Paper reading (48):a Library of optimization algorithms for organizational design

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0 summary

0.1 subject

2005Levchuk: Optimization algorithm library for organization design (A library of optimization algorithms for organizational design)

0.2 background

This paper introduces the algorithm library used to solve the optimization problems widely appeared in the standard design of various organizations , To meet the needs of specific tasks . Use of specific optimization algorithms at different stages of the design process , triggered Task structure and organization 、 resources / Effective matching between constraints . The algorithm library constitutes the core of the designed software environment , Used to integrate organizations consistent with their tasks . This allows the analyst to achieve acceptable trade-offs among multiple objectives and constraints , And meet the requirements of computational complexity and solution efficiency .

0.3 Bib

@techreport{
Levchuk:2005:library,
author = {
Georgiy M Levchuk and Yuri N Levchuk and Jie Luo and Fang Tu and Krishna R Pattipati},
title = {
A library of optimization algorithms for organizational design},
institution = {
Connecticut Univ Storrs Dept of Electrical Engineering and Computer Science}
year = {
2005},
}

1 introduce

1.1 motivation

The best organizational design problem (optimal organizational design problem) yes find Enables organizations to achieve superior performance when performing specific tasks The best organizational structure ( example Such as " Strategy layer Time junction structure 、 Yes " Strategy person ( d e c i s i o n − m a k e r s , D M s ) Of information Source And job can branch with , With And through Letter junction structure ) _{ For example, decision hierarchy 、 For decision makers (decision-makers, DMs) Allocation of resources and functions , And communication structure )} example Such as " Strategy layer Time junction structure Yes " Strategy person (decisionmakers,DMs) Of information Source And job can branch with , With And through Letter junction structure ) and Strategy ( example Such as D M s ren service branch with , ren service Of board That's ok order Column ) _{( for example DMs Task assignment , Task execution sequence )} ( example Such as DMs ren service branch with , ren service Of board That's ok order Column ). In recent years , Research in organizational decision-making shows that , There is a strong functional dependency between the specific structure of the task environment and the accompanying optimal organizational design . And then , Relevant research shows that , Optimality of organizational design Ultimately, it depends on the actual task parameters ( And organizational constraints ). This premise leads to the application of system engineering technology in human team design , Then advocate the use of Canonical algorithm To optimize the performance of human teams .

1.2 Related research

In complex task modeling and corresponding organization design , Various task sizes ( example Such as work can 、 The earth The reason is 、 The earth shape ) _{( For example, function 、 Geography 、 terrain )} ( example Such as work can The earth The reason is The earth shape ) And the depth of the required model granularity determines the complexity of the design process . Our task modeling and organization design approach allows a series of small and good optimization problems to be solved iteratively , Overcome computational complexity with integrated solutions . These methods are used to specify that I am on 1999 In the proposed Overview 、 Software environment for organizational design , To help users deal with complex tasks and comprehensively organize . The component structure of the software environment allows analysts to Mix and match different optimization algorithms at different stages of the design process . Included task modeling and 3 An iterative design phase is an example chart 1. In particular ,3 The stage design process solves 3 There are different sub optimization problems .

chart 1:3 Stage organization design

1.2.1 planning stage (scheduling phase)

Set up about Mission – Resource allocation (task-resource allocation) Optimization problem , The term it relies on is Platform to task (platform-to-task) Distribution matrix , Optimization objectives ( example Such as ren service End become when between , or person End become when between 、 accurate indeed sex 、 work do negative load 、 information Source eliminate Consumption , With And Outside Ministry Association transfer etc. Group close ) _{( For example, task completion time , Or completion time 、 accuracy 、 The workload 、 resource consumption , And external coordination )} ( example Such as ren service End become when between , or person End become when between accurate indeed sex work do negative load information Source eliminate Consumption , With And Outside Ministry Association transfer etc. Group close ) It's under constraints ( example Such as branch with 、 _{( Such as distribution 、} ( example Such as branch with information Source can use sex 、 _{ Resource availability 、} information Source can use sex flat platform speed degree 、 _{ Platform speed 、} flat platform speed degree With And chart shape − − phase Turn off _{ And graphics -- relevant } With And chart shape phase Turn off ( example Such as optimal First level and Same as Step ) ) _{( For example, priority and synchronization ) )} ( example Such as optimal First level and Same as Step )) Minimize under .

1.2.2 Aggregation stage (I) (clustering phase)

Set up about DM– Resource allocation Optimization problem , The term it relies on is DM– platform Distribution matrix , Optimization objectives ( example Such as most Big Inside Ministry and _{( For example, maximum internal and } ( example Such as most Big Inside Ministry and Outside Ministry work do negative load Of Add power total and _{ Weighted sum of external workloads } Outside Ministry work do negative load Of Add power total and , or person D M Of Count The amount 、 _{, perhaps DM The number of 、} , or person DM Of Count The amount D M Of the Examination 、 _{DM Experience 、} DM Of the Examination can use flat platform , _{ Available platforms ,} can use flat platform , With And Residence civil information Source Of Group close ) _{ And the combination of resident resources }) With And Residence civil information Source Of Group close ) Distribution is in DM Minimization under workload constraints .

1.2.3 Structural optimization stage (II) (structural optimization phase)

Set up about Organizational hierarchy (organizational hierarchy) Optimization problem , Its final expression form is tree , The links in the tree indicate the relationship between support and supported . Optimization objectives ( example Such as straight Pick up ( One Yes One ) and between Pick up Association transfer _{( For example, direct ( one-on-one ) And indirect coordination } ( example Such as straight Pick up ( One Yes One ) and between Pick up Association transfer lead rise Of most Big layer Time work do negative load , _{ Maximum level workload caused ,} lead rise Of most Big layer Time work do negative load , or person D M between Of Yes effect chain Pick up Count 、 _{ perhaps DM Number of valid links between 、} or person DM between Of Yes effect chain Pick up Count Group weave layer level junction structure Of deep degree , _{ The depth of the organizational hierarchy ,} Group weave layer level junction structure Of deep degree , With And Letter Rest flow Of Group close ) _{ And the combination of information flow )} With And Letter Rest flow Of Group close ) In graph dependent constraints ( example Such as Letter Rest interview ask 、 _{( For example, information access 、} ( example Such as Letter Rest interview ask layer level junction structure ) _{ Hierarchical structure )} layer level junction structure ) Minimize under .

1.2.4 Online adaptation phase (III) (on-line adaptation phase)

stay Resource or decision node failure When the , Branch and bound (branch-and-bound) Method is applied to the preference matrix of task resource scheduling , So as to generate the next best allocation , This will involve a new task resource allocation strategy . This strategy enables adaptation options to run quickly and efficiently ; The dynamic scheduling account is used for online correction , Without completely solving the problem ; If the newly obtained task resource scheduling matrix does not match the organizational constraints , Stage II and III A new organizational structure will be generated . under these circumstances , Stage II There will be an evolution mechanism , That is, the platform cluster is obtained by recombining the old platform group , Not a different world from scratch . Final , If a viable organizational structure cannot be generated , The current task will be forced to terminate .

1.3 Article layout

chapter 2 Provides an overview of the task modeling and organization design environment , chapter 3 The description contains 3 A two-stage optimization algorithm , chapter 4 Make a summary and make a prospect .

2 Multi objective optimization and organization design software environment

In recent days, , I have carried out model design and deployment on the software platform to automate the organization design process , It allows user-defined changes to be iterated through different stages of the design process . To assist the analyst , Our software environment can be used to display organizational performance indicators 、 Represent the achievement of task objectives , And specify the load distribution of the organization element of interest .
The designed software environment includes the following Seven key components
1) Resource description (asset/resource description);
2)DM analysis (DM structure profiler);
3) Task modeling (mission modeling);
4) Performance standards (performance criteria/measures);
5) Planning generation (schedule generation);
6) Resource allocation (resource allocation); as well as
7) Hierarchical structure (hierarchy construction).

chart 2: Software environment architecture

2.1 Model architecture

The first three components of the designed software environment are used to assist in analyzing task modeling and organizational constraints under different time complexity , The results will be used as input to the design process , Performance standards Components are used to define the optimization objectives of the design process , A loss function is defined, which combines the mission objective with the design parameters .

2.2 Optimization construction and algorithm design

Of software environment The last three constructs allow the analyst to design the organizational structure step by step , At the same time, user-defined design modifications are implemented at all stages of the design process , To adjust the performance standards of the organization . Specially , Planning generation Component generation I Stage Adaptive task resource allocation scheme . Resource allocation artifacts (II Stage ) Define by grouping platforms DM function , And provide balance between internal and external coordination . Hierarchical structure artifacts (III Stage ) Export organization hierarchy , To minimize the workload of indirect external coordination caused by hierarchy .
generally , Planning generation 、 Resource allocation , And the three parts of the hierarchy belong to NP difficult problem . therefore , It is necessary to design efficient heuristic methods to solve large-scale problems . Our software environment allows different algorithms to be applied at different design stages to deal with specific problems . Iterations of multiple algorithms allow us to make acceptable tradeoffs between design goals , Optimize multiple performance standards at the same time .
Organizational structure is the result of the design process , It specifies the relationship between organizational entities :
1) Mission - Resource Planning ;
2)DM- Resource allocation ;
3)DM Organization level ;
4)DM Inter coordination structure .
Organizational structure By assigning each DM Information and resources under control , It is endowed with corresponding ability , And for DM The coordination between them makes rules . Organizational structure and a set of constraints DM The threshold of workload , Jointly determine the feasible organizational strategy ( That is, all feasible DM- Mission - Resource allocation and coordination strategy ) Space boundary of . Organizations can choose specific policies to implement . Feasible strategic space defines the strategic adjustment that an organization can make , Without major restructuring .

3 Optimization algorithm library

This section describes the optimization algorithm library used in the organization design software environment . The library is evolving , And new algorithms and performance standards are being added , To expand the scope of application of the software environment .

3.1 Dispatch (scheduling)

3.1.1 Problem definition

Scheduling focuses on allocating limited resources to tasks over time . Resources and tasks take many forms , For example, a resource can be a platform 、 Human team 、 Monitor assets 、 Information resources, etc , The task can be the takeoff and landing of the aircraft 、 Evaluation and decision making 、 Operability and information . They can be convergent or independent 、 Offensive or defensive , Each task has its own priority and opportunity window .
Scheduling is a decision-making process , It needs to optimize one or more optimization objectives , These goals also need to address many platforms . One possible goal is to minimize task completion time , Others are in violation of the mandate .
The scheduling of the optimization design process can be roughly described as follows . A group with a specified processing time 、 Resource requirements 、 A task with a location and priority relationship needs to be assigned by a given set of resource capabilities 、 Operating range and speed of platform execution . Resource requirements and resource capabilities are represented by vectors of the same length , Each entry corresponds to a specific resource type . The way tasks are assigned to platform groups is , For each such assignment , Each component of the resource demand vector of a task is less than or equal to the aggregate resource capacity of the platform group assigned to it . Only when all predecessors have completed and all platforms in the group assigned to it have reached their positions , To start processing this task . A resource can only be assigned to one task at the same time . The platform will route between tasks , In order to make Overall completion time ( It is called task completion time —— The completion time of the last task ) To minimize the .

3.1.2 Example

























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