ECCC-67同时作业和计划在热送热装上的优势

The advantages of simultaneous assignment and scheduling for hot and direct chargingAuthorVivian De Smedt (AIS Advanced Information Systems nv – A PSI Metals Company)ContactVivian De SmedtAddress:PSI BrusselsAllée de la recherche, 65B1070 Brussels,BelgiumPhone: +32 2 558.88.26Email: vdesmedt@psi.deKeywordsScheduling, Assignation, Hot Charging, Decoupling, Standard SlabsAbstractThe assignment and scheduling challenges for a Hot Strip Mill are typically run in two separate business processes. However, studies show that the size of the schedules depends directly to the size of the assigned slab yard. In the context of a highly constrained line, an increasing freedom in the assignment procedure can be leveraged to ease the scheduling of the mill and build longer schedules, hence also reducing the average residence time of the slabs in the yards. Further, in the context of decoupling point and slab yard standardization the freedom in the assignment process increases significantly the opportunities of improvement. By assigning and scheduling in the same process, the amount of assigned slabs suitable for scheduling can be increased by up to 30%. Hence, this increases the average size of the schedules in this same impressive proportion. The advantages of the method are particularly clear when the requirement to reduce the stocks is important or in the case of hot and direct charging. This paper will explain why doing simultaneous scheduling and slab to coil order assignment give more freedom in the scheduling process making more coil orders available for sequencing and improving the schedule length. In the hot charging con-text this is particularly true, since the scheduler can only use slabs which were just produced (during the last few hours). This reduces dramatically the number of available slabs. In such a scheduling context, being able to leverage the assignment flexibility can help increasing the size of the hot charging schedules. Experience shows that without changing the scheduling process, running the assignment process taking into account the scheduling rules can increase the size of the schedules by at least 20%.The problemThe hot strip mill get slabs from a slab yard and have to mill them to produce coils. In the process the thickness change radically from around 200 mm to up to 1.5 mm but the width of the material unit only vary slightly or slightly more in case an edger is available and the weight and the chemical composition don’t change. In consequence not all slabs are suitable to produce a given coil. A hot strip mill schedule is then the result of two choices:The choice of an input slab for every coil of the schedule, the assignment.The choice of sequence of coils to process, the schedule.Simultaneous slab assignment and HSM schedulingThe goal of this paper is to explain why assigning the slabs to coil orders before scheduling the coils in the hot strip mill is suboptimal.We will explain why pre-assigning slabs to coil orders lead to a number of bad assignments. These bad assignments mean that parts of the slabs fail to be scheduled in the coming hours. This increases the average slab residence time in the slab yard and represents a direct financial cost for the company.Pre-assignment can also deteriorate the schedule quality. Some coils that could have been scheduled or that could have allowed other coils to be scheduled (critical coils) will not be scheduled because they are unassigned or assigned to unavailable slabs and this has a significant impact on the schedule size and the schedule quality.The validity of these arguments, although not contestable in principle, has to be confronted to the reality of the plant and of the hot strip mill line in particular.We show how to measure the tension between the slab yard size and the schedule size and how to measure the impact that the freedom of slab assignment can bring to address that tension in real case examples.The following paragraphs explain the root of the freedom of slab assignment and why that freedom helps to increase the schedule size by addressing some hot strip mill specific problematic as the width thickness profile problem, the pack problem or the hot charging problem.The relation between assignable orders and schedule sizeWhen the slab yard is not infinite the amount of available orders has a direct impact on the size of the schedule. Variations on the amount of available order up to 30% induce variation on the size of the schedules up to 30%.In the following graph you see the evolution of the size of the slab yard in tons of a French steel producer (in blue) together with a graph of the individual HSM schedules sizes (in red). The two graphs match nearly exactly showing that for that particular production unit increasing the number of available slabs for scheduling of 30% will likelyinduce an increase of the schedule size by 30%.Figure 1: Schedule Size vs. Yard sizeThe freedom of slab assignmentSimultaneously scheduling and assigning slabs to coil orders does not increase the size of the slab yard but can increase the number of orders available for scheduling. To analyse that, we studied the relation between the number of assignable orders compared to the number of preassigned orders at a Belgium steel producer for various slab yard sizes.The following graph shows the number of assignable orders versus preassigned orders according to the size of the slabyard. We see that for a small slab yard, around 10k tons, the number of assignable orders is 90% bigger that the number of preassigned orders and that for bigger slab yards, around 75k tons, the number of assignable orders is still 25%bigger that the number of preassigned orders. Figure 2: Assignable Order vs. Assigned Order in function of Yard SizeThe more the slab yard is small the more the freedom of slab assignment impact the amount of available orders.A business caseFew months ago we implemented in Belgium a SteelPlanner solution that assign slabs to coil orders simultaneously with the generation of the rough scheduling of the hot strip mill for next 3 production days. In a first stage the schedules were not used for production, they only used the induced assignation of slabs to coil orders. From this assignation the schedulers built their schedule the usual way. During this first phase of the project, only the new slab assignment procedure was validated, the schedule length was not a first business objective. Surprisingly, the size of the schedules increased by about 20% from one day to the next. People started to investigate and look at which other factor could have impacted the size of the schedules. The proof came a few weeks later. For IT-integration reasons, they had to switch back to the previous assignation procedure for few days. Again the size of the schedules were immediately impacted and shortened.The root of the freedom of slab assignmentThere is more than one way to assign slabs to coil orders. The most obvious degree of freedom is the final thickness of the coil. If you have two coil orders for the same steel grade and the same width the slabs you can assign to both will be the same whatever the final coil thickness or the coil order would be. Some hot strip mill have some width reduction capabilities, sometime up to 400 mm (In the Netherlands) which give some freedom about the slab width you can choose for a given coil order. But the assignation rule of slab steel grade to coil orders mechanical restrictions lead also to some other degree of freedom.More and more steel plant take advantage of these degree of freedom to standardize they slab yard and cover most of their coil order demand with a very limited number of slab specifications. We can then consider that some freedom exist in the assignation process that this freedom is not small and that it tends to increase more and more for some technical, logistical and strategic reasons.Indeed standardized slab yard are more and more popular because increase the assignment flexibility by the choice of slab design that maximize the amount of coil orders that they fit by choosing the right width, length and chemical composition to do so.Even in the context of a classical planning made of two separated steps: assignment and scheduling standardized slab yard allows the constitution of stock that helps to reduce total lead time, un pilling and due date performance.Why the amount of available order impact the schedule sizeWhen assignation has to be performed before scheduling the assignation algorithm can't take into account the scheduling restrictions. Pretty often the assignation process is a constructive algorithm that for each slab and each cost category look for the coil order that could be assigned to the slab in the given cost category and assign the slab to the most due coil order. When optimization algorithm are used by definition the algorithm can only take into account what is known at this process stage, assignation cost, due date, order completion, product flow fulfillment.If they were no restrictions about how to schedule a hot strip mill, pre-assigning slabs to coil orders would not be a problem but some hot strip mill restrictions make it sub optimal. The following paragraph explains why.The width & thickness problemThe main constraint of the mill is the width profile.The mill schedule has to start with easy to roll narrow coils.The highest width have to be reached quickly without wearing the cylinder too much to avoid marks on the roll surface that will later induce coil surface quality problems. That part of the schedule is often called the run-up.When the highest width is reached, difficult to roll coils can be rolled but the width of the coils has to be decreasing steadily to avoid surface quality problems. That part of the schedule is often called the run-down. To ensure some stability to the hot band it is not possible to roll coils of the same width for more than a given size.The second main constraint is the thickness profile. There are three classical thickness restrictions that apply to hot strip mill schedules.The startup zones, the zones of the schedules where the cylinders are “cold” and where the level-2 model is “learning”how the new cylinders behave. This zone has to be filled with thick coils.The mill can't start rolling thin coils if they are not preceded by coils of intermediate thickness.For some mills after milling a bunch of thin coils it is important to “relax” the rolls and switch back to rolling none thin coils.Another family of restrictions is the grouping restrictions. Quite often the milling people define type of material that has to be rolled together and sometime preceded by some preparation material.Put together that means that a schedule is made of different zones of limited size that should contains coils of similar width, that should be filled with coils of a given group and for each of these zones a suitable repartition of coil thickness should be available to reach the maximum size of the zone and optimize the overall schedule size. If slabs are pre-assigned to coil orders that optimal repartition is in general not available and the zone will have to be shorter and theoverall schedule size will suffer.Figure 3: Width Thickness profile of Hot Strip Mill ScheduleIn the above screen shot you see the width and the thickness profile of a schedule. The run down is made of five width zones made of different type of materials (yellow and green) on each one the zone contains thin material (thickness below 200 micron) and relief material (thickness above 200 micron).An exampleLet’s simplify the problematic to be able to describe quickly a short example where the pre-assigning ofslabs to coil orders lead to suboptimal schedules. Suppose you have the following coil orders. For simplification, we are considering only a very limited amount of attributes:Coil Order DueDateCoilWidthCoilThck.Length #O13A 2008-10 1300 mm 2 mm 1.5 km 4 O13B 2008-09 1300 mm 2 mm 1.5 km 4 O13C 2008-10 1300 mm 2 mm 1.5 km 2 O13D 2008-11 1300 mm 3 mm 1 km 2 O13E 2008-10 1300 mm 4 mm 0.75 km 4 O13F 2008-10 1300 mm 4 mm 0.75 km 4O12A 2008-09 1200 mm 2 mm 1.5 km 4 O12B 2008-09 1200 mm 2 mm 1.5 km 4 O12C 2008-10 1200 mm 2 mm 1.5 km 4 O12D 2008-10 1200 mm 2 mm 1.5 km 4 O12E 2008-09 1200 mm 3 mm 1 km 2 O12F 2008-11 1200 mm 4 mm 0.75 km 4 O12G 2008-11 1200 mm 4 mm 0.75 km 4 Table 1: Order BookAnd the following slabs available:Slab TypeSlabWidthSlabWeight#S13A 1300 mm 20 tons 18S12A 1200 mm 20 tons 18Table 2: Slab YardSuppose the schedulers have to fill one in the 1300 mm width and the other in the 1200 mm and suppose that:Each zone should be of maximum 20 kmEach zone can contains maximum 12 km of coil of thickness below 2 mm andThat to make the transition between coils of 2 mm and 4 mm you need a coil of 3 mm of thickness.If slabs were pre-assigned to coil orders only the green ones, the one due on week 9 and 10 will be assigned.When the scheduler has to schedule the 1300 mm width zone he will have only coils of 2 mm and 4 mm of thickness to schedule and it will not be possible for him to make the transition. He will probably be forced to not schedule the thin material, hence ending with a zone of only 6 km (O13A, O13F).If the assignation could have taken into account the scheduling constraints he would have assigned the two coils of 3 mm thickness (O13D) instead of two of 2 mm thickness (O13C) the thickness transition would have been possible and the zone will be filled with 20 km of coils.When he will schedule the 1200 mm width zone because of the limitation of 12 km of thin material he will only be able to put 14 km of coils (O12A, O12B, O12E).If the assignation could have taken into account its scheduling constraints he will have assigned the 8 thick coils (O12F, O12G) instead of the thin ones (O12C, O12D) allowing him to build a zone of 20 km of coils.The pack problemOn a hot strip mill there is some material that has to be scheduled in packs. To schedule them you have to fill a small template with some preparation material, a group of a minimum size that form the core of the template and, sometimes, some relief material at the end of the pack.The reasons of willing to schedule material in pack are:Because you may have to prepare the zone of introduce a transition at the end of the zone with coil order that could be rare you have to limit the number of times you need this transitions.Because the material you have to roll is difficult and that you have to calibrate the mill in order to roll them it is better to put them in block. Suppose that in average, because of calibration, you miss the first two of the block if the average block size is 10 pieces your success rate will be 80% but if you average block size is only 4 pieces your success rage will only be 50%.When slabs are pre-assigned to coil orders, the assignation procedure leaves the scheduler with only parts of the pack. He'll then have to wait for the other parts to be assigned in order to schedule the full pack.If the assignation can take into account the scheduling constraints all the coils of the pack together with their accompanying material will be assigned to slabs or none of them avoiding that some coils remains in the yard waiting some other to come for being able to be scheduled.The hot charging contextWe explain why doing scheduling and slab to coil order assignation together give more freedom in the scheduling process making more coil orders available for sequencing and improving the schedule length. This is particularly true when the number of available slabs is small.In the hot charging context this is particularly true, since the scheduler can only use slabs which were produce during the last 16 hours if they are lucky or during the last 8 hours otherwise. This reduces dramatically the number of available slabs. In such a scheduling context, being able to leverage the assignation flexibility can help increasing the size of the hot charging schedules.In Argentina where we implemented such approach they were able to increase the percentage of hot charging by 20%.ConclusionIn the context of a highly constrained line such as the hot strip mill, the increasing freedom in the assignation procedure can be leveraged to ease the scheduling of the mill and build longer schedules and reduce the average residence time of the slabs in the yards.In the context of decoupling and slab yard standardization the freedom in the assignation process increases even more and the opportunity for this technique are bigger.Experience shows that without changing the scheduling process having an assignation process that takes into account the scheduling rule can increase the size of the schedules of 20%.AcknowledgmentsI would like to acknowledge Jean-Pierre Coste from ArcelorMittal and Gauthier Havelange from Duferco La Louvière for the study they made of their respective problematic and for allowing me to site them in this paper.。