Coil scheduling method and system for electrogalvanizing line in steel industry

A coil scheduling method for electrogalvanizing line in steel industry, comprising:

• Step 1:
• describing a technological process and determining constraints of the technological process;
• Step 2:
• selecting coils according to a current state of an electrogalvanizing line;
• the selecting step comprising:
• selecting the coils of the electrogalvanizing line to be processed according to a current line state and an inventory and production conditions of preceding lines:
• firstly, judging postprocessing liquid k adopted by the current line;
• computing the total weight WkP of the coils that have been processed by using the postprocessing liquid k;
• determining a current processing capacity of the postprocessing liquid according to a rated processing range of the postprocessing liquid[Lkp, Ukp] set by a system:
• Q=UkP−WkP;
• if UlP−WkP≦U, the selection steps of the coils are as follows:
• Step 2.1:
• judging the current processing state of the line;
• finding a width of a last coil in a production schedule before a current formulated production schedule, that is an upper limit of an available processing width WA of a current roller;
• Step 2.2:
• determining a total weight of available coils in a current production period according to a preceding inventory of the electrogalvanizing line and a processing condition of a preceding production line;
• classifying the coils in a required postprocessing mode;
• computing a total tonnage Wk of the available coils which should be processed by using the postprocessing liquid k and have the width of not greater than WA;
• judging as follows:
• if Wk≦Q, all the coils, which should be processed in the required postprocessing liquid k and have the width of not greater than WA, are selected;
• recording all related coil numbers;
• if Wk>Q, selecting from the coils which should he processed in the required postprocessing liquid k and have the width of not greater than WA, the selecting step comprising:
• Step 2.2.1:
• if there is no coil whose width is greater than or equal to WA+LW in a coil set, selecting coils from narrow to wide until newly added coils cause a current total weight of the selected coils to exceed UkP−WkP;
• Step 2.2.2:
• if there are coils whose widths are greater than or equal to WA+LW in the coil set, computing a total tonnage W′ of the coils whose widths are not less than WA+LW;
• if W′≧UkP−WkP, selecting coils whose width is not less than WA+LW from wide to narrow until the total weight of the selected coils exceeds UkP−WkP;
• otherwise, selecting all the coils Whose widths are not less than WA+LW and selecting coils whose width is less than WA+LW from narrow to wide until the total weight of the current selected coils exceeds UkP−WkP;
• Step 2.2.3:
• if the total weight of the selected coils does not meet a lower bound of the total weight of the selected coils, selecting coils required to be processed in the other postprocessing liquid;
• selecting coils according to an ascending order of postprocessing codes, i.e., firstly selecting the coils in a postprocessing mode g=k+1;
• updating an upper weight limit of the selected coils as U′=U−(UkP−WkP):
• (1) if the total weight of available coils required to be processed by using a postprocessing liquid g meets Wg≧U′, selecting coils required to be processed by using the postprocessing liquid g from narrow to wide until the total weight of selected coils exceeds U;
• (2) if the total weight of available coils required to he processed by using the postprocessing liquid g meets Wg<U′, selecting all the coils required to be processed by using the postprocessing liquid g, updating k=k+1, and going to step 2.2,3;
• wherein, updating k as the smallest postprocessing code if a current postprocessing code k in the step 2.2.3(2) is the largest postprocessing code;
• the current postprocessing code g of selecting means the postprocessing code that the selected coils correspond to;
• If UkP−WkP>U, the selection steps of the coils are as follows:
• Step 2-1:
• judging the current processing state of the line;
• finding the width of the last coil in the schedule before the current formulated schedule, that is the upper limit of the available processing width WA of the current roller;
• Step 2-2:
• determining the total weight of available coils in the current production period according to the preceding inventory of the electrogalvanizing line and the processing state of a preceding production line;
• classifying the coils in a required postprocessing mode;
• computing the total tonnage Wk of the available coils which are required to be processed by using the postprocessing liquid k and have the width of not greater than WA;
• judging as follows:
• if Wk≦U, all the coils, which are required to be processed by using the postprocessing liquid k and have the width of not greater than WA, are selected;
• recording all related coil numbers;
• if Wk>U, selecting from the coils which are required to be processed by using the postprocessing liquid k and have the width of not greater than WA:
• Step 2-2-1:
• if there is no coil whose width is greater than or equal to WA+LW in the coil set, selecting coils from narrow to wide until the selected coils result in that the total weight of the selected coils exceeds U;
• Step 2-2-2:
• if there are coils whose widths are greater than or equal to WA+LW in the coil set, computing the total tonnage W′ of the coils whose widths are not less than WA+LW;
• if W′≧U, selecting coils whose width is not less than WA+LW from wide to narrow until the selected coils result in that the total weight of the selected coils exceeds U;
• otherwise, selecting all the coils whose widths are not less than WA+LW and selecting coils whose width is less than WA+LW from narrow to wide until the total weight of the selected coils exceeds U;
• Step 2-2-3:
• if the total weight of the selected coils does not meet the lower bound of the total weight of the selected coils, selecting coils in the other postprocessing mode;
• selecting coils according to the ascending order of the postprocessing codes, i.e., firstly selecting the coils in the postprocessing mode g=k+1;
• updating the upper weight limit of the total weight of the selected coils as U′=U−Wk:
• (1) if the total weight of available coils required to be processed by using the postprocessing liquid g meets Wg≧U′, selecting coils in the postprocessing mode g from narrow to wide until the total weight of the selected coils exceeds U;
• (2) if the total weight of available coils required to be processed by using the postprocessing liquid g meets Wg<U′, selecting all the coils in the postprocessing mode g, updating k=k+1, and going to step 2-2-3;
• Step 3:
• setting an initial processing schedule of the selected coils of the electrogalvanizing line;
• classifying the selected coils, then the coils with same postprocessing code form a cluster;
• for any coil cluster, scheduling the coils from thick to thin or from thin to thick in order to minimize the total changeover costs of a coil schedule in the cluster;
• for two adjacent clusters, if the coils in a preceding cluster are scheduled from thin to thick or from thick to thin, the coils in a next cluster are scheduled from thick to thin or from thin to thick;
• in this way, the thickest or thinnest coil in the next cluster is processed after the thickest or thinnest coil in the preceding cluster;
• the method is as follows:
• Step 3,1:
• initializing the current postprocessing code k as a minimum postprocessing code in the selected coils;
• Step 3.2:
• if all the coils in the postprocessing mode are scheduled, obtaining an original processing schedule of the coils and outputting a result;
• otherwise, going to step 3.3;
• Step 3.3:
• scheduling coils required to be processed by using the postprocessing liquid k from wide to narrow;
• classifying the coils required to be processed by using the postprocessing liquid according to their widths, thus g coil sets Ωk1, Ωk2, . . . , Ωkg are formed;
• Step 3.4:
• scheduling the coils in the coil sets Ωk1, Ωk2, . . . Ωkg, respectively, to form a first and a second coil schedules, wherein the first schedule comprising:
• scheduling the coils in the coil set Ωkg with odd labels from thick to thin;
• scheduling the coils in the coil set Ωkg with even labels from thin to thick;
• the second schedule comprising the steps:
• scheduling the coils in the coil set Ωkg with odd labels from thin to thick;
• scheduling the coils in the coil set Ωkg with even labels from thick to thin;
• comparing the first and second schedules;
• setting the coil schedule with the minimum total stability defects as the initial coil schedule SI of the selected coils of the electrogalvanizing line;
• Step 4:
• improving the coil schedule of the electrogalvanizing line in time;
• the improving method comprises the following steps:
• Step 4.1:
• initializing the parameters of the improving method of a system stability;
• setting a current processing schedule SB of the coils of the electrogalvanizing line as SI;
• obtaining a current selected coil set CS and a current available coil set CA, wherein CS is a coil set for all the coils selected in the current processing schedule of the electrogalvanizing line;
• CA is a coil set of all the coils which are in inventory or can be sent to the electrogalvanizing line in time based on the processing state of the preceding line but not selected in the current coil processing schedule of the electrogalvanizing line;
• |CS| is the number of the coils in the current selected coil set CS;
• |CA| is the number of the coils in the current available coil set CA;
• obtaining the coil processing schedules m1, m2, . . . , m|CS| corresponding to the current coil processing schedule SB of the electrogalvanizing line, wherein mi is a coil which is the ith processed coil in the current coil processing schedule of the electrogalvanizing line;
• setting a stability estimation value as the formula:
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• in the formula, the stability estimation value is a system stability penalty of the coil processing schedule S, the smaller the penalty is, the stabler and more practicable the coil schedule is.
• Step 4.2:
• computing the stability estimation value f(SB) of the current coil processing schedule of the electrogalvanizing line;
• Step 4.3:
• determining a candidate improvement set P of the current coil processing schedule SB of the electrogalvanizing line;
• obtaining the improving method of the coil processing schedule, as follows:
• (1) inserting the coils:
• on a premise of not violating the production capacity constraints and postprocessing batching constraints, obtaining a candidate improved coil processing schedule by inserting new coils h in the current coil processing schedule;
• the positions of the new coils h in the coil processing schedule shall meet the processing constraints (1) to (11) set by the system;
• (2) deleting the coils:
• on the premise of not violating the production capacity constraints and postprocessing batching constraints, obtaining a candidate improved coil processing schedule with lower stability estimation value by deleting the coil (i=1, 2, . . . , |CS|) from the current coil processing schedule while ensuring that the width and thickness switching range of coil mi−1 and coil mi+1 does not violate the constraints (10), (11) after deleting the coil mi;
• (3) adjusting coil selection schemes:
• on the premise of not violating the production capacity constraints, postprocessing batching constraints and the processing constraints (2) to (11) set by the system, obtaining a candidate improved coil processing schedule with lower stability estimation value by exchanging the coils in the coil CS in the current coil processing schedule and the coils in the current available coil set CA;
• (4) adjusting the coil processing schedule:
• On the premise of not violating the production capacity constraints and postprocessing batching constraints, obtaining a. candidate improved coil processing schedule with lower stability estimation value by adjusting the positions of the coils in the current coil processing schedule through the exchange neighborhood and the 2-opt neighborhood of the current coil processing schedule;
• wherein, the exchange neighborhood of the current coil processing schedule refers to:
• a set of all the possible coil schedules obtained by exchanging the positions of any two coils in the coil processing schedule of the electrogalvanizing line on the premise of not violating the processing constraints (2) to (11) set by the system;
• 2-opt neighborhood refers to:
• a set of all the possible coil schedules obtained by exchanging any two coil adjacent relations in the coil processing schedule of the electrogalvanizing line on the premise of not violating the processing constraints (2) to (11) set by the system;
• Step 4.4:
• establishing a reference set of improvement schemes of the coil processing schedule;
• adding the previous b1 candidate improvement schemes with better stability estimation values in the current candidate improvement set P into the reference set, i.e. RefSet={x1, . . . , xb1};
• removing the b1 candidate improvement schemes from the candidate improvement set P;
• computing the minimum distance between each candidate improvement scheme in the current candidate improvement set P and the current coil scheduling scheme in the reference set;
• adding the candidate improvement scheme of the coil processing schedule with the largest minimum distance from the reference set into the reference set RefSet;
• removing it from the candidate improvement set P;
• repeating the process b2 times;
• then, the current reference set RefSet={x1, . . . , xb}, b=b2+b2;
• Step 4.5:
• generating b(b-1) new coil improvement schemes based on any pair of coil processing schedules in the reference set RefSet by using the combined method of the coil scheduling schemes;
• improving the new improvement schemes;
• obtaining candidate coil scheduling improvement schemes with better stability by using steps 4.3 (1) to (4);
• the combined method of the coil scheduling schemes comprises the steps:
• firstly, contrasting the coil selection of two coil processing schedules;
• obtaining a set comprised by the coils selected by the two coil scheduling schemes;
• secondly, determining the processing positions of the coils in the set comprised by the coils selected by the two coil scheduling schemes;
• if adjacent coils both belong to set comprised by the coils selected by the two coil scheduling schemes, the adjacent relation in the coil processing schedules with better system stability is adopted;
• if adjacent coils do not belong to the set comprised by the coils selected by the two coil scheduling schemes, trying to insert the coils into primal positions;
• obtaining the coil processing schedule with better evaluation;
• Step 4.6:
• updating e candidate improvement set P;
• replacing solutions with poor stability in the candidate improvement set P by the new candidate coil scheduling improvement schemes with better stability;
• Step 4.7:
• if the time that the best candidate improvement scheme in the candidate improvement set P is not improved reaches the upper limit of non-improvement iterations, stopping selecting the candidate improvement scheme with the best evaluation value in the candidate improvement set P as the current improvement scheme;
• otherwise, going to the step 4,4.