyone of claims 1 to 15.

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