Research on Collaborative Planning and Symmetric Scheduling for Parallel Shipbuilding Projects in the Open Distributed Manufacturing Environment
Abstract
:1. Introduction
2. Literature Review
2.1. Shipbuilding Project Planning and Scheduling
2.2. Resource Constrained Project Scheduling
2.3. Symmetric DecisionMaking
2.4. Conclusions on the Reviewed Literature
 (1)
 Conduct a deep analysis of the shipbuilding project planning and scheduling processes to find the relationship between tasks;
 (2)
 Define the unified mathematical model. Through mathematical methods, a unified mathematical model is constructed to link the whole project planning with the scheduling process;
 (3)
 In view of the success of MAS theory in system modeling, draw lessons from existing research and find suitable methods to build the framework of planning and scheduling with the characteristic of symmetric collaborative decision making and design the negotiation method and scheduling strategy.
3. The Shipbuilding Projects’ Collaborative Planning and Symmetric Scheduling Process
3.1. Project Planning and Scheduling Process
 According to the requirements of the order contract, the general contractor of each project sets the overall goal of the project and breaks down the project into multiple tasks;
 The general contractor publishes the task requirements to qualified cooperative enterprises with the ability to complete the task, and negotiates with them to determine the scheduling plan for each task;
 The project planning scheme is a combination of these task scheduling schemes. The logical constraints between tasks can be considered and obtained through local scheduling optimization;
 Multiple projects are planned simultaneously, and these projects are independent of each other. Therefore, resource conflicts occur from time to time and need to be resolved by the resource owner;
 The general contractor and the cooperating enterprise conduct multiple rounds of negotiation according to their respective goals to determine the subcontractor and corresponding scheduling plan for each task.
3.2. Symmetric Collaborative DecisionMaking Process
4. Symmetric Collaborative DecisionMaking System
4.1. The System Framework
 Management Agent: Responsible for managing the overall system. When new projects and project plans need to be adjusted, the MA opens the project planning function of the system. In the planning process, the MA receives and verifies the PAs and SAs; then, the MA organizes the project planning and the auction process;
 Project Agent: Each project sets up one PA to complete the project planning and realize the project objective. After receiving the project information, the PA sends the registration requests to the MA, breaks the project down into numerous executable tasks by analyzing the order demand information, identifies qualified subcontractors, and inquires into the manufacturing efficiency and resource price for all tasks. Based on the auction mechanism and the project objective, PAs then adjust and finalize the project plans, determining the subcontractor and completion plan of each task;
 Subcontractor Agent: Each subcontractor sets up one SA to complete the related operations during the project, who provides the resource information to each PA, including manufacturing efficiency and resource price. Based on the auction mechanism and local objectives, SAs assist in finalizing the project plan;
 Project Schedule Agent: The PSA determines the resource use plan based on a local scheduling algorithm and sends the resource use plan to the PA.
 Task Schedule Agent: The TSA formulates the specific scheduling scheme based on the information of resources and tasks.
4.2. Project Planning Module
4.2.1. Mathematical Formulation
Parameters  
$n$  Number of projects required to complete 
${P}_{i}$  Project code 
$de{l}_{i}$  Delivery date of ${P}_{i}$ 
$dde{l}_{i}$  Deadline for delivery of ${P}_{i}$ 
${\theta}_{i}$  Fine coefficient for delay of ${P}_{i}$ 
$\left[1,dde{l}_{i}\right]$  Time window of ${P}_{i}$ 
${n}_{i}$  Number of tasks of project ${P}_{i}$ 
${T}_{ij}$  Task code 
$Loa{d}_{ij}$  Total workload of ${T}_{ij}$ 
$PT{G}_{ij}$  The predecessor group of ${T}_{ij}$ 
$m$  Number of qualified cooperative enterprises 
${E}_{l}$  Enterprise code 
${m}_{l}$  Types of available resources of ${E}_{l}$ 
${R}_{k}^{l}$  Resource code 
${a}_{k}^{l}$  Total available amount of ${R}_{k}^{l}$ 
${c}_{kt}^{l}$  Unit resource using cost of ${R}_{k}^{l}$ at time t 
${v}_{l}$  Types of variable resources of ${E}_{l}$ 
${f}_{l}$  Types of fixed resources of ${E}_{l}$ 
$CS{G}_{ij}$  Candidate subcontractors group of ${T}_{ij}$ 
$ure{s}_{ij}^{l}$  Minimum inputs of combination resource 
$u{a}_{ijk}^{l}$  Minimum resource input of ${R}_{k}^{l}$ in ${T}_{ij}$ 
$Cap{a}_{ij}^{l}$  Workload per unit time accomplished by minimum resource inputs $ure{s}_{ij}^{lv}$ 
$du{r}_{ij}^{l}$  Duration in one scheme of ${T}_{ij}$ completed by ${E}_{l}$ 
$s{t}_{ij}^{l}$  Start time in one scheme of ${T}_{ij}$ completed by ${E}_{l}$ 
$re{s}_{ij}^{l}$  Resources inputs of ${E}_{l}$ in one scheme of ${T}_{ij}$ 
${a}_{ijk}^{l}$  Input amount of ${R}_{k}^{l}$ per unit time in one scheme of ${T}_{ij}$ 
$re{s}_{ij}^{lv}$  Variable resources inputs of ${E}_{l}$ in one scheme of ${T}_{ij}$ 
$re{s}_{ij}^{lf}$  Fixed resources inputs of ${E}_{l}$ in one scheme of ${T}_{ij}$ 
${a}_{ijk}^{l}\left(L\right)$  Input amount of ${R}_{k}^{l}\left(k=1,\dots ,{v}_{l}\right)$ at the last time slot of ${T}_{ij}$ 
$\left[E{F}_{ij},\text{}L{F}_{ij}\right]$  The earliest and the latest finish time window of ${T}_{ij}$ 
${q}_{ij}^{l}$  Quality of ${T}_{ij}$ completed by ${E}_{l}$ 
Decision Variables  
${x}_{ijt}^{l}$  If ${T}_{ij}$ is assigned to ${E}_{l}$ and completed at time period t, ${x}_{ijt}^{l}=1$; else, ${x}_{ijt}^{l}=0$. 
${y}_{ij}^{l}$  Production efficiency, representing the variable resource input per unit of time 
Objective Function  
$F{T}_{i}$  The final time of project ${P}_{i}$ 
$d{p}_{i}$  The delay penalty for project ${P}_{i}$ 
${\mathrm{C}}_{i}\left(R\right)$  The resources cost of ${P}_{i}$ 
$F{C}_{i}$  Total cost of project ${P}_{i}$ 
$F{Q}_{i}$  Total quality of project ${P}_{i}$ 
 (1)
 If task ${T}_{ij}$ completed by enterprise ${E}_{l}$, the quality ${q}_{ij}^{l}$ is constant;
 (2)
 The task duration $du{r}_{ij}^{l}$ is affected by the inputs of the resource, which is up to subcontractor ${E}_{l}$ to negotiate with the general contractor;
 (3)
 The start time $s{t}_{ij}^{l}$ is later than the end time of the predecessor tasks.
4.2.2. Iterative Combinational AuctionBased Negotiation Method
4.3. Task Scheduling Module
4.3.1. Encoding and Decoding
$US$  the unscheduled task matrix order by the scheduling sequence 
$PS$  the scheduled task matrix 
${\mathrm{j}}^{\ast}$  the task with premier order in matrix $US$ 
${\mathrm{p}}_{\mathrm{j}}$  the predecessor group of task $\mathrm{j}$ 
${\mathrm{ES}}_{\mathrm{j}}$  the earliest start time of task $\mathrm{j}$ 
${\mathrm{EF}}_{\mathrm{j}}$  the earliest finish time of task $\mathrm{j}$ 
${\mathrm{LS}}_{\mathrm{j}}$  the latest start time of task $\mathrm{j}$ 
${\mathrm{LF}}_{\mathrm{j}}$  the latest finish time of task $\mathrm{j}$ 
${\mathrm{s}}_{\mathrm{j}}$  the start time of task j 
${\mathrm{f}}_{\mathrm{j}}$  the finish time of task j 
${\mathrm{A}}_{\mathrm{j}}$  the order of task j 
${\mathrm{M}}_{\mathrm{j}}$  the selected subcontractor of task j 
$\mathrm{d}\left(\mathrm{j}\right)$  the duration of task j 
$\mathrm{r}\left(\mathrm{j}\right)$  the resource requirement of task j 
Algorithm 1: Schedule Generation 

4.3.2. Initialize the Population
4.3.3. Rapid NonDominated Sorting and Tournament Selection
4.3.4. Evolution Operation
Algorithm 2: Competition Operation 

Algorithm 3: Collaborative Crossover Operation 

Algorithm 4: SelfLearning Operation 

4.3.5. Determine the Optimal Scheme
5. Experiment and Results Analysis
6. An Application Case
7. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Project  Task  Workload  Predecessors  Candidate Scheme  

Enterprise  Quality  Resources  
Project code: ${P}_{1}$ Complete windows: 2019.4.01–2019.5.20 Deadline: 2019.5.31 Fine coefficient: US$10,000  ${T}_{1}$           
${T}_{2}$  10  ${T}_{1}$  ${E}_{3}$  6  0,2,2,0  
${T}_{3}$  15  ${T}_{1}$  ${E}_{1}$  10  6,0,0,5  
${E}_{2}$  3  0,10,5,0  
${E}_{3}$  2  0,10,0,4  
${T}_{4}$  14  ${T}_{1}$  ${E}_{2}$  5  3,0,8,0  
${T}_{5}$  15  ${T}_{2}$,${T}_{4}$  ${E}_{3}$  1  10,0,6,0  
${T}_{6}$  15  ${T}_{5}$  ${E}_{1}$  7  9,0,0,8  
${E}_{2}$  2  6,0,0,5  
${E}_{3}$  6  0,2,0,5  
${T}_{7}$  12  ${T}_{4}$  ${E}_{3}$  9  0,8,0,6  
…  …  …  …  …  …  
${T}_{33}$  12  ${T}_{29}$  ${E}_{1}$  1  6,0,0,5  
${E}_{2}$  8  8,0,10,0  
${E}_{3}$  9  0,7,7,0  
${T}_{34}$  14  ${T}_{30}$,${T}_{32}$  ${E}_{2}$  1  10,0,6,0  
${T}_{35}$  10  ${T}_{27}$,${T}_{31}$  ${E}_{1}$  4  0,2,0,5  
${E}_{3}$  8  0,5,5,0  
${T}_{36}$    ${T}_{33}$,${T}_{34}$,${T}_{35}$        
Project code: ${P}_{2}$ Complete windows: 2019.4.11–2019.5.30 Deadline: 2019.6.10 Fine coefficient: US$10,000  ${T}_{1}$           
${T}_{2}$  14  ${T}_{1}$  ${E}_{1}$  6  6,0,0,1  
${E}_{2}$  6  0,10,8,0  
${T}_{3}$  10  ${T}_{1}$  ${E}_{2}$  8  0,10,5,0  
${E}_{3}$  8  0,10,0,4  
${T}_{4}$  15  ${T}_{1}$  ${E}_{1}$  4  3,0,0,7  
${E}_{2}$  7  3,0,8,0  
${E}_{3}$  3  3,0,0,3  
${T}_{5}$  14  ${T}_{2}$,${T}_{4}$  ${E}_{2}$  1  10,0,6,0  
${T}_{6}$  12  ${T}_{5}$  ${E}_{3}$  6  0,2,0,5  
…  …  …  …  …  …  
${T}_{33}$  10  ${T}_{29}$  ${E}_{1}$  2  6,0,0,5  
${E}_{2}$  4  8,0,10,0  
${E}_{3}$  6  0,7,7,0  
${T}_{34}$  11  ${T}_{30}$,${T}_{32}$  ${E}_{1}$  8  5,0,0,1  
${E}_{2}$  1  0,7,10,0  
${E}_{3}$  4  0,7,0,8  
${T}_{35}$  13  ${T}_{27}$,${T}_{31}$  ${E}_{1}$  6  0,2,5,0  
${T}_{36}$    ${T}_{33}$,${T}_{34}$,${T}_{35}$       
Enterprise  ${\mathit{R}}_{1}$  ${\mathit{R}}_{2}$  ${\mathit{R}}_{3}$  ${\mathit{R}}_{4}$  

${\mathit{a}}_{1}$  ${\mathit{c}}_{1}$  ${\mathit{a}}_{2}$  ${\mathit{c}}_{2}$  ${\mathit{a}}_{3}$  ${\mathit{c}}_{3}$  ${\mathit{a}}_{4}$  ${\mathit{c}}_{4}$  
${E}_{1}$  20  1000  23  1000  26  1000  36  1000 
${E}_{2}$  20  1000  23  1000  26  1000  36  1000 
${E}_{3}$  20  1000  23  1000  26  1000  36  1000 
Task  Subcontractor  Duration  Start Time  Start Time  Resources 

${T}_{1}$    0 days  2019/4/1  2019/4/1   
${T}_{2}$  ${E}_{3}$  5 days  2019/4/1  2019/4/6  0,16,8,0 
${T}_{3}$  ${E}_{1}$  5 days  2019/4/1  2019/4/6  18,0,0,5 
${T}_{4}$  ${E}_{2}$  2 days  2019/4/1  2019/4/3  15,0,8,0 
${T}_{5}$  ${E}_{2}$  5 days  2019/4/6  2019/4/11  20,0,6,0 
${T}_{6}$  ${E}_{3}$  2 days  2019/4/11  2019/4/13  0,16,0,5 
${T}_{7}$  ${E}_{2}$  5 days  2019/4/3  2019/4/8  0,24,0,6 
${T}_{8}$  ${E}_{3}$  5 days  2019/4/6  2019/4/11  15,0,3,0 
${T}_{9}$  ${E}_{1}$  2 days  2019/4/8  2019/4/10  18,0,0,7 
${T}_{10}$  ${E}_{1}$  6 days  2019/4/11  2019/4/17  0,20,0,5 
${T}_{11}$  ${E}_{3}$  4 days  2019/4/22  2019/4/26  0,9,6,0 
${T}_{12}$  ${E}_{3}$  4 days  2019/4/13  2019/4/17  0,18,2,0 
${T}_{13}$  ${E}_{3}$  4 days  2019/4/17  2019/4/21  0,21,0,2 
${T}_{14}$  ${E}_{2}$  5 days  2019/4/11  2019/4/16  6,0,6,0 
${T}_{15}$  ${E}_{3}$  4 days  2019/4/26  2019/4/30  18,0,0,5 
${T}_{16}$  ${E}_{2}$  4 days  2019/4/17  2019/4/21  0,21,0,8 
${T}_{17}$  ${E}_{3}$  1 day  2019/4/21  2019/4/22  0,26,5,0 
${T}_{18}$  ${E}_{2}$  3 days  2019/4/30  2019/5/3  5,0,0,0 
${T}_{19}$  ${E}_{3}$  6 days  2019/4/21  2019/4/27  2,0,0,0 
${T}_{20}$  ${E}_{2}$  4 days  2019/4/22  2019/4/26  18,0,0,1 
${T}_{21}$  ${E}_{2}$  12 days  2019/4/26  2019/5/8  6,0,0,5 
${T}_{22}$  ${E}_{1}$  2 days  2019/5/8  2019/5/10  18,0,0,3 
${T}_{23}$  ${E}_{3}$  6 days  2019/5/3  2019/5/9  20,0,6,0 
${T}_{24}$  ${E}_{1}$  4 days  2019/5/10  2019/5/14  0,8,0,5 
${T}_{25}$  ${E}_{3}$  5 days  2019/5/9  2019/5/14  0,16,0,6 
${T}_{26}$  ${E}_{2}$  7 days  2019/5/8  2019/5/15  16,0,0,6 
${T}_{27}$  ${E}_{1}$  2 days  2019/5/14  2019/5/16  16,0,0,6 
${T}_{28}$  ${E}_{2}$  6 days  2019/5/15  2019/5/21  0,20,0,5 
${T}_{29}$  ${E}_{1}$  4 days  2019/5/10  2019/5/14  0,9,6,0 
${T}_{30}$  ${E}_{1}$  6 days  2019/5/14  2019/5/20  0,12,2,0 
${T}_{31}$  ${E}_{2}$  3 days  2019/5/21  2019/5/24  10,0,0,5 
${T}_{32}$  ${E}_{3}$  3 days  2019/5/9  2019/5/12  15,0,6,0 
${T}_{33}$  ${E}_{3}$  4 days  2019/5/14  2019/5/18  0,21,7,0 
${T}_{34}$  ${E}_{2}$  5 days  2019/5/21  2019/5/26  0,14,10,0 
${T}_{35}$  ${E}_{1}$  2 days  2019/5/24  2019/5/26  0,18,5,0 
${T}_{36}$    0 days  2019/5/26  2019/5/26   
© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Mao, X.; Li, J.; Guo, H.; Wu, X. Research on Collaborative Planning and Symmetric Scheduling for Parallel Shipbuilding Projects in the Open Distributed Manufacturing Environment. Symmetry 2020, 12, 161. https://doi.org/10.3390/sym12010161
Mao X, Li J, Guo H, Wu X. Research on Collaborative Planning and Symmetric Scheduling for Parallel Shipbuilding Projects in the Open Distributed Manufacturing Environment. Symmetry. 2020; 12(1):161. https://doi.org/10.3390/sym12010161
Chicago/Turabian StyleMao, Xuezhang, Jinghua Li, Hui Guo, and Xiaoyuan Wu. 2020. "Research on Collaborative Planning and Symmetric Scheduling for Parallel Shipbuilding Projects in the Open Distributed Manufacturing Environment" Symmetry 12, no. 1: 161. https://doi.org/10.3390/sym12010161