CN104573855B - The maximum work dispatching method of the iterative and incremental for meeting temporal constraint based on bipartite graph - Google Patents
The maximum work dispatching method of the iterative and incremental for meeting temporal constraint based on bipartite graph Download PDFInfo
- Publication number
- CN104573855B CN104573855B CN201410818220.5A CN201410818220A CN104573855B CN 104573855 B CN104573855 B CN 104573855B CN 201410818220 A CN201410818220 A CN 201410818220A CN 104573855 B CN104573855 B CN 104573855B
- Authority
- CN
- China
- Prior art keywords
- personnel
- task
- node
- bipartite graph
- sequential
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired - Fee Related
Links
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
- G06Q10/00—Administration; Management
- G06Q10/06—Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
- G06Q10/063—Operations research, analysis or management
- G06Q10/0631—Resource planning, allocation, distributing or scheduling for enterprises or organisations
- G06Q10/06311—Scheduling, planning or task assignment for a person or group
- G06Q10/063112—Skill-based matching of a person or a group to a task
Landscapes
- Business, Economics & Management (AREA)
- Human Resources & Organizations (AREA)
- Engineering & Computer Science (AREA)
- Strategic Management (AREA)
- Educational Administration (AREA)
- Economics (AREA)
- Entrepreneurship & Innovation (AREA)
- Development Economics (AREA)
- Game Theory and Decision Science (AREA)
- Marketing (AREA)
- Operations Research (AREA)
- Quality & Reliability (AREA)
- Tourism & Hospitality (AREA)
- Physics & Mathematics (AREA)
- General Business, Economics & Management (AREA)
- General Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
- General Factory Administration (AREA)
Abstract
The invention discloses a kind of maximum work dispatching method of the iterative and incremental for meeting temporal constraint based on bipartite graph.Send the task of work to be ranked up one group of wait first, calculate conflict between any two or sequential relationship, obtain a collison matrix；To each task, according to the constraint of ability and time, optional personnel's subset is calculated respectively, personnel is remerged into and always collects；And " attending to anything else " technology is used, to reach the purpose that iterative increment sends work.Then utilize collison matrix, construct sequential bipartite graph, the task node that the left side of figure is ordered into, the right is then personnel's node containing " attending to anything else ".Finally, obtain the maximum of sequential bipartite graph using Hungary Algorithm to match, optimal solution is selected as the result for sending work according to the principle of optimality.The present invention has taken into full account the various constraintss sent during work, sends work result more accurate reasonable, intelligent level is high.Timing feature for sending work problem, sends work by iterative and incremental, substantially increases operating efficiency.
Description
Technical field
It is specifically a kind of based on bipartite graph the invention belongs to the maximum matching technique in Assignment Problems, for sequential about
After beam optimizes, the maximum work dispatching method of task can be assigned iterative and incremental.
Background technology
With level of IT application more and more higher, non-support cable, office automatic have become more and more popular.But
Many service organizations (such as housekeeping company) are also using original manual work dispatching method, and this seems somewhat incompatible with the epoch.
Work is sent manually, is not only wasted time and energy, efficiency is low, and because a variety of restrictive conditions, tends not to make overall plans, and obtains maximum
Benefit.At this moment, an outstanding work dispatching method is just particularly important.Certainly, it is desirable to reach raising efficiency, reduce the mesh of cost
, this work dispatching method just has to enough intelligence.And bipartite model then be solve this kind of problem optimal selection it
One.
Bipartite graph is also referred to as bigraph (bipartite graph), is a kind of particular module in graph theory.If G=(V, E) is a non-directed graph, if
Summit V can be divided into two mutually disjoint subset (V1, V2), and each edge in figure<I, j>Two associated summits
I and j is belonging respectively to the two different vertex sets (i in V1, j in V2), then it is referred to as a bipartite graph to scheme G.Bipartite graph refers to
Send the mathematical modeling of problem, wherein vertex set V1Represent a group task, V2Represent a group of people.Connect summit i and j Bian Zebiao
Task i can be assigned to personnel j by showing.How quickly the emphasis for sending work Study on Problems is exactly, effectively and reasonably by the left side
The task personnel as much as possible for being dispatched to the right.
A bipartite graph G is given, in a G subgraph M, if do not depended in any two of collection E same
Individual summit, then it is a matching to claim subgraph M.The maximum subset of side number as being found in bipartite graph is referred to as maximum matching and asked
Topic.So, solve the problems, such as the above-mentioned thinking for sending work translate into find corresponding to maximum in bipartite model have matched.One
Obviously algorithm is：All matchings are first found out, what then coupling number was most is exactly maximum matching naturally.But this algorithm
Time complexity exponentially increase with the increase of side number, once matching scale it is big, efficiency certainly decline it is very strict
Evil, so practicality is not strong.
In fact early in nineteen sixty-five, Edmonds just proposes more efficient algorithm, and the core of the algorithm is to constantly search for
Augmenting path.An augmenting path is often found, just by xor operation, increases a matching side on the basis of original matching.
When again can not find augmenting path, obtained matching is exactly maximum matching.Here it is famous Hungary Algorithm.Hungary calculates
The scope of application of method is very wide, such as Assignment Problems, marriage problem etc..And Assignment Problems, as a kind of specific question, it is asked with other
The maximum difference of topic is exactly timing, is mainly shown as between different task there is temporal context, same personnel
Also different task can be completed in different time sections.When analyzing particular problem, this timing will appear as a kind of sequential about
Beam.It will be apparent that Hungary Algorithm does not optimize for temporal constraint in itself, a personnel can only assign a task,
So obtained maximum matching may not be maximum truly.In the case where meeting temporal constraint, consider to certain
A little personnel repeat to send work (be referred to as iterative and incremental sends work), are entirely possible to find a bigger matching.
The content of the invention
It is an object of the invention to provide a kind of based on bipartite graph, by the optimization to temporal constraint, can iteration increase
Send to amount formula the maximum work dispatching method of work.
The technical solution for realizing the object of the invention is：The iterative and incremental for meeting temporal constraint based on bipartite graph
Maximum work dispatching method, comprises the following steps：
The first step, the task of work is sent to pre-process one group of wait.It is mainly suitable according to the priority of job start time
Sequence is ranked up, and is obtained one group of orderly task, is designated as R '.Then to each task r in R 'iCalculating can complete this
Personnel's subset P of businessi, each personnel in subset not only have the ability to complete the task, and also will not be with arrangement of time
The task conflict of work has been sent before, i.e., meets technical ability constraint and time-constrain simultaneously.Finally, from the middle rejecting P of R 'iFor the task of sky
ri(because task nobody can complete, affirmative sends work to fail), forms final orderly task-set R.
Second step, collison matrix C is calculated by orderly task-set R.C=R × R, therefore C is N × N square formation, N is to appoint
The quantity of business.Each element c in matrixijSpan all be 1 or 2.cij=1 represents task riWith task rjIn the time
On have a conflict, and cij=2 represent riAnd rjThere is front and rear sequential relationship.Collison matrix is following computing staff always collection and conflict side
Basis.
3rd step, by personnel's subset PiComputing staff always collects P.Detailed process is, during i=1, by P1In node directly add
Enter in P；As i ＞ 1, by PiWith P1, P2..., Pi-1" merge-attend to anything else " operation is performed one by one, merging is exactly to take the meaning of union,
Merging is carried out every time, but it is before identical personnel node occur in two son concentrations and corresponding two tasks are present to attend to anything else
Just performed during sequential relationship afterwards.To be attended to anything else node and PiIn remaining node include P set, node itself because it is existing just not
Include again.So finally always collect P with regard to personnel can be formed.That is, same personnel have itself and divided in personnel always collect P
Two kinds of existence forms of body, this is one of the characteristics of iterative and incremental sends work.
4th step, the task-set R obtained using first three step, collison matrix C and personnel always collect P, construction sequential bipartite graph G.
Sequential bipartite graph is a kind of special bipartite graph G=(V1, V2, E), wherein V1Corresponding task-set R, task node according to it is front and rear when
Sequence arranges from top to bottom, V2Counterpart personnel always collects P, includes zero to multiple nodes of attending to anything else.E is side collection, represent task and personnel it
Between appointment relation.
5th step, conflict side is calculated, and save as CE set.Conflict side is two can not appear in a matching simultaneously
Side, the reason for it occurs is that itself node in right node and node of attending to anything else (being actually same personnel) are attempted to be associated with
Two left siblings (two the having conflict of the tasks) of conflict, if two of formation are assigned relation to be selected in same matching,
It will cause to send work to fail, so needing to filter conflict side in the result.
6th step, if CE is sky, directly using Hungary Algorithm, obtained maximum matching is exactly to send work result.And such as
Fruit CE is not sky, that is, conflict side be present, it is necessary to sequential bipartite graph G using the Hungary Algorithm after improving, obtains one group most
Big matching.Then filtered according to conflict side CE, obtain effective maximum matching.Finally according to the customized principle of optimality,
Select an optimal result.
The improved cardinal principle of Hungary Algorithm is as follows：
If bipartite graph is connection, by recycling Hungary Algorithm, all maximum of bipartite graph are obtained
Match somebody with somebody.If do not connected, bipartite graph is first divided into the subgraph of several connections, obtains all of subgraph using Hungary Algorithm respectively
Maximum matching.Then subgraph merges, and arithmetic result does cartesian product computing, all maximum with regard to that can obtain whole bipartite graph
Match somebody with somebody.
The present invention compared with prior art, its remarkable advantage：(1) sending the overall process of work has algorithm and system support, people
Work participation is low, and automatization level is high.(2) sizable human resources and other resources are saved, greatly reduce send work into
This.(3) send work speed to greatly promote, reduce between sending man-hour, improve and send work efficiency rate.(4) send and take into full account during work
The restrictive condition such as capacity consistency and time-constrain, as a result more accurate reasonable, intelligent level is high.(5) result of work is sent to be passed through
Optimize to greatest extent, the timing feature for sending work problem, send work by iterative and incremental, improve human resources
Utilization ratio, bigger economic benefit can be obtained.
Brief description of the drawings
Fig. 1 is the task pretreatment schematic diagram of the present invention.
The node that Fig. 2 is the present invention is attended to anything else schematic diagram.
Fig. 3 is the sequential bipartite graph organigram of the present invention.
Fig. 4 is flow chart of the method for the present invention.
Embodiment
The present invention is substantially a kind of improvement based on Hungary Algorithm.
The present invention is described in further detail below in conjunction with the accompanying drawings.
It is as follows to the process of group task pretreatment with reference to Fig. 1：The time-sequencing started according to task, is appointed in order
Business group R={ r1, r2, r3, r4}.Now with three staff { p1, p2, p3, respectively to each task riCalculate PiObtain P1
={ p2, p3, P2={ p2, p3, P3={ p1, p3, P4={ p3}.Wherein, P1={ p2, p3Mean the completion task r that has the ability1
And the personnel that task can be completed within the specified period are p2And p3.Similarly, P2、P3And P4And it is understood that.
Because the sample different in size of each task execution time, the small rectangle length of task is represented in Fig. 1 also not
Equally, task r2The execution time to be substantially longer than r3And r4., and or any two task is conflict in sequential
It is orderly.From figure 1 it appears that r1And r2It is to conflict, r1And r3It is then orderly r1And r4And orderliness
's.By that analogy, conflict relationship is designated as 1, and sequential relationship is designated as 2, it is possible to obtains collison matrix C.
With reference to Fig. 2, the process that computing staff always collects P is described in detail.Original state, P is sky, so directly by P1In section
Point includes P set.Then P is handled2, P2Need and P1Carry out " merge-attend to anything else " operation, and because r2With r1Conflict in sequential,
So only need to carry out " mergings " to operate, that is, by P1In be not present and P2Present in node include P set.Next
Handle P3, P3Need and P2、P1" merge-attend to anything else " operation is carried out one by one, and process is as follows：r3And r2Conflict, so P3And P2Only carry out
Simply " merging " operates；But r3And r1There is sequential relationship, so P3And P1Merging will also carry out " attending to anything else " behaviour after being over
Make.Detailed process such as Fig. 2 of " attending to anything else " operation, from node p3A new node is replicated, is named as p3-3, show this new section
Point is corresponding r3P3Attend to anything else node.Then a line is moved<r3, p3>Arrive<r3, p3-3>, r3And p3-3Connect, " attending to anything else "
Operation is completed.Finally, to P4Also above-mentioned identical processing is carried out.What be should be noted is a bit, to avoid repeating attending to anything else, r4To r1
P3Do and attend to anything else to obtain p3-4Afterwards, cannot be again to r3P3-3Do and attend to anything else.Personnel may finally so be obtained and always collect P=
{p1, p2, p3, p3-3, p3-4}。
With reference to Fig. 3, illustrate to construct sequential bipartite graph and then solve the process of maximum matching.By it is above " merge-point
After body " operation, it is only necessary to arrange the task in set R in order, the personnel in set P are also reasonably arranged, it is easy to
With regard to the sequential bipartite graph such as Fig. 3 can be constructed.
The method for calculating conflict side is as follows：(1) same node and its subset attended to anything else, P ' in right node are calculated3={ p3,
p3-3, p3-4}；(2) in P '3In optional two different node p3And p3-3, because in the presence of two sides<r2, p3>、<r3, p3-3>, and r2
And r3There is conflict, so this two when being a pair of conflicts.(3) second step is repeated until P '3In all combination inspection finish.
According to this method, calculate in Fig. 3 and liquidated nib in the presence of two, point be separately<r2, p3>With<r3, p3-3>Conflict,<r2, p3>With<r4,
p3-4>Conflict.
Because conflict side be present, improved Hungary Algorithm is needed to use to try to achieve maximum matching.Algorithm principle is as follows：
(1) sequential bipartite graph G is divided into connected subgraph, G={ G1, G2..., Gn}；(2) each subgraph G in G is circulatedi, to GiCalculate
All maximum matchings, one group of obtained matching are designated as Mij, j=1,2 ...；(3) subgraph merges, the matching M of subgraphiIt is Descartes
Product computing, obtains G all matchings, is designated as M.Wherein, number is matched | M |=| M1|×|M2|×…×|Mn|；(4) according to punching
Nib filtering matching M, obtain Lothrus apterus side one group are effectively matched subset M '；(5) if | M ' |=1, M ' be last solution, if
| M ' |=0, then without solution.Otherwise exist it is multiple be effectively matched, according to the customized principle of optimality, a weights are assigned for each edge,
Calculate the weights being each effectively matched and choose an optimal solution as work result is sent, complete.
4 task { r cited by the present invention1, r2, r3, r4And 3 personnel { p1, p2, p3Situation, be intended merely to more
Work dispatching method clearly described, it is not restricted to number of tasks and personnel's number during practical application.
Claims (5)
- A kind of 1. maximum work dispatching method of the iterative and incremental for meeting temporal constraint based on bipartite graph, it is characterised in that including with Lower step：The first step, the task of work is sent to pre-process wait；The task that work is sent in one group of wait is carried out according to the priority of time started Sequence, obtains an orderly set of tasks, then to each task in set, according to two constraint bars of ability and time Part calculates the optional personnel that can complete task, optional personnel's subset corresponding to formation, if optional personnel's subset of task is Sky, just the task is rejected from set of tasks, finally give an orderly task-set；Second step, calculate collison matrix；In the orderly task-set that the first step obtains, otherwise any two task is punching in sequential It is prominent, otherwise it is orderly, in N × N matrix, to represent conflict relationship between two tasks with 1, represented with 2 Orbution between two tasks, with regard to that can calculate a collison matrix, wherein N is ordered into the quantity of task in task-set；3rd step, computing staff always collect；According to collison matrix, optional personnel's subset is merged into a total personnel one by one and gathered In, form a personnel and always collect, to the two of sequential relationship tasks be present, their optional personnel's subset will also before the combining Wherein repeater person's node is replicated, it is total that node itself and the node of attending to anything else copied are then merged into personnel together Collection；4th step, construct sequential bipartite graph；Orderly task-set, collison matrix and the personnel obtained using first three step are always collected, and are constructed One special bipartite graph for carrying sequential relationship, is the task node arranged according to sequential on the left of bipartite graph, right side be containing The personnel's node attended to anything else；5th step, calculate conflict side；If the task node in sequential bipartite graph on the left of two sides collides with each other, and right side Personnel's node is actually same personnel, and just this two are marked in sequential bipartite graph and owned while labeled as a pair of conflicts Conflict side；6th step, calculating are effectively matched；To the sequential bipartite graph direct reuse Hungary Algorithm of connection, obtain sequential two and divide All maximum matchings of figure；To disconnected sequential bipartite graph, recycled breast after the subgraph of several connections is divided into Tooth profit algorithm, and result is combined, that is, obtain all maximum matchings of whole sequential bipartite graph；Some of which matching contains Conflict side, referred to as invalid matching, and the conflict side calculated using the 5th step filters out invalid matching, and being effectively matched for obtaining is exactly Final sends work result；Hungary Algorithm process is as follows：(1) sequential bipartite graph G is divided into connected subgraph, G={ G1, G2..., Gn}；(2) G is circulated In each subgraph Gi, to GiAll maximum matchings are calculated, one group of obtained matching is designated as Mij, j=1,2 ...；(3) subgraph Merge, the matching M of subgraphiCartesian product computing is done, G all matchings is obtained, is designated as M；Wherein, number is matchedAccording to conflict side filtering matching M, obtain Lothrus apterus side one group is effectively matched Subset M '；(5) if | M ' |=1, M ' be last solution, if | M ' |=0, no solution；Otherwise exist it is multiple be effectively matched, according to The customized principle of optimality, a weights are assigned for each edge, calculate the weights being each effectively matched and choose an optimal solution and make To send work result, complete.
- 2. the maximum work dispatching method of the iterative and incremental according to claim 1 that meet temporal constraint based on bipartite graph, It is characterized in that the step of computing staff always collects is as follows：The first step, the personnel of original state are set always to collect P for sky, by optional personnel's subset P corresponding to first task1In people Member node be directly brought into P set；Second step, in the case that personnel always collect P not for sky, by optional personnel's subset P corresponding to i-th of taskiWith first i-1 son Collection merges successively, if running into identical personnel's node during merging, is between two tasks corresponding to then It is no sequential relationship to be present, to determine whether to attend to anything else to personnel's node, if there is no sequential relationship, then need not attend to anything else, Otherwise, a node of attending to anything else just is manufactured, the node that then will attend to anything else includes P set；3rd step, second step is repeated, until all optional personnel's subsets are disposed, finally give a personnel and always collect P.
- 3. the maximum work dispatching method of the iterative and incremental according to claim 1 that meet temporal constraint based on bipartite graph, It is characterized in that：Order relation arranges task node on the left of the sequential bipartite graph figure from top to bottom on time, schemes the personnel on right side Node includes zero to multiple nodes of attending to anything else, but in the absence of the node of attending to anything else attended to anything else, in addition, each task node at least one Bar side is connected to personnel's node, and wherein there may be zero and arrive multipair conflict side.
- 4. the maximum work dispatching method of the iterative and incremental according to claim 1 that meet temporal constraint based on bipartite graph, It is characterized in that the step of calculating conflict side is as follows：The first step, calculate on the right side of sequential bipartite graph itself and its node set attended to anything else of same node in personnel's node；Second step, optional two different node a, b in the set, if such two sides in figure be present<r1, a>、<r2, b>, and And collison matrix shows task r1And r2There is conflict in sequential, then this two, when being exactly a pair of conflicts, they are recorded Come；3rd step, second step is repeated, is finished until all combination of nodes all check, records all conflict sides pair.
- 5. the maximum work dispatching method of the iterative and incremental according to claim 1 that meet temporal constraint based on bipartite graph, It is characterized in that when the calculating is effectively matched, if sequential bipartite graph does not connect, sequential bipartite graph is first divided into several companies Logical subgraph, all maximum matchings of each subgraph are obtained with Hungary Algorithm respectively, then subgraph merges, and Descartes is in matching Product computing, all maximum matchings of whole sequential bipartite graph can be obtained.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201410818220.5A CN104573855B (en) | 2014-12-24 | 2014-12-24 | The maximum work dispatching method of the iterative and incremental for meeting temporal constraint based on bipartite graph |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201410818220.5A CN104573855B (en) | 2014-12-24 | 2014-12-24 | The maximum work dispatching method of the iterative and incremental for meeting temporal constraint based on bipartite graph |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN104573855A CN104573855A (en) | 2015-04-29 |
| CN104573855B true CN104573855B (en) | 2018-01-23 |
Family
ID=53089870
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201410818220.5A Expired - Fee Related CN104573855B (en) | 2014-12-24 | 2014-12-24 | The maximum work dispatching method of the iterative and incremental for meeting temporal constraint based on bipartite graph |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN104573855B (en) |
Families Citing this family (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2019005890A1 (en) * | 2017-06-27 | 2019-01-03 | Schlumberger Technology Corporation | Methods and apparatus for optimizing well testing operations |
| CN108256741A (en) * | 2017-12-26 | 2018-07-06 | 新智数字科技有限公司 | Work dispatching method and system |
| CN110298539A (en) * | 2019-05-22 | 2019-10-01 | 深圳壹账通智能科技有限公司 | Task data processing method, device, computer equipment and storage medium |
Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103149839A (en) * | 2013-04-10 | 2013-06-12 | 国家电网公司 | Operational control method for electrical equipment based on Kuhn-Munkres algorithm |
Family Cites Families (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20110231215A1 (en) * | 2010-03-16 | 2011-09-22 | Santos Cipriano A | Optimization of a resource matching model by mapping a model to a bipartite graph |
| US20130231953A1 (en) * | 2012-03-01 | 2013-09-05 | Shahram Ebadollahi | Method, system and computer program product for aggregating population data |
-
2014
- 2014-12-24 CN CN201410818220.5A patent/CN104573855B/en not_active Expired - Fee Related
Patent Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103149839A (en) * | 2013-04-10 | 2013-06-12 | 国家电网公司 | Operational control method for electrical equipment based on Kuhn-Munkres algorithm |
Non-Patent Citations (4)
| Title |
|---|
| 基于二分图资源分配动力学的推荐排序研究;孙林，吴相林，罗松涛，周莉，张红艳;《计算机工程与设计》;20101231;第31卷(第23期);5032-5035 * |
| 基于时间优化的指派问题研究;彭勇，田澎，蒋馥;《上海管理科学》;20031231(第6期);48-50 * |
| 最短时限最少耗费指派问题的一种解法;任德华，卢桂章;《自动化与仪表》;20050525(第3期);1-4 * |
| 用"匈牙利算法"求解一类最优化问题;常庭懋，韩中庚;《信息工程大学学报》;20040331;第5卷(第1期);60-62 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN104573855A (en) | 2015-04-29 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN105959401B (en) | A kind of manufacturing service supply-demand mode and dynamic dispatching method based on super-network | |
| Yassine | An introduction to modeling and analyzing complex product development processes using the design structure matrix (DSM) method | |
| Braglia et al. | A new value stream mapping approach for complex production systems | |
| CN104573855B (en) | The maximum work dispatching method of the iterative and incremental for meeting temporal constraint based on bipartite graph | |
| CN102354144B (en) | Method for converting ladder diagram into PLC (Programmable Logic Controller) program command | |
| CN107301485A (en) | The method and system that task is distributed automatically | |
| CN103440309A (en) | Automatic resource and environment model combination modeling semantic recognition and recommendation method | |
| Pate et al. | A graph theoretic approach to problem formulation for multidisciplinary design analysis and optimization | |
| CN105654240A (en) | Machine tool manufacturing system energy efficiency analysis method | |
| CN106384161B (en) | Optimization method for division of aerospace patrol plan region | |
| CN105321045A (en) | Service process formal model construction method and system | |
| CN107315834A (en) | A kind of ETL work flow analysis methods based on breadth-first search | |
| Alakaş et al. | Problem specific variable selection rules for constraint programming: a type ii mixed model assembly line balancing problem case | |
| CN102799960A (en) | Parallel operation flow anomaly detection method oriented to data model | |
| CN103853559B (en) | Semantic Web service composite automatic validation method and system | |
| Bejjani et al. | Flow chart based information modeling for factory planning | |
| Wang et al. | Developing a holistic modeling approach for search-based system architecting | |
| CN106056299A (en) | Decision support method and device based on process mining | |
| CN107122849B (en) | Spark R-based product detection total completion time minimization method | |
| CN108520168A (en) | A kind of fault tree module extension decomposition method based on linear time algorithm | |
| CN103970934B (en) | Layout planning method for multivoltage on-chip network chip of integrated network device | |
| CN104715122B (en) | The method and apparatus that the example of the meta-model constructed based on train technical demand is operated | |
| CN114037341A (en) | DDQN-based intelligent workshop dynamic self-adaptive scheduling method and system | |
| Zhang et al. | A better algorithm for societal tradeoffs | |
| CN115081802B (en) | Method and device for generating passenger task set, corresponding electronic equipment and storage medium |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant | ||
| CF01 | Termination of patent right due to non-payment of annual fee |
Granted publication date: 20180123 Termination date: 20201224 |
|
| CF01 | Termination of patent right due to non-payment of annual fee |