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Complete assembly coordinate constraint ：All parts in the rocket which part belongs to must ensure complete assembly coordinate. That is to say the end time of part which have been scheduled need to be considered when schedule the part . The part of the rocket scheduling later must refer to end time of the previous scheduled part. （2）Adjacent rail constraint ：The parts belong to the same rocket should be assembly in adjacent rails as far as possible. （3）Liner space resources constraint: An independent rocket part can be assembled at any rail in theory, but it must be limited to the remaining space of the rail. Rocket assembly scheduling also subject to the traditional scheduling constraint such as priority, due time, earliest start time and so on. According to the actual demand of the rocket assembly production, the scheduling constraints are divided into major and secondary constraints. The core of the rocket assembly scheduling is achieving complete assembly coordinate and maximizing the use of rail resources. Scheduling constraints is analyzed by the two aspects. Constraints among the parts of the rocket do not exist alone and they are interrelated and mutual restraint. Rocket Assembly Technical Framework Technical Ideas of Rocket Assembly Scheduling Systems. The goal of rocket assembly scheduling is to make the job an orderly, coordinated, controlled and efficient operation. Operative plan's fast generation and rapid response processing the disturbance of production events is the core and key of the scheduling system. Rocket assembly scheduling maximizing the use of space resources as guidance, addressing the complete assembly coordinate of the same rocket and adjacent rail as a starting point, hierarchical assembly to multitask mixed lines for background, balancing the multiple scheduling constraints and rapid response to the dynamic disturbance as the solving thoughts, established a technology of multi-task-oriented hierarchical assembly of liner rail space dynamic scheduling. For the problems and characteristics of rocket assembly scheduling in the production process, the technical framework of linear rail space dynamic scheduling technology for multi-tasking hybrid assembly sections is shown in the figure 1. Figure 1 The general technical framework of rocket assembly scheduling Technical framework is summarized as follows: （1）Scheduling parts filter rules based on multiple constraints : The scheduling algorithms described in this article is based on the remaining space of rails to make the scheduling scheme. The first thing need to be thinking is how to arrange the appropriate scheduling part into remaining rail space. Rocket assembly scheduling results need to meet the various constraints of the rocket assembly, therefore the heuristic scheduling algorithm is used in this system. The constraints of rocket assembly scheduling are developing into a flexible scheduling constraint rule algorithm to select a unscheduled part which is the most reasonable part to be assembly. By implementing the each part be arranged reasonable to make the assembly of rocket orderly, coordinated, controlled and efficient. （2）Space resources optimum utilization algorithm: The short board of rocket assembly process efficient is rail resources, so the core of rocket assembly scheduling is to improve the utilization of assembling rail. Therefore improving the utilization of assembling rail in details can ensure that the space resource of rocket assembly rail turn around efficiently which indirectly ensures the complete assembly coordinate of single rocket and assembling in adjacent rail. （3）Quick response dynamic scheduling technology: The environment of rocket assembly is dynamic and complex, dealing with disturbance of rocket assembly in timely and dynamic can make sure the scheduling scheme accord with actual production demand. Rocket Assembly Objectives and Parameters Defined. A unified mathematical description can express the nature of the problem, the constraints in the system are described by using a mathematical formula, it can make the work more rigorous and rational. In order to ensure the unity of the expression in symbolic meaning, the mathematical symbols in this article are explained here.
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： expresses a rocket, the subscript is the only mark of rocket.
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: expresses a classification part and the corresponding scheduling, the subscript expresses the classification part that belongs to rocket , the subscript expresses the classification part expresses that the part is the No j part of rocket.
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: is one classification parts of rocket, also expresses the start point of scheduling block on the rail, take the orbital coordinate as accordance.
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: is one classification parts of rocket, also expresses the end point of scheduling block on the rail, take the orbital coordinate as accordance.
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: is the length list of scheduling block in accordance with the rocket classification part, that also means the length of rail occupied by the rocket classification part.
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: is the time list of the rocket task issued, also means the earliest time of rocket task is started.
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: is the time list of the rocket task delivery, also means the latest time of rocket task is finished.
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: is the latest start time list of rocket classification part, also means the latest time of rocket classification part started to be processed. In order to ensure- the rocket is finished on time and the added constraint added by the coordinate.
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: is the assembly start time list of rocket classification part , also means theoretical starting time got from scheduling results by rocket classification part assembly.
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: is the assembly work time list of rocket classification part , also means the rocket classification part theoretically needed time.
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: is the end time list of rocket classification part assembly, also means the theoretical end time got from scheduling results by rocket classification part assembly;. Key Technology Space Resources Optimum Utilization Algorithm. The Process of Space Resources Optimum Utilization Algorithm. The core problem that the rail resources scheduling solves is the position arrangement of rocket part tasks. When the idle space range is bigger than the space range needed by the rocket part, there are two space range ways: first, according to the direction of the venues rail linear coordinates close to the arrangement, including adjacent idle space, the place of adjacent idle space and the tight before and tight after replacement of classification part that is already scheduling; second, place free according to the length of idle range. This algorithm takes use of the adjacent form. When it arranges the rocket parts, the phenomenon of free placement will not happen because of considering the full use of rail resources, free placement will waste space resources. And at the same time, considering the complex time and space coordination of rocket assembly, the judgment for current tightly before and tightly after arrangement of rocket part is very difficult, and this is the core of space resources optimum utilization algorithm. The more grading part be scheduled, the more function it takes. Supposing the rocket part that is not scheduled is collection US, ; Rocket part selected by rail space is ; The one scheduling part before scheduling remaining rail space is ; The one scheduling part after scheduling remaining rail space is ; The process of space resources optimum utilization algorithm is shown in figure 3. Figure 3 Space resources optimum utilization algorithm flow chart Quick Response Dynamic Scheduling Technology. Dynamic Scheduling Algorithm Processes. In a complex production environment, production disturbances are the fundamental driving force for dynamic scheduling in the drive shop. Types and sources of production disturbances are more complicated and only systematic analysis of a variety of disturbance factors and separate treatment can make the scheduling work plan consistent with the actual production[]LIU Mingzhou, SHAN Hui，JIANG Zengqiang，et al. Dynamic Rescheduling Optimization of Job-shop under Uncertain Conditions[J]. JOURNAL OF MECHANICAL ENGINEERING, 2009, 45(10): 137-142. , []M A Adibi, M Zandieh, M Amiri. Multi-objective scheduling of dynamic job shop using variable neighborhood search[J]. Expert Systems with Applications, 2010, 37（1）: 282-287. ]. By analyzing the processes of these disturbance events, we have developed three basic algorithms: insertion algorithm, mobile algorithm and re-scheduling algorithm. Classification of dynamic disturbance events at the same time provides a unified approach to the dynamic adjustment of scheduling programs and simplifies the disturbance treatment processes. The entire dynamic scheduling process is shown in Figure 4. Figure 4 Dynamic Scheduling Algorithm flow chart Rocket Assembly Scheduling System Implementation Combined with the proposed algorithm, we developed the rocket assembly and production scheduling system which takes the rocket as an instance. In the underlying data, the system has a total of six assembly rails. The length of each rail is 100, numbered 0 to 5. The basis data of the rocket part : rocket part belonging rocket , the length of rocket part , the rail length of rocket part , working hours of rocket part , the earliest start time of rocket part , the delivery date of rocket part . Based on the above algorithm, based on VC++ IDE development platform, we developed the system. System scheduling results in a list output as shown in Figure 5. Figure 5 The rocket assembly scheduling results output by list Shown in Figure 5 the scheduling results Rocket1's the end time difference of the earliest assembly finished part and the latest assembly finished part is two days, because Rocket1" the assembly time of all part is a minimum of 17 days. Therefore, "Rocket1" is able to meet the requirement of rocket complete assembly in the actual production. "Rocket1, has four parts, its final assembly rails respectively are rail1, rail 1, rail 1, and rail 0. Meet the requirement of the rocket assembly rail adjacency in the actual production. Summary Represented by the rocket production, linear rail space site scheduling problem is the bottleneck of the large one-piece manufacturing process. In this article, rocket assembly scheduling as a two-dimensional scheduling with time window constraints (one dimension is time, the other dimension is space) is considered. We developed the system in order to meet the actual needs of the rocket assembly. The advantage and innovation of linear rail space dynamic scheduling technology has three parts.
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A uniform scheduling handling framework is established, taking complete assembly, priority, delivery date, site resource utilization, and the adjacent rail constraints in rocket assembly into consideration.
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Establish heuristic scheduling rules which can be adapted in the rocket assembly scheduling, such as scheduling resource constraints, priorities, and complete assembly control, proximity arrangement.
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Summary various disturbances in the production process and send them into four categories: the task layer, the production process layer, the material resources layer and production execution layer. Foundation items: Project supported by the National Natural Science Foundation，China (No. 51175045).
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