Dynamic scheduling with production process reconfiguration for cold rolling line

Dynamic scheduling with production process reconfiguration for cold rolling line Li Wang, Jun Zhao, Wei Wang, Liqun Cong Research Center of Information and Control, Dalian University of Technology, Dalian 116024, China (e-mail: wangli ly@ 126.com; zhaoj@dlut.edu.cn; wangwei@dlut.edu.cn). Shanghai Baosight Co. Ltd.,Shanghai 201203, China (E-mail:congliqun@baosight.com). Abstract: The manufacturing process of cold rolling line in steel industry is often complicated due to its long production flow, a large number of product categories and machines. The static production plans usually have to be repeatedly assigned when some unexpected circumstances occur, for example machine malfunction and material delay. In this study, a distributed dynamic scheduling model based on multi-agent is established for solving the rescheduling problem of cold rolling line, in which a dynamic reconfiguration of the production flow is further studied to realize the balance of machine yields ability and load. For solving the established model, an ant colony optimization based on dynamic constraints is proposed. The practical experiments with real data of Shanghai Baosteel Co. Ltd demonstrate that the proposed method is effective to the production rescheduling of cold rolling line. Keywords: Cold Rolling; Planning and Scheduling; Multi-agent; Ant Colony Optimization; Reconfiguration, 1. INTRODUCTION Along with the production process gets more and more complex in steel industries, the reasonable order planning for cold rolling line becomes a key issue to improve the competition ability of cold rolling plants, reduce the production cost and enhance the delivery satisfaction. There are many studies concerning production planning and scheduling for the cold rolling lines. Verdejo (2009) proposed the scheduling method of galvanizing lines with continuous annealing mill. Zhao et al. (2008) constructed the coil-merging optimization and batch planning model for a cold mill. The discrete differential evolution algorithm and a hybrid heuristics were put forward. Liu et al. (2006) formulated a multi-objective order planning model for manufacturing steel sheets and designed a modified particle swarm algorithm. Wang et al. (2009) presented an order scheduling model using a multi-objective programming for the whole cold rolling process and a time-segment ant colony algorithm was proposed. However, most of the achievements was centralized and static scheduling, ignored some practical problems, such as unexpected faults, multiple production flows and so on, and could not satisfy the requirement of parallel, dynamic, distributed and continuous production of cold rolling production. Multi-agent technology had been regarded as a promising approach to resolve the scheduling and optimization problem. Lai et al. (2007) presented a general framework for modeling a distributed scheduling problem and attaining The corresponding author of this paper is Jun Zhao, e-mail: zhaoj@dlut.edu.cn. the globally beneficial schedule via fuzzy constraint-based agent negotiation mechanism. Xiao et al. (2009) proposed a distributed self-adaptable scheduling algorithm based on Q-learning in an open multi-agent system to resolve a tasks allocation by means of the interaction and decision-making process. In addition, Anosike and Zhang (2009) proposed a multi-agent approach based on an integration decision platform for manufacturing planning and control. A dynamic scheduling system based on the multi-agent for cold rolling production is established in this paper, where the orders are automatically allocated to multiple flows and the process of a part of orders is reconfigured. Then, the dynamic constraint ant colony optimization (DCACO) is put forward. In the algorithm, the restrictive conditions of searching process are variables along with the inventory, unexpected faults, scheduling date and orders priority, etc. The simulation shows that the presented approach is effective to the production scheduling of cold rolling lines. 2. PROBLEM DESCRIPTION Figure 1 depicts the main production flows of a cold rolling plant in BaoSteel. Four production flows corresponding to the products include: 1) from the pickling line to the cold mill; 2) from the pickling line to the skin passing mill or the second cold mill; 3) from the pickling line to 1# tinning line passing; 4) from the pickling line to 2# tinning line. The cold rolling mill is the core of production process in steel industry, after which the production process is divided into multiple parallel flows. The production process of orders is able to be reconfigured between the second Copyright by the International Federation of Automatic Control (IFAC) 12114

The architecture of multi-agent system is open, agile and flexible, can be categorized into centralized architectures, distributed architectures and hybrid architectures and mix communication and negotiation mechanism. The multiagent system is more suitable for the distributed scheduling system (Zhang and Xie 2007; Guo and Zhang 2010). This paper proposes a dynamic scheduling system based on multi-agent and Figure 2 depicts the architecture of proposed system, the relationship among modules, the directions of transferring data and the control flows. Fig. 1. Main process flows of cold rolling plant cold mill and skin-passing mill due to the similarity of products, and the same is true between two tinning mills. In the course of planning, many factors should be adequately taken into account such as the diversity of orders, productivity of mills, and limitation of inventory and so on. Moreover, the production process is dynamic due to the change in order priority, processing delay, machine breakdown, and the unavailability of row materials, etc. At present, the major drawbacks of current production scheduling mode reads as follows: 1) The order plan is generally conducted by skilled dispatchers. However, it is very difficult to make the practical order plan because of hardly considering all constraints at the same time. 2) The planning horizon is only for a few days, which is against the demand to forecast a long-term production condition. 3) The flexibility, robustness, applicability and stability of production process are difficult to be guaranteed since the lack of real-time in the manual method. 3. MULTI-AGENT BASED DYNAMIC SCHEDULING FOR COLD ROLLING LINE Along with the transformation of production mode of steel plant, the centralized planning and scheduling method has not fulfilled the requirement of mass customization, parallel production and distributed control. The multi-agent technology meet the request of complexity, heterogeneity and dynamicity of distributed production process (Shen et al. 2006). Cowling et al. (2004) proposed a multi-agent architecture for integrated dynamic scheduling of the hot strip mill and the continuous caster and uses a tabu search algorithm to obtain the scheduling result. Ji and Lu (2009) constructed a hybrid multi-agent scheduling system with extremal optimization, which was used to deal with the integrated scheduling for steel making, continuous cast and hot strip mill. Li et al. (2010) presented an approach to facilitate the integration of planning and scheduling, and an optimization agent was used to manage the interaction and communication between agents. However, the multiple parallel flows and reconfigurable process of cold rolling plant of BaoSteel determines that the mentioned methods cannot be satisfied with the requirement of practical production. 3.1 Architecture of Multi-Agent System Fig. 2. Architecture of MAS dynamic scheduling system According to the realities of the whole cold rolling line, the assumptions are given as follow. Hypothesis 1. Orders in stores are satisfied with constraints and can be yielded. Hypothesis 2. Cost and time of transportation between mills can be ignored. Hypothesis 3. The capacity of production of mills is a constant except machine halt in scheduling day. Three definitions related to the production demand are given below Definition 1. The latest feeding time LMT l and the earliest feeding time EMT l indicate the date at which the hot rolled coils have to be provided and before which raw hot rolled coils are forbidden to be offered to the production line, respectively. The two of terms LMT l and EMT l are used to ensure the continuous producing and prevent over stock. Definition 2. Slack time window is the interval between the latest feeding time in two different flows, which is represented with RP T = LMT l1 LMT l2. where l1 and l2 depict two different productions flows. Definition 3. The latest fabrication time LST ahead of delivery date is at which order has to be put into production, otherwise the delivery date of this order will be exceeded since the process cycle P T is necessary. LST i = LF T i P T i, where LF T i and P T i represent the latest delivery date and the process cycle of order i, respectively. 3.2 Agent Description 1) Planning Agent The planning agent that optimizes the orders assignment in the whole production flow is the core module in the dynamic scheduling system. The scheduling result can be adjusted according to the practical data from other agents. The planning agent is defined as a six tuple S j = sc j, sd j, ac j, reo j, ren j, r j }, where sc j represents the current state of agent j, sd j depicts scheduling objective of agent j, ac j express the action to employ, reo j represents 12115

resource to utilize, renj denotes the required and insufficient resource of agent j and r j implies the rules and constraints in the course of orders allocation. S j will be changed in the light of object to communicate with. Notations in objective function as follow: f ca is the objective functional value for scheduling, N is the number of orders, N t is the number of orders allocated at the t day, and T means the scheduling cycle, l = 1,, L is the flow sign and L = 2 because there only are two master flows at present,and m is the identification of mill. W i is the weight of order i, tf i is the make span of order i where tf i = td i + P T i, tdi is the date at which order i put into operation, and EF T i and LF T i represent the earliest delivery date and the latest delivery date respectively. CP lmt is the normal productivity of mill m in the l flow at the t day. α, β and γ depict the compression coefficient of three sub-objectives for unifying the order of magnitude. ω 1, ω 2 and ω 3 denote the significance of three sub-objective, and ω 1 + ω 2 + ω 3 = 1. s lmt expresses the stock in the stuff inventory of mill m in flow l, SL m is the minimum stock level of material of mill m, SH m is the maximum stock level of material of mill m. O lmt represents the output of mill m at t day, and T H t expresses the productivity of cold rolling mill at t day. tp l is the feeding time in l production flow direction. ytm i 1 swith of mill m to order i at t day = x i 1 order i allocated to mill m of l flow at t day lmt = Objective function N f ca = ω 1 α min( max0, tf i LF T i } s.t + N maxef T i tf i, 0}) +ω 2 β min T M N m=1 M l t=1 l=1 m=1 y i tm T L N t +ω 3 γ min( ( W i x i lmt CP lmt ) ) (1) s lmt = s l m(t 1) + O l (m 1)(t 1) O l m(t 1) (2) SL m s lmt SH m (3) L N l W li x i lt T H t (4) l x i = 1 (5) i N EMT l tp l LMT l (6) Equation (1) consists of three parts: the first item is to minimize the earliness and tardiness of orders, the second one is to minimize the number of the shift times of equipments for various products, and the third is to minimize the violation degree of productivity restriction. Equation (2) is the constraint of the change of the material stock of mill m at t day. Formula (3) represents the limitation of material inventory of mill m. Formula (4) is the constraint of capacity of the whole line, i.e. the total quantity of orders of newly entering the production line must be less than the capacity of cold mill. Formula (5) represents order is only selected once. Formula (6) is the feeding time constraint of l production flow direction. Exceed the limitation LMT l, the production process is to halt and ahead of the EMT l, the cost of inventory of work in process is to be increased. 2) Reconfiguration Agent In many conditions, the assigned raw material of mills dissatisfy the their capacity because of various unexpected reasons so that it is difficult to exert full capacity of production flows. For solving the problem, the process of orders in the second cold mill, the skin-passing mill and two tinning mills can be reconfigured just as description in section 2. The reconfiguration agent receives data from the mill agent and the storage agent, then dynamically rearranges the production process of orders, and transmits the result to the planning agent. Notations in the course of reconfiguration: f cr is the objective functional value of reconfiguring order allocation, N r is the number of reconfigured orders, W i represents the weight of order i, m = 1, 2,, M} is the identification of mill, the m denotes the identification of reconfiguration target mill, P m is the maximum capacity of mill m, SH m is the maximum material inventory of mill m, SL m is the minimum inventory of mill m. CP m is the normal capacity of mill m, ip m is the original material orders of mill m. ST m is the material inventory allocated to mill m before reconfiguration. 1 swith of mill due to reconfiguration of order i s i = 1 reallocating order i to mill m x im = Objective function of reconfiguring production process: N r f cr = ω 1 α min( s i ) s.t. +ω 2 β N r M ( W i x im P m ) m=1 +ω 3 γ min Nr ( M N r (CP m W i x im ip m ) m=1 (7) W i x im + ST m ) SH m (8) Nr SL m (ST m W i x im ) (9) Nr W i x im CP m (10) 12116

i N r = 1 (11) Equation (7) is the objective function of order reconfiguration, including three parts: the first item is to minimize the number of times of switch owing to reconfiguration for picking reconfigurable order, the second one is to minimize the level of exceeding capacity of mill, and the final one is to minimize the level of waste capacity for the objective of reconfiguration. Equation (8) represents the level of material inventory of mill m has to be less than the maximum stock after receiving reconfiguration orders. Equation (9) indicates the level of remaining material inventory of mill m has to be greater than the minimum stock after delivering reconfiguration orders to target mill m. Equation (10) and (11) represent the constraint of the quantity of reconfiguration orders of signal mill and each order is only selected once, respectively. 3) Task Agent Each order is defined as a task agent, denoted by C i = time i, cons i, weit i }. time i is the process time constraint in different stage and is to be altered along with production process and time i = [est im, lst im ]. est im and lst im represent the earliest process time and the latest process time of order i in mill m, respectively. cons i depicts the specification of order, including width, thickness and hardness, and so on. weit i represents the weight of order i. Task agent can be created, preserve the information of order state and autonomously decide whether to be allocated. It has a life cycle from entering cold rolling line to the achievement of production which makes task agent show different states in different stage. 4) Other Relative Agent Various mill agents and material storage agents are used to monitor the state of mill and the transformation of material stock of mills and to transmit information to the management agents. The estimating result agent is to evaluate the production planning according to the knowledge base comprising the regulations about mill, output and inventory. If don t suffice the capacity of the whole flow, the result of the scheduling will be the initial value for rescheduling. The mill manage agent and the inventory manage agent receive data from mill agents and storage agents, interact with reconfiguration agents, and transmit production and state data. 4. DYNAMIC SCHEDULING METHOD BASED ON ANT COLONY OPTIMIZATION Because ant colony optimization (ACO) searches the optimal solution based on the solution space model, the search direction, the length of candidate solution and the termination conditions are controlled. ACO shows the obviously capability to solve multi-objective combinational optimization and has more advantage to massive optimal scheduling problems (Dorigo et al, 2006; Yagmahan et al, 2008; Xing et al, 2010). However, most of the studies are based on static information against the practical dynamic distributed production of cold line. Recently, the dynamic scheduling system based on multi-agent with ACO has emerged, which decreased cost of the negotiation and communication and more likely gained the global optimization. Xiang and Lee (2008) combined ant colony intelligence with local agent coordination to make autonomous adaptive agents. Leung et al. (2010) presented an ant colony optimization algorithm was incorporate into an established multi-agent system platform to realize integration process planning and shop floor scheduling. Methods above could not be directly applied to cold scheduling system because of particular properties of production process. The dynamic constraint ant colony optimization (DCACO), which uses the rolling searching strategy daily to establish solution and utilizes time, productivity and inventory as the dynamic constraints of pheromone and heuristic value for the whole flow planning and reconfiguration of orders, is proposed in this paper. 4.1 Method for orders allocation in the whole flow The daily capacity of cold rolling mill is considered as the productivity of the whole line because the cold rolling mill is the common mill of the whole flow. The assignment of orders is completed in the course of ant colony searching foods. In order to decrease the search space, the algorithm searches orders within seven days on every time. 1) Heuristic Value Equation 12 shows two different heuristic values at latest feeding time and at slack time window. Moreover the closer the delivery date of order is to scheduling day and the smaller the deviation between the weights of order and the remaining capacity of cold mill is, the greater the heuristic value of the order will be. If the order i of flow l having reached the latest feeding time has highest priority to be allocate the capacity, then the heuristic value of order i is calculated firstly and is greatest and one of another flow a is calculated. W i η i = e LF Ti LMT l t = LMT, i N mat l C l W (12) j η j = e LF Tj LMTa j (N N l ) T H mat l Where η i is the heuristic value of order i to be picked into flow l, Mat l represents the necessary material amount to be assigned to flow l, W i denotes the weight order i into flow l. η j is the heuristic value of remaining order j to be distributed to flow a, W j is the weight of order j to be allocated to flow a. it is the scheduling date, TH represent the capacity of cold mill, LF T is the latest delivery date of order, N is the total amount of orders assigned and N l is the number of orders allocated into flow l. Equation 13 indicates heuristic value in the slack time window. W i η i = e LF Ti t (13) T H C m C m is the capacity consumed in the slack time window. 2) Initial Pheromone τ i 0 = cv i j N t cv j (14) 12117

cv i = LF T i t P T i (15) where, cv i is the critical value of order i denoting the urgency of putting on operation, P T i represents the productive cycle. 3) Pheromone Updating Rule and Selection Probability In this paper, updating pheromone and selection probability in DCACO algorithm is implemented according to the update rule of ant colony system (ACS)(Dorigo et al, 2006). 4.2 Method for reconfiguration of orders The process of reconfiguration of orders is divided into two different directions, one is the second cold mill and skinpassing mill and the other is two tinning mills. The orders to be reconfigured include orders which exceed the capacity of mill and can t be produced during mill downtime because of unexpected fault or scheduling maintenance. The total amount of foods for ant colony in DCACO is calculated according to orders to be reconfigured and the capacity of target mill. 1) Heuristic Value η i W i r = + CP m C mt ηp i W i = CP m C mt Q q=1 e SPqi SPqj (16) where ηr i is the heuristic value for reconfiguration of orders in second cold mill and skin-passing mill, ηp i is the heuristic value for reconfiguration of orders in tinning mills, CP m is the capacity of mill m, C mt is the capacity having be employed of mill m, W i is the weight of order i to be reconfigured, and q = 1,, Q} represent the identifications of indexes, including the width, the thickness and the hardness, SP q is the index q. 2) Initial Pheromone for Reconfiguration Process τ 0 = e RTi t (17) where RT i is the date of order i reaching the material inventory of mill, t is the date of reconfiguration. The pheromone of orders reaching the material inventory over three days is set to 0. 3) Constraint of Search Range The search range of algorithm has to be restricted for the continuous production, the reduction of wasting capacity and the avoidance of confused reconfiguration. The limitations include that the orders to be reconfigured in the material storage are only search, the orders in the inventory over three days is not reconfigured, the mill is to stop receiving orders for reconfiguration when reaching upper limit of material inventory, the material stock of mills is more than the lower limit, and the reconfiguration is to be forbidden if the two mills reconfiguring have surplus capacity. 5. SIMULATION The actual data from a cold rolling plant in seven months in BaoSteel, including static information and dynamic information such as the scheduling maintenance, production process switch, unexpected downtime and the change of inventory, etc, are used to demonstrate the validity of the proposed method. The major objectives and sub-objectives correspond to the weighted sum of sub-objectives and sub-objectives of the Equation (1). The number of orders is from 502 to 662 every month. The width of products in orders ranges from 700mm to 1040mm, the thickness ranges from 0.15mm to 0.83mm, and weight of orders ranges from 20 and 1000 tons. Table 1 shows the halt time data of the main machines (time in hours) in seven months, including skin-passing mill (SPM), second cold mill (SCRM), 1# tinning mill (1# TM) and 2# tinning mill (2# TM), in which more than 2-hour downtime is calculated as statistical results. From the table, the downtime of the machines usually exceeds dozens of hours and even the sum of shutdown days of four mills surpasses twenty days every month. The recurrent shutdowns lead to the discontinuity of production process, the reductionn of the flexibility and applicability. Table 1. Description of downtime data Month Amount of orders SPM SCRM 1#TM 2#TM (hour) (hour) (hour) (hour) 1 502 441.6 341.8 126.3 222.7 2 637 478.4 208.9 71.5 281.7 3 662 449.5 281.7 53.3 343.6 4 631 398.2 373.2 66.3 403.5 5 557 489.6 171.5 134.8 203.6 6 616 199.2 171.9 248.3 114.9 7 583 298.7 97.1 42.2 133.4 Table 2 shows the comparative result from the proposed method, genetic algorithm (GA) and tabu search (TS). The result of the approach presented is better than others. The length of individual on behalf of the number of orders to be allocated is constant in GA and TS, but the length is difficultly defined because the number of orders is a variable along with different production conditions. In the research background of this paper, the process of search orders with GA and TA deviates from the actual condition. Table 3 denotes the comparison among the results of manual manner, static scheduling (Wang et al. 2009) and dynamic scheduling proposed. The sum is the sum of three sub-objectives of Equation 1, time is the first subobjective, num is the second one and cap is the third one. Table 2. Comparison of results among algorithms Month Amount of orders GA TS DCACO 1 502 5.34 5.25 5.21 2 637 6.20 6.31 6.02 3 662 6.03 5.85 5.70 4 631 7.61 7.26 7.06 5 557 5.70 5.73 5.56 6 616 6.54 6.73 6.38 7 583 6.20 6.17 6.06 The smaller objective function values are, the better the results of order planning and scheduling will get. The 12118

Table 3. Comparison of three methods ID Results by scheduler Results by static method Results by method proposed sum time num cap sum time num cap sum time num cap 1 6.68 10.5 7.3 3.01 5.12 8.56 5.8 2.37 4.92 8.06 5.4 2.21 2 6.05 12.5 8.8 2.70 5.63 10.3 7.0 2.44 5.33 9.83 6.2 2.14 3 5.41 15.6 9.0 2.22 5.97 9.26 7.6 1.80 5.65 9.06 7.1 1.70 4 6.79 15.3 8.9 2.93 5.67 13.8 8.3 2.23 5.07 12.3 7.5 2.01 5 6.42 12.4 8.7 2.74 4.93 9.61 7.1 2.13 4.50 8.70 6.6 1.93 6 6.63 13.6 8.5 2.89 5.36 11.3 8.0 2.34 5.12 10.5 7.5 2.01 7 6.44 10.5 8.0 2.89 5.48 10.2 7.3 2.21 4.91 9.82 6.7 2.02 objective value of the proposed method in this paper is 7% less than the result of static scheduling, and is much better than one of manual. The presented approach achieves the dynamic order planning and scheduling by means of the productivity and inventory so as to improve the agility and productivity, reduce the imbalance of capacity distribution and hold rational inventory and to decrease the impact of scheduling maintenance and unexpected halt. 6. CONCLUSION The major goal of order planning and scheduling in cold rolling line is to ensure the delivery date, rationally arrange productivity and reduce cost. The traditional scheduling methods were not suitable for the distributed production and led to the reduction of the adaptability, agility, and flexibility. This paper proposes a dynamic scheduling approach based on multi-agent and a class of dynamic constraint ant colony optimization on account of the production practice for the dynamic scheduling of the whole flow. The practical data is used to demonstrate the validity of the approached proposed. The simulations show that method proposed is effective and meets actual production. ACKNOWLEDGEMENTS This work is supported by the National Natural Science Foundation of China (61034003). The cooperation from the cold rolling plant of Shanghai Baosteel Co. Ltd., China in this work is greatly appreciated. REFERENCES Anosike A.I, Zhang D.Z. (2009) An gent-based approach for integrating manufacturing operations. International Journal of Production Economics, 121(2): 333-352. Dorigo M, Birattari M, and Stiitzle T. (2006) Ant colony optimization. IEEE Computational intelligence magazine, 1(4): 28-39. Guo Q. L, Zhang M. (2010) An agent-oriented approach to resolve scheduling optimization in intelligent manufacturing. Robotics and Computer-Integrated Manufacturing, 26(1): 39-45. Ji R. G. and Lu Y. Z. (2009) A multi-agent and extremal optimization system for steelmaking continuous casting - hot strip mill integrated scheduling. 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