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The scheduling systems of the caster and the hot strip mill have very different objectives and constraints. ... Email: [email protected], Fax: +44 115 9514249, Tel: +44 115 9514215. 2 .... Raw materials are first melted together in a blast furnace.
A Multi-Agent Architecture for Dynamic Scheduling of Steel Hot Rolling P. Cowling1, D. Ouelhadj2, S. Petrovic3 School of Computer Science and IT, University of Nottingham, Jubilee Campus, Nottingham, NG8 1BB, UK. Abstract

Steel production is a complex process and finding coherent schedules for the wide variety of production steps in a dynamic environment where disturbances frequently occur is a challenging task. Steel production involves a range of processes: continuous caster, hot strip mill, furnaces. The scheduling systems of the caster and the hot strip mill have very different objectives and constraints. It is important that the schedules for these two processes are able to react to the presence of real time information concerning production failures and customer requests. In this paper we propose a multi-agent architecture for integrated dynamic scheduling of the Hot Strip Mill and the Caster. Each process in the steel production environment is assigned to an agent which performs, independently, its dynamic scheduling at a local level by using a Tabu search meta-heuristic optimisation method. In this architecture, we have elaborated the dynamic scheduling of the Hot Strip Mill Agent. The other agents in the architectures simulate the production of the coil orders and the real-time events concerning the non-availability of coils. The dynamic scheduling of the Hot Strip Mill agent takes into account local objectives, real time information and information received from other agents. To address the problem of dynamic scheduling of the Hot Strip Mill, schedule repair and complete rescheduling strategies are presented and their performance is assessed with respect to measures of utility, stability and robustness. We report experiments which have been carried out to evaluate the performance of these strategies. Key words: Steel production, dynamic scheduling, rescheduling, multi-agent systems, Tabu search.

1. Introduction For decades, the steel industry has been a powerful symbol of an increasingly global market economy, providing the most important material for many other industries. In recent years, global competitiveness and changing customer requirements have further underlined the importance of effective planning, scheduling and control systems. Competitive pressures are moving manufacturers to respond to emerging trends including high quality, low-cost, just in-time (JIT) delivery, smaller order size for a more precisely defined product, as well as the reduction of product life cycles [Tan 00b][Tan 01]. Steel production needs to handle the dynamic nature of demands. From an emphasis on the scheduling optimality for simplified models of steel production, the focus has moved to scheduling flexibility using complex models.

1

Steel production is a multi-stage process involving a variety of processes [Cow 01b][Cow 00a]: continuous casters, furnaces, hot strip mill, slabyard. The scheduling process for Casters and the Hot Strip Mill have very different objectives and constraints and are both subject to real time events. Most of the literature dealing with steel production scheduling is dominated by static scheduling concerned by the search for techniques to achieve optimal schedules using simplified models solved by operational research techniques such as branch and bound [Bal 91][Lal 87][Tan 00a]. To achieve acceptable solutions to more complex models heuristics are used such as simulated annealing, tabu search, genetic algorithms, neural networks, and expert systems [Cow 00a][Cow 99][Cow 95] [Dor 96][Lop 98][Num 94][Tan 00a][Tan 01]. Unfortunately, in the production environment, as soon as the schedule is released to the shop, it is subject to unpredictable disruptions (machine breakdowns, rush

Email: [email protected], Fax: +44 115 9514249, Tel: +44 115 9514215. Corresponding author. Email: [email protected], Fax: +44 115 9514249, Tel: +44 115 8466521. 3 Email: [email protected], Fax: +44 115 9514249, Tel: +44 115 951 4222. 2

orders, non-availability of raw materials, etc.), which may render the initial schedule infeasible. Dynamic scheduling is an important issue in steel production. It is a challenging new research area [Tan 01]. The problem of updating schedules in the most effective way in the presence of real-time information is one that is receiving increasing attention. Robustness is a desirable attribute of a predictive schedule as it focuses on minimising the effects of disruptions on the performance measure. Wu et al. [Wu 93] consider two possible measures: the deviation from the original job starting times, and the deviation from the original sequence (stability) for one-machine problem in the presence of machine breakdown. The scheduling objective is to minimise shop efficiency (makespan) and at the same time minimise system impact caused by schedule changes. Cowling et al. [Cow 01a] propose two measures, utility and stability, to decide whether to reschedule or schedule repair. The utility is the improvement of the objective function the stability is the deviation from the original schedule. Recently, Multi-Agent Systems (MAS) have proven a major success in dynamic scheduling and have been used for developing a wide range of dynamic scheduling applications [Cow 00b][Eug 99][Par 99][She 01]. The Yams system developed by Parunak [She 98] was one of the earliest agent-based manufacturing system which assigns an agent to each node in a control hierarchy (factory, cell workstation, machine). The main idea of Yams is the use of the CNP (Contract Net Protocol) [Smi 89][Fer 99] for inter-agent negotiation. Ouelhadj et al. [Oue 99], Rabelo et al. [Rab 98] describe a multi-agent architecture for dynamic scheduling in FMS where resources are represented by agents. The resource agents are responsible for scheduling the resources and they have no control over each other. They cooperate using the CNP, to produce a global schedule. Kouis et al. [Kou 97] propose the combination of multi-agent approach and dispatching rules. Shen et al. [She 01][She 00] present the combination of the mediation mechanism and the CNP for the scheduling/rescheduling of FMS. Ramos et al. [Ram 99] propose a holonic architecture for scheduling in manufacturing systems in which tasks and resources are represented by Holons and used the CNP for scheduling/rescheduling of tasks. Steel manufacturing involves several stages of production and it is an interconnected and interdependent system where both information and decision-making are logically and geographically distributed. Multi-agent systems appear to be well suited to complex steel production applications. Using a multi-agent system, the steel manufacturing shop floor becomes populated by the number of integrated heterogeneous intelligent agents with diverse goals, constraints and capabilities. These agents perform scheduling tasks in a dynamically adaptive fashion and have the ability to adapt themselves to the changes within the steel manufacturing shop floor.

This paper presents a new architecture for dynamic robust scheduling of Steel production. Section 2 briefly presents the steel production environment. Section 3 describes our architecture for the dynamic scheduling of Steel Hot Rolling Production. Section 4 will introduce the measures of utility, stability, and robustness used to evaluate a schedule in a dynamic environment. Section 5 presents results for our simulation prototype. Finally, conclusions are presented in section 6.

2. Steel production environment Each customer order requires the production of a number of coils with the required properties and each coil corresponds to one slab. A coil is described by its delivery due date and its physical proprieties such as: hardness, width and thickness. Steel production involves a range of processes (Fig. 1) [Cow 01b][Cow 95][Tan 00a][Lop 98]. Raw material

Ladle

BF

LT

BOF

Continuous Caster (CC) Slabs Coils

RF Hot Strip Mill (HSM) Fig.1 Steel production processes Raw materials are first melted together in a blast furnace (BF) to produce pig iron. The molten iron is transported to the steel-making shop. The principal stages of steelmaking take place in basic oxygen furnace (BOF) ladle treatment (LT), continuous casters (CC) and hot strip mill (HSM). In the basic oxygen furnace, oxygen is passed through the molten iron to reduce the carbon content. The resulting steel is then processed further in the ladle treatment facility to make steel of a certain chemical grade. The molten steel is transported to one or more continuous casters to form solid slabs with different dimensions. The slabs produced are stored in the slabyard (SY). Before the slabs are rolled to coils in the hot strip mill, they need to be reheated in the reheat furnaces (RF). The HSM has two sections: the roughing mill and the finishing mill. The roughing mill consists of one stand that reduces the thickness of a slab. The resulting strip is sent to the finishing mills, where there are several rolling

stands to progressively reduce the thickness of the steel strip to a required final thickness and width. The thin strip, thousands of feet in length is then coiled.

3. Multi-agent architecture proposed for dynamic scheduling of Steel Hot Rolling In this paper, we consider only the CC(s), the HSM and the SY whose schedule integration poses one of the greatest challenges. The Multi-agent architecture proposed is organised as a population of heterogeneous agents having a set of special skills: it implements the local scheduling model of the resource assigned to it, performs optimisation of its own objective function, reacts to realtime events and communicates and cooperates with other agents for global scheduling/rescheduling. We use a predictive-reactive methodology to handle real-time events based on the construction of a predictive schedule, which is modified through the dynamic interaction and cooperation of the agents. The architecture involves the following agents (Fig. 2): Hot Strip Mill Agent (HSMA), Continuous Caster Agents (CCA), SlabYard Agent (SYA) and User Agent (UA). User agent HSM Agent

3.1. Hot Strip Mill Agent (HSMA) The HSMA is responsible for creating an initial predictive schedule and the dynamic scheduling of the HSM in the presence of any unexpected event. The HSM scheduling problem is subject to various constraints [Cow 01b][Cow 00][Cow 99][Cow 95][Lop 98][Tan 00][Tan 01]. The first scheduling constraint concerns the rollers of the HSM that suffer wear and tear, therefore they are replaced at regular intervals. The set of coils produced between two consecutive changes of the finishing mill rollers is called a turn. The set of coils processed between two consecutive changes of the roughing mill rollers is called a shift. Rolling is then organised into shifts, where each shift is a set of turns. The second main constraint is set on smooth jumps in coil thickness and coil width. Smooth jumps in width and thickness, as well as wear on the rollers caused by coil edges require scheduling the coils of each turn in a coffin shape with respect to coil width (Fig. 3).

Rolls change

Shift

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certain coils from the original schedule can no longer be produced from the CCA due to production failures (raw material fails to arrive on time, slabs manufactured fail to meet right specifications, etc.), real-time events on the non-available coils are sent from the SYA to the HSMA in order to react to these events. Section 4 details the predictive-reactive scheduling of the HSMA in response to these real-time events.

CC-1 Agent

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Fig. 2 Multi-agent architecture for integrated dynamic scheduling of steel production Coil width Cooperation among the agents for generating and maintaining dynamically production schedules is realised by the exchange of asynchronous messages between the agents. Each agent has a message box where all incoming messages are stored. HSMA receives a request from the UA to produce the coils. After receiving the message, it uses a tabu search heuristic to find a good schedule and delegates to the SYA the task of producing the coils of the turn. SYA agent sends an announcement message to the CCA to provide a production schedule for the slabs. When

Fig. 3 Coffin shape The resulting scheduling problem has been formulated as the well-known Prize Collecting Travelling Salesman Problem (PCTSP) [Bal 91][Lop 98][Tan 00]. The coils are represented by a digraph G=(N, A), where N is the set of nodes and A the set of arcs with weights on both nodes and arcs. Each node i∈N corresponds to a coil, and the weight on the coil represents priority (score) of the coil to be scheduled. The weight Pij on an arc (i, j) represents the

combination of width, gauge and hardness penalties to produce coilj immediately after coili. The penalty is expressed by: P ij = P ij =

α (W

i

− W

)

2

j

+ β (G G

γ (W

i

− W

)

2

j

− G

i

2

j

j

+ β (G G

i

− G

) )

if W

i

≥ W

j

otherwise

j

N



i =1

score

i

Yi −

N

N

∑ ∑ i=1

j =1

3. 3. User agent (UA)

2

j

Wi and Gi are the width and gauge of coili, respectively. α,β, and γ are constant parameters, whose values were fixed using knowledge gained from previous work [Cow 95] as: α = 1×103,β = 6×107,γ = 4×103 The scheduling problem is then: max

into several slabs. A casting sequence is a sequence of heats with smooth jumps in width and chemical grade.

P ij X

ij

Xij = 1 if coilj is scheduled right after coili, Xij = 0 otherwise. Yi = 1 if coili is scheduled, Yi = 0 otherwise. Where Xij and Yi values are chosen so as to give rise to a path in G. To solve this complex optimisation problem, we used a Tabu search meta-heuristic [Glo 97]. The search process starts from Greedy solution. The first coil of the sequence is the widest of all the coils. If more than one coil is found to be the widest, then the coil with the highest score is selected. The next coil is the one that yields the highest objective value in conjunction with the current coil. The process is repeated until the turn is constructed. Given the Greedy initial sequence, the solution is improved by using three moves: swaps of two coils, insertion of a coil and reversal of a sequence of coils. These moves are applied on the scheduled and unscheduled coils until the stopping criterion is reached. The stopping criterion we used is a fixed number of iterations, set at 50. In this way we simulate the need to very quickly regenerate schedules following real-time events. To avoid cycling, moves which would give the same solution as a recently examined one, are added to a short-term memory known as the tabu-list and forbidden or declared tabu for a certain number of iterations. In addition, an aspiration criterion accepts a tabu move if it leads to a sequence which has a better objective function value than the best found so far.

3.2. Continuous Caster Agent (CCA) The caster agent provides dynamic scheduling and rescheduling of the continuous caster. The main constraints imposed on the schedule of orders are chemical and width compatibility constraints. Slabs to be casted must be grouped in heat lots with each heat cast

The user agent provides the user interface to the system. It manages and announces the orders to produce, and deals with dynamic changes of order conditions (rush orders, changes in the deadline of orders, etc.).

3.4. Slabyard agent (SYA) This agent is responsible for the management of the slabs produced by the CCA(s). The SYA is the mediator agent between the CCA(s) and the HSMA. It allows negotiation between the CCA(s) and the HSMA to provide a globally good schedule.

4. Robustness, stability and utility measures for dynamic rescheduling of the HSM In the present architecture, we are concerned with creating predictive-reactive schedules to react to the real-time events, which affect the HSM. The real -time events considered are non-availability of coils. In the presence of unforeseen events, it is desirable to generate schedules that are robust [Cow 01a][Sha 99][Wu 93]. We first construct a predictive schedule and then modify the schedule in response to real-time events so as to minimise deviation between the performance measure values of the realised and predictive schedules In order to make a decision whether to do as little as possible locally repair the schedule or reschedule from scratch (complete reschedule), we use three measures: robustness, utility and stability.

4.1. Robustness, utility and stability measures Utility measures the improvement of the original schedule objective due to schedule revision. The utility is the difference between the value of the objective function (Fdynamic) of the new schedule (Sdynamic) after taking into account the real time information (E) and the objective function (Fstatic) of the initial schedule (Sstatic) before taking into account real time information. It is expressed by: Utility( Sstatic, Sdynamic, E, t) = F dynamic - Fstatic

Stability measures the deviation from the original schedule caused by schedule revision. The deviation is expressed by the sum of the absolute difference between the original completion time (C) of the original schedule and the new completion time (C’) after the occurrence of the real-time event for each coil, which is expressed by:

Stability ( S static , S dynamic , E , t ) =



N i =1

Ci − Ci



The completion time of a coil not in the schedule is expressed as the completion time of the turn plus its processing time. The robustness measure of a schedule S combines the maximisation of the efficiency (utility) and the minimisation of the deviation (stability) from the original schedule. The robustness is expressed by: Robustness(S)= R .Utility - (1-R).Stability, where R is a real valued weight in the range [0,1].

4.2. Rescheduling strategies In order to take into account real-time events, we defined eight strategies. On the occurrence of a disruption, the preoptimised schedule becomes invalid and a new schedule is needed for the set of the remaining coils. Then given the sequence of the remaining coils and a value of R, we reoptimise so as to maximise the robustness. For each strategy the utility, stability and robustness measures are evaluated. We apply the strategy which maximises robustness. The strategies are the following: • Do-nothing (NOT) ignores the real-time event. • Simple Replacement (SR) removes the non-available coils from the sequence, and tries to replace them with the best unscheduled coils. The replacement is based on a one-for-one swap of non-available coils with unscheduled coils. For each non-available coil this strategy finds the best swap with the unscheduled coils, which maximises robustness. • Closed Schedule Repair (CSR) removes the nonavailable coils and re-optimise the resulting sequence without referring to the unscheduled coils using Tabu search. • Open Schedule Repair (OSR) removes the nonavailable coils and re-optimise the sequence considering the unscheduled coils using Tabu search. • Hybrid Closed Schedule Repair (HCSR) is a combination of SR and CSR strategies. Tabu search starts from the sequence found with SR and tries to reoptimise this sequence without referring to the unscheduled coils. • Hybrid Open Schedule Repair (HOSR) is a combination of SR and OSR strategies. Tabu search starts from the sequence found with SR and tries to reoptimise this sequence considering the unscheduled coils.

• Partial Reschedule (PR) reschedules from the first coil non-available. Rather than re-optimising the sequence of the remaining coils, we reschedule the sequence starting from the first non-available coil using Tabu search. • Complete Reschedule (CR) regenerates a new feasible schedule from scratch.

4.3. Rescheduling for non-availability of coils When the HSMA receives the announcement of nonavailability of coils from the SYA, it selects and applies the best strategy according to the robustness measure. If new coils have been introduced by the selected strategy, the HSMA sends an announcement message to the SYA to produce the emergent coils. Then, the SYA on its turn sends a message to the CCA to schedule the emergent coils. If the strategy chosen is reschedule, the HSMA has to send a message to the SYA to cancel the production of coils not considered in the new schedule and announces the emergent production of the new ones to the CCA.

5. Prototype system and simulation results The current prototype has been developed in Microsoft Visual C++/MFC. The proposed architecture consists of four agents, implemented as objects: UA, HSMA, SYA, and CCA. The UA is responsible for introducing the coil orders. The HSMA performs the dynamic scheduling/ rescheduling of the coils. The SYA generates real-time events and passes them to the HSMA to simulate nonavailable coils. The CCA simulates the production of slabs requested from the SYA. The cooperation between the agents is done with the exchange of asynchronous messages formatted using XML (Extensible Mark-up Language). A set of simulation runs was performed to evaluate the behaviour of the HSMA in response to realtime events concerning the non-availability of coils. We carried out 5 runs, each consisting of 5 events with an initial population of 148 coils provided by a steel manufacturer. The SYA generates the first event at 10% of the scheduled turn, and the next events every 20% thereafter. Up to 5 non-available coils were generated randomly for each event. For each simulation run, we considered the strategies proposed for different values of R (0, 0.01, 0.25, 0.50, 0.75, 0.95, 1). For each event, the HSMA evaluates the best strategy for different values of R using the robustness function discussed above. Figure 4 summarises our results on the performance of the average values of the utility, stability, and robustness measures. These results demonstrate clearly that in an environment where an efficient stability should be maintained, the schedule repair strategies give better performance. More

schedule repair or reschedule strategy to respond to the real-time events. The experimental results show that regardless the value of R, schedule repair strategies have a consistent behaviour and maintain a better performance in both utility and stability measures compared to Complete Reschedule. 700 600 500 Stability

precisely, Open Schedule Repair, Closed Schedule Repair, Hybrid Open Schedule Repair and Hybrid Closed schedule repair outperform the other repair strategies in both utility and stability measures. Even in an environment where we tolerate significant changes in stability and efficient improvement in utility, Complete Reschedule, Open schedule Repair, Closed Schedule Repair and Partial Reschedule are competitive, therefore there is no need for Complete Reschedule. Figure 5 shows the average frequency of each strategy applied, in response to real-time events, over the five simulation runs. The results demonstrate that regardless of the importance given to the stability or the utility, the Open Schedule Repair and Closed Schedule Repair strategies give better performance compared to Complete Reschedule. However, we remarked that the Complete Reschedule strategy is often selected when a large number of real-time events disturb the schedule.

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Fig. 6 Performance of each strategy when the same strategy is used to react to real-time events.

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6. Conclusion

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Fig. 4 Performance of each strategy when the best strategy is applied in response to real-time events for different values of R. Frequency 0 .5 0

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Figure 6 shows the average values of utility, stability and robustness measures when we always apply the same

This paper has presented a multi-agent architecture for dynamic scheduling in steel production and in particular the dynamic scheduling of the Hot Strip Mill. Two key properties of the architecture developed are: the integration of scheduling activities of the CC and the HSM, and self-adaptation to real-time events. The proposed architecture consists of 4 dedicated agents: the User Agent, the Hot Strip Mill Agent, the SlabYard Agent and the Continuous Caster Agent. In the simulation prototype, the agents were implemented as C++ objects and their cooperation was carried out with the exchange of asynchronous messages formatted using XML. The scheduling problem for the HSM is modelled using the Prize Collecting Travelling Salesman Problem model and solved using a Tabu search meta-heuristic. To address the problem of real-time events, the HSMA generates predictive-reactive schedules based on three measures (utility, stability, robustness), and a number of schedule repair and complete reschedule strategies which use Tabu search meta-heuristics for the search of the best predictive-reactive schedules. The experimental results showed that the schedule repair strategies give better performance for both stability and utility measures. Even in an environment where we tolerate significant changes in stability and require improvements in utility, schedule repair strategies are competitive. Complete Reschedule is, however, often the best strategy after a large number of real-time events have occurred. When we apply the same

strategy to react to real-time events, we found that schedule repair strategies have a consistent behaviour and give better performance in both utility and stability measures compared to Complete Reschedule. Future work will continue the investigation of the dynamic scheduling within the CCA and the cooperation mechanisms, as well as extending the scale of our work to problems having a much larger number of coils.

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